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Math Basics for Healthcare Professionals (4th Edition)
9780133104158
ISBN:
013310415X
Edition: 4 Pub Date: 2013 Publisher: Prentice Hall
Summary: Michele Lesmeister is the author of Math Basics for Healthcare Professionals (4th Edition), published 2013 under ISBN 9780133104158 and 013310415X. Five hundred eighty one Math Basics for Healthcare Professionals (4th Edition) textbooks are available for sale on ValoreBooks.com, two hundred thirty five used from the cheapest price of $24.71, or buy new starting at $48.80
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A comprehensive Calculus review app written by a Math PhD. Functions, Limits, Derivatives and Integrals are all covered with 55+ worked examples. For quick access to equations, the "Equations" tab displays commonly used properties and equations for derivatives and integrals
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Find a Des PlainesAlgebra 2 (or Intermediate Algebra) revolves mainly around the introduction, classification, and manipulation of functions of an indeterminate variable (i.e. equations symbolized by 'f(x)'). Successful completion of the course serves as an essential foundation for the future calculus student. A...
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Mathematics A Discrete Introduction
9780534398989
ISBN:
0534398987
Edition: 2 Pub Date: 2005 Publisher: Thomson Learning
Summary: With a wealth of learning aids and a clear presentation, this book teaches students not only how to write proofs, but how to think clearly and present cases logically beyond this course. All the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective.
Scheinerman, Edward R. is the author of Mathematics A Discrete Introduction, published 2005... under ISBN 9780534398989 and 0534398987. Two hundred six Mathematics A Discrete Introduction textbooks are available for sale on ValoreBooks.com, twenty eight used from the cheapest price of $6.34, or buy new starting at $57
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Summary
THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT!Glencoe Algebra 2is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments.
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ALEX Lesson Plans Writing equations for parallel lines
Description:
Students 34: Write a function that describes a relationship between two quantities.* [F-BF1] [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]
Subject: Mathematics (8 - 12) Title: Writing equations for parallel lines Description: Students
Title: Exponential Growth and Decay
Description:
ThisStandard(s): [MA2013] AL1 (9-12) 7: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] ALC (9-12) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALT (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama)
Subject: Mathematics (9 - 12) Title: Exponential Growth and Decay Description: This
Title: Density
Description:
D CHE (9-12) 1: Differentiate among pure substances, mixtures, elements, and compounds. [S1] ENV (9-12) 1: Identify the influence of human population, technology, and cultural and industrial changes on the environment. 15: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4] [MA2013] AL1 (9-12) 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI ALC (9-12) 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama)
Subject: Mathematics (9 - 12), or Science (8 - 12) Title: Density Description: D
Title: What is the slope of the stairs in front of the school?
Description:
The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8-EE6 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. GEO (9-12) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]
Subject: Mathematics (8 - 12) Title: What is the slope of the stairs in front of the school? Description: The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.
Title: Marathon Math
Description:
ThisStandard(s): CA2 (9-12) 11: Critique digital content for validity, accuracy, bias, currency, and relevance. [ELA] (9) 14: Use the research process to locate, select, retrieve, evaluate, and organize information to support a thesis on a nonliterary topic. [MA2013] DM1 (9-12) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama) [MA2013] DM1 (9-12) 2: Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers, and pentagonal numbers. (Alabama) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2] [MA2013] AL1 (9-12) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [F-IF3]
Subject: English Language Arts (9), or English Language Arts (9), or Mathematics (9 - 12), or Technology Education (9 - 12) Title: Marathon Math Description: This
Thinkfinity Lesson Plans
Title: Finding Our Top Speed
Description:
This Illuminations lesson sets the stage for a discussion of travel in the solar system. By considering a real-world, hands-on activity, students develop their understanding of time and distance. The mathematics necessary for the lesson relate to measuring time and distance as well as graphing to portray the data collected.
Standard(s): [S1] (6) 11: Describe units used to measure distance in space, including astronomical units and light years. [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5,Science Title: Finding Our Top Speed Description: This Illuminations lesson sets the stage for a discussion of travel in the solar system. By considering a real-world, hands-on activity, students develop their understanding of time and distance. The mathematics necessary for the lesson relate to measuring time and distance as well as graphing to portray the data collected. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Apple Pie Recording Chart
Description:
This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects.
Standard(s): [MA2013] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6-RP (7) 20: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7-SP Apple Pie Recording Chart Description: This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Building Bridges
Description:
In this lesson, from Illuminations, students attempt to make a transition from arithmetical to algebraic thinking by extending from problems that have single-solution responses. Values organized into tables and graphs are used to move toward symbolic representations. Problem situations involving linear, quadratic, and exponential models are employed
Subject: Mathematics,Professional Development Title: Building Bridges Description: In this lesson, from Illuminations, students attempt to make a transition from arithmetical to algebraic thinking by extending from problems that have single-solution responses. Values organized into tables and graphs are used to move toward symbolic representations. Problem situations involving linear, quadratic, and exponential models are employed. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Gallery Walk
Description:
In Gallery Walk Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Automobile Mileage: Age vs. Mileage
Description:
In this lesson, one of a multi-part unit from Illuminations, students plot data about automobile mileage and interpret
Subject: Mathematics Title: Automobile Mileage: Age vs. Mileage Description: In this lesson, one of a multi-part unit from Illuminations, students plot data about automobile mileage and interpret Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: To Fret or Not to Fret
Description:
In In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Exploring Measurement, Sequences, and Curves with Stringed Instruments
Description:
In this lesson, one of a multi-part unit from Illuminations, students measure lengths on stringed musical instruments. They Exploring Measurement, Sequences, and Curves with Stringed Instruments Description: In this lesson, one of a multi-part unit from Illuminations, students measure lengths on stringed musical instruments. They discuss how the placement of frets on a fretted instrument is determined by a geometric sequence. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Graphing What
Description:
This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs.
Standard(s): [MA2013] (6) 17: Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6-EE6 Graphing What Description: This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: To Fret or...
Description:
This reproducible activity, from an Illuminations lesson, features questions dealing with measuring distances on fretted stringed instruments Least Squares Regression
Description:
In interpret Least Squares Regression Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Not to Fret
Description:
This Not to Fret Description: ThisTitle: Graph Chart
Description:
This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs.
Standard(s): 2: Recognize and represent proportional relationships between quantities. [7-RP2 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] AL2 (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1 Graph Chart Description: This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: To Fret or Not to Fret
Description:
This reproducible worksheet, from an Illuminations lesson, presents a series of questions related to fretted instruments and geometric sequences. In the lesson, students This reproducible worksheet, from an Illuminations lesson, presents a series of questions related to fretted instruments and geometric sequences. In the lesson, students compare geometric sequences with exponential functions. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Fretting
Description:
In this lesson, one of a multi-part unit from Illuminations, students use their discoveries from the first lesson to place frets on a fretless instrument. They then Fretting Description: In this lesson, one of a multi-part unit from Illuminations, students use their discoveries from the first lesson to place frets on a fretless instrument. They then compare geometric sequences with exponential functions. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Bathtub Water Levels
Description:
In from Bathtub Water Levels Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Seeing Music, Hearing Waves
Description:
Using Description: Using, Hearing Waves: Selected Answers and Solutions
Description:
This reproducible teacher sheet, from an Illumin: Selected Answers and Solutions Description: This reproducible teacher sheet, from an Illumin
Description:
In this Illuminations lesson, students calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations Description: In this Illuminations lesson, students calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: The Effects of Outliers
Description:
This
Standard(s): 43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [S-ID3 [MA2013] PRE (9-12) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [S-IC1]
Subject: Mathematics Title: The Effects of Outliers Description: This Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Traveling Distances
Description:
In
Standard(s): [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between Traveling Distances Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Automobile Mileage: Comparing and Contrasting
Description:
In key Automobile Mileage: Comparing and Contrasting Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Hearing Music, Seeing Waves
Description:
This reproducible pre-activity sheet, from an Illuminations lesson, presents summary questions about the mathematics of music, specifically focused on sine waves and the geometric sequences of notes that are an octave apart.
Standard(s): [MA2013] AL1 (9-12) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [F-IF3T (9-12) 38: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. [F-TF2] [MA2013] ALT (9-12) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [F-TF5 Linear Alignment
Description:
In
Standard(s): Linear Alignment Description: In Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
Title: Make a Conjecture
Description:
In this lesson, one of a multi-part unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart.
Standard(s): 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2] [MA2013] AL1 (9-12) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context. [A-CED 42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [S-ID2 5: Determine approximate rates of change of nonlinear relationships from graphical and numerical data 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] [MA2013] AL2 (9-12) 38: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] [MA2013] ALT (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1T (9-12) 37: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [S-ID4] [MA2013] PRE (9-12) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [S-IC1] [MA2013] PRE (9-12) 45: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. [S-IC2] [MA2013] PRE (9-12) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3] [MA2013] PRE (9-12) 49: Evaluate reports based on data. [S-IC6] [MA2013] ALT (9-12) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] [MA2013] ALT (9-12) 42: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7 Health,Mathematics Title: Make a Conjecture Description: In this lesson, one of a multi-part unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Exact Ratio
Description:
This
Standard(s): [MA2013] AL1 (9-12) 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [N-RN 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9 Mathematics Title: Exact Ratio Description: ThisWeb Resources
Interactives/GamesLearning Activities withThinkfinity Learning Activities
Title: Flowing Through Mathematics
Description:
This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.
Standard(s): GEO (9-12) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [G-GMD3] [MA2013] GEO (9-12) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [G-MG1]
Subject: Mathematics Title: Flowing Through Mathematics Description: This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Product Description
Student will realize the power of algebra and that armed with knowledge of algebra, you can find out fascinating things about place, people and real-life situations. This series concentrates on the essentials of algebra plus provides a thorough breakdown of difficult concepts using step-by-step explanations and visual examples.The Standard Deviants Teaching Systems are simply the most effective method for students to learn and for teachers to teach. This educational programming is optimized for classroom use. Each module is a topic-based video accompanied with a digital workbook that uses a humorous and unique style and approach to difficult concepts with the learner's perspective in mind. Each video contains "Full Public Performance Rights" and a digital workbook which includes teacher's guides, classroom notes, quizzes, games, and graphic organizers. The subject matter correlates directly to state standards and is produced and designed by the Cerebellum Academic Team of professional scriptwriters, students, professors, actors, comedians, and teachers.Grade Level: 8 -12. 182 minutes
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major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields.
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Mathematics End of Course Supports
Topic outline
General
Mathematics End-of-Course Supports
Welcome to the WA Mathematics End-of-Course Supports Moodle. This is a place for educators to share resources and collaborate as they prepare students for the End-of-Course (EOC) exams. Uploaded resources will not be reviewed by OSPI staff, but instead are the responsibility of the teacher to analyze resources and determine if they suit the needs of their students. If there are questions regarding the use of this site, please email [email protected] or [email protected].
This course contains the following sections:
Section 1: Discussion Forums
Section 2: Teacher-Created Resources Database
Section 3: Other Sources of Sample EOC items
Section 4: EOC Item Writing
Section 5: Calculator Policy
Section 6: Common Core Resources
Section 7: Mathematics Collection of Evidence
View each section by scrolling down the page or by clicking on the Section Links in the upper left corner of the page.
This is the PowerPoint presentation delivered at the WERA conference in December 2011. This presentation highlights EOC information, resources and key documents including EOC Updates for 2012 and 2011 Lessons from Scoring Student Work.
Other Sources of EOC Sample Items
The purpose of these documents is to identify sample items and previously released items that align to the 2008 Mathematics Standards assessed on the End-of-Course Exams. Links to released items, sample items and draft COE tasks are listed by PE so that teachers are able to easily locate items aligned to each Performance Expectation.
This document contains information for eductors about EOC Exams and Retake Exams as well as new EOC sample items for Year 1 and Year 2. Sample items for Year 1 begin on page 14; sample items for Year 2 begin on page 29.
This document contains sample EOC items in multiple choice, completion, and short answer formats, with solutions. Sample items for Year 1 begin on page 13; sample items for Year 2 begin on page 18.
EOC Item Writing
2012 Item Writing for End-of-Course Exams
The Office of Superintendent of Public Instruction Mathematics Assessment office held the end-of-course exams Item Writing Workshop February 28 - March 1, 2012.
Participants received instruction in writing multiple-choice, completion, and short-answer items aligned to Washington State Mathematics Standards, wrote sample EOC items for classroom use, and wrote exam items that will be used on the Washington Comprehensive Assessment Program. Participants described this experience as an excellent opportunity for professional development that provided them with insights for teaching and assessing standards.
The Powerpoint presentation: 2011 EOC Item Writing was used in March 2011 to train Washington State teachers to write items for the state-level end-of-course exams. The presentation was given over 3 days and represents approximately 10 hours of training. This is great information for a teacher who wants to know more about design, validity, and formatting considerations for the state-level end-of-course exams.
The Test & Item Specs Activity and EOC Item Spec Scavenger Hunts are activities that can help teachers delve deeper into the format of and information in the Test and Item Specifcations. We suggest using these as group activities and discussing your responses for each activity.
The Word Problems vs. Process Items helps distinguish the difference between items assessing content Performance Expectations that ask students to solve word problems and items assessing process Performance Expectations that require problem solving strategies. Teachers can use these examples to classify the work they are asking students to do to ensure students have practice both solving word problems and solving problems.
These item templates are used as general guidelines for the format of EOC assessment items. Examples of EOC assessment items can be found in the Item Writing Guidelines document (link above) and in the EOC Sample Item Booklet, EOC Updates to 2012, EOC Updates to 2011, and the Released Item Documents and Quick Guides (links at the top of this page under OSPI Links and Resources).
These rubric templates are used as general guidelines for the format of rubrics for EOC short-answer items. Examples of completed EOC item rubrics based on the new standards can be found in the Item Writing Guidelines document (link above) and in the Sample EOC Short-Answer Items documents below.
Calculator Policy and Resources
Approved calculators may be used on the EOC exams. A scientific calculator is sufficient for all items on all end-of-course (EOC) mathematics assessments, but students may use any calculator that does not have any of the prohibited features listed in the calculator policy. Proctors must clear calculator memory both before and after each testing session. Follow the link above to view the complete calculator policy.
The Illustrative Mathematics Project will provide guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.
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Mathematics Collection of Evidence (COE)
Please click here for information regarding the Mathematics Collection of Evidence, eligibility requirements, and tasks for Algebra and Geometry.
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AWM Electronic Newsletter
Mathematics Foundation of America (MFOA)
posted Jun 17, 2010, 10:29 PM by Glenna Buford
The purpose of MFOA is to ensure that the mathematically talented high school student receives mathematics education appropriate for a future mathematician by providing suitable mathematics summer programs and mathematics mentors.
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This book in graph theory is intended the typical freshman or sophomore in computer science and related disciplines with a first exposure to the mathematical topics essential to their study of computer science or digital logic.There is an introduction of graph and tree in this book.This focus on the description of basic problems involving graph and tree and their applications.
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Improper Riemann Integrals is the first book to collect classical and modern material on the subject for undergraduate students. The book gives students the prerequisites and tools to understand the convergence, principal value, and evaluation of the improper/generalized Riemann integral. It also illustrates applications to science and engineeringThe first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers—... more...
The book "Single variable Differential and Integral Calculus" is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book is unique in the field of mathematical analysis in content and in style. It aims to define, compare and discuss topics in... more...
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Art And Craft of Problem Solving
9780471789017
ISBN:
0471789011
Edition: 2 Pub Date: 2006 Publisher: John Wiley & Sons Inc
Summary: You' ve got a lot of problems. That's a good thing. Across the country, people are joining math clubs, entering math contests, and training to compete in the International Mathematical Olympiad. What's the attraction? It's simple--solving mathematical problems is exhilarating! This new edition from a self-described "missionary for the problem solving culture" introduces you to the beauty and rewards of mathematical p...roblem solving. Without requiring a deep background in math, it arms you with strategies and tactics for a no-holds-barred investigation of whatever mathematical problem you want to solve. You'll learn how to: get started and orient yourself in any problem. draw pictures and use other creative techniques to look at the problem in a new light. successfully employ proven techniques, including The Pigeonhole Principle, The Extreme Principle, and more. tap into the knowledge gained from folklore problems (such as Conway's Checker problem). tackle problems in geometry, calculus, algebra, combinatorics, and number theory. Whether you're training for the Mathematical Olympiad or you just enjoy mathematical problems, this book can help you become a master problem-solver! About the Author PaulAmerican
Zeitz, Paul is the author of Art And Craft of Problem Solving, published 2006 under ISBN 9780471789017 and 0471789011. Five hundred thirty seven Art And Craft of Problem Solving textbooks are available for sale on ValoreBooks.com, one hundred thirty seven used from the cheapest price of $41.50, or buy new starting at $53 newly revised Second Edtion of this distinctive text uniquely blends interesting problems with strategies, tools, and techniques to develop mathematical skill and intuiti [more]
The newly revised Second Edtion of this distinctive text uniquely blends interesting problems with strategies, tools, and techniques to develop mathematical skill and intuition necessary for problem solving. Readers are encouraged to do math rather
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Using and Understanding Mathematics - 4th edition
Summary: Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative literacy skills they'll need to make good decisions throughout their lives. Common-sense applications of mathematics engage students while underscoring the practical, esse...show morential uses of math.
Features
Practical Matters. Focusing on matters of high practical importance, this feature highlights common-sense applications of math such as avoiding credit card trouble and spotting a bad cell phone deal.
A Brief Review. This feature reviews key mathematical skills students should have learned previously, but which many students still need review and practice. They appear in the book wherever a particular skill is first needed, and exercises based on the review boxes can be found at the end of the unit.
Thinking About. Building upon the main narrative, this feature reaches beyond to a deeper level of mathematical understanding. Examples include boxes on the proof of the Pythagorean theorem and on Zeno's paradox.
Time Out to Think. Appearing throughout the book, the Time Out to Think features pose short conceptual questions designed to help students reflect on important new ideas. They also serve as excellent starting points for classroom discussions.
Margin Features. A wide margin leaves room for students to make notes while studying. The margin also contains material that spurs student interest in three basic forms:
By the Way features contain interesting notes and asides relevant to the topic at hand
Historical Note remarks give historical context to the ideas presented in the chapter
Technical Notes contain details that are important mathematically for students looking for more depth
Now Try Exercises. At the end of every in-text example students are directed to Now Try a specific exercise, immediately testing their comprehension of the material.
Does It Make Sense? These qualitative exercise questions test conceptual understanding by asking whether given statements are sensible and asking students to explain why or why not.
Basic Skills and Concepts. Covering concepts from the unit, these exercises can be used for homework assignments or for self-study. Answers to most odd-numbered exercises appear in the back of the book.
Web Projects. The Web Projects require students to search for data or other information online. They can be used for extended projects, discussions, group activities, or essays.
In the News. In these exercises, students are challenged to find examples of unit concepts in the news or in their daily lives. These questions may be assigned as homework or used for class discussions.
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A book that is designed to cover all the mathematics required for physics being studied at undergraduate level (at least first and second year). It does what it says on the cover. It is very comprehensive, however, reading it is not easy. The print is small, and the book is so large, that not only is it physically difficult, but you become depressed by the fact that no matter how fast you read or understand, it'll take a while to get through it!! Probably two years! Probably the only book you need for the maths involved in undergraduate physics, if only for reference.
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
This book is simply the best. It is lightyears better than Boas (the most often suggested alternative), and it basically contains all the maths You'll ever need in all but the most theoretical undergraduate course of any natural science (well, except maths, if that's a science ;-) ).
In fact, now slowly finishing my PhD in physics, I think I can say that unless You are doing actual theoretical/mathematical physics, it probably contains all or most of the maths You'll need for the rest of Your life.
This book is a watershed in the teaching of calculus and the essential mathematical methods required by undergraduate mathematicians, physicists and engineers.It will easily become the standard reference for methods courses , if it has not done so already.It starts right at the beginning with a refresher in basic calculus etc , and then proceeds to carefully develop multi-variable calculus, linear differential equations,complex variables, calculus of variations , tensors, representations, numerical analysis and prob&stats.What I really like about this book is the way general curvilinear coordinate transformations are explained at the end of the vector calculus section, to which you can refer when reading the chapter on tensors.I know of no other methods textbook which introduces tensors like this:many lesser texts (and that means all the rest) seem to feel that it is sufficient to teach people about raising indices, and give readers some vague hand-waving about coordinate transformations.This book is one to buy for this alone, as you will then have a firm grasp of why the tensor notation is like it is.Indeed, I would say that this book makes most other methods textbooks look the half-arsed disgrace that they are.Jacobians could be more carefully introduced, and the writing style can be a little Enid Blyton (phrases like 'one can consult the many excellent textbooks on such and such' can become rather monotonous), but apart from tiny niggles like this, this really is a truly comprehensive methods book, which really starts from the beginning and takes you well into the foothills of genuinely advanced techniques, and which you will keep through your professional life.An instant classic.
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
I phrased the title of this review carefully. Riley, Bence and Hobson is a standard text for many engineering and physics undergraduate courses with good reason. It covers the majority of topics required to complete a physics degree and will remain useful after you graduate. I bought mine in my first year (now in year 2) and it looks like i'll be using it for a long time yet.
There are plenty of derivations, discussions and perhaps most importantly for physics/engineering students, examples that are related to the course. This could be relating partial derivatives and heat transfer, fourier transforms and Fraunhofer diffraction - you get the idea. There are plenty of general maths examples and enough problems to keep you busy for a few nights.
On the downside, this is - for me at any rate - a reference text first and foremost. Students looking for a lucid account of the mathematics behind the physics should look no further, but it isn't necessarily the book to buy if you want lots of simple problems for practice. The solutions manual goes a little way towards sort this out, you can buy it them both as a pack (recommended) and it covers many of the examples in depth. If you just want a book for practising your vector calculus or ironing out your calculus worries, look to one of Schaum's outlines instead.
Whilst the discussion is, on the whole, pretty lucid, it does move quickly. A certain amount of reading between the lines is required for some topics and this isn't necessarily a bad thing, but it might put some people off. I found better explanations of things like Fourier transforms in books on digital signal processing, for instance. What you will find is that almost all the maths you'll ever do on a science course is in the book, even if it doesn't have a lengthy paragraph explaining it.
Mainly it is important to understand where the maths is coming from instead of blindly applying the required formula to set situations. Inevitably there will come a time when you actually have to know what the symbols are doing, rather than what process to apply to them. When that time comes, this is what you look to.
The verdict: It's a great book, it covers all the bases and has just the right amount of explanation to jog your memory on a forgotten topic. I would not recommend it for learning new principles from though, unless you really need to and stick to Schaum's for general practise - and for that I'd give it a 4.5.
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
I have been looking for a complete guide to higher level Mathematics (for revision of a wide range of methods such as Fourier Transforms, Calculus, Group Theory etc.) and spent a considerable time looking at the various choices on Amazon. This book seemed to have the most consistent set of 5 star reviews - so I took the plunge.
I am delighted - it is well written, thoroughly comprehensive, has every topic I was looking for, and, although HUGE (well over 1300 pages!), is clearly laid out and easy to read.
I wish I had had this book when I was younger (I am now over half a century old!). I am a Computer Science PhD, rather than an Engineer or Physicist - but this book is the one for me!
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
I am a games developer and I was looking for a good textbook that I could turn to for the math involved in advanced rendering and physics. I am very pleased to have bought the third edition of this excellent work. For me this book is an absolute winner. It covers a huge range of topics, from quadratic equations to spherical harmonics, differential equations and quantum operators; yet the treatment does not feel hurried and terse like it does in some other books that cover such a scope (Kreyszig for example). It's written in a clear and engaging style and the print is not small - presumably profquantum is refrerring to an earlier edition in his/her review. Run, don't walk, to buy this book
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
Contains most (if not all) of the mathematical material needed for and undergrade physics course (definitely up to Yr3, possibly after) whilst at the same time being very accessible for first/ second year ability. Each chapter starts from the basics , and gradually builds up to required level. Very useful to have answers at the back, useless otherwise (cant check whether you are correct or not). Exceptionally good section on vector calculus, as well as applications to different parts of physics.
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
This is simply the best maths textbook for physicists. By the best I mean the easiest to understand, the easiest to find what your looking for and the most comprehensive. There are worked examples and the questions in the book are also good with answers for the odd numbered questions. Yes it may look like a door stop but you do need alot of maths!! anyway it is easy to find what your looking for so thie size isn't an issue.
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
I ordered this to refresh my mathematics 40 years after taking a degree in physics. I was looking for a book to cover all the techniques that I vaguely remember with a practical approach that starts with the very basics but includes all the detail needed. This book does just that. The emphasis is on the application of mathematical techniques and examples from physics and engineering are frequently explored to illustrate the theory.
| 677.169 | 1 |
0941355, Grades 3-4 (Math by All Means)
The lessons in this book actively involve students in exploring geometric ideas through hands-on investigations with two- and three-dimensional shapes. Students also develop greater proficiency in logic, number, and measurement.
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William Briggs
"Briggs's book is in some sense an update of Polya's classic, How to Solve It. Certainly Briggs pays due homage to the master, cites his four main principles of problem solving, and organizes his text in a manner that at least pays homage to Polya. But Briggs goes much further. His writing style is lively and attractive. He gets in the reader's face and stays in his/her face from page one. He does this in a friendly way, one that gets the reader involved and keeps him/her involved as the work progresses. …The student will be carried along by this book, and ever anxious to learn the next new idea. I like Briggs's book so well that I would certainly make considerable use of his text the next time that I teach problem-solving." -- Steven G. Krantz, Washington University in St. Louis.
Mathematics educators agree that problem solving is one of the essential skills their students should possess, yet few mathematics courses or textbooks are devoted entirely to developing this skill. Supported by narrative, examples, and exercises, Ants, Bikes, and Clocks: Problem Solving for Undergraduates is a readable and enjoyable text designed to strengthen the problem-solving skills of undergraduate students. The book, which provides hundreds of mathematical problems, gives special emphasis to problems in context, often called story problems or modeling problems, that require mathematical formulation as a preliminary step. Both analytical and computational approaches, as well as the interplay between them, are included.
With its lively and engaging writing style and interesting and entertaining problems, Ants, Bikes, and Clocks will strengthen students' mathematical skills, introduce them to new mathematical ideas, demonstrate for them the connectedness of mathematics, and improve both their analytical and computational problem solving. One of the remarkable and unusual features of this text is that it encourages students to use the computer for experimentation. In fact, Briggs uses a variety of tricks that encourage students to use any tool at hand to test their ideas.
Audience
Ants, Bikes, and Clocks is an excellent text for an undergraduate problem-solving course or as a resource for mathematics educators, providing hundreds of mathematical problems that can be used in any course. Mathematically the book relies on two semesters of calculus, although much of the book requires only precalculus skills.
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Arguing that computers are essential to teaching mathematics, Kemeny discusses not only how to use computers in the classroom, but also which mathematical topics should be taught in the age of computers. He explains his philosophy of using computers to teach mathematics and illustrates this philosophy with a number of concrete examples. (Atlanta, GA, 1988)
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Precalculus
MAT 110 with minimum grade of C or appropriate score on the Mathematics Placement Test, and MAT 080 or geometry proficiency.
III. Course (Catalog) Description
This course focuses on the study of functions including polynomial, rational, exponential, logarithmic and trigonometric functions. Additional topics include the conic sections, series, parametric equations, and polar equations. Use of technology is integrated throughout. lectures, discussions, demonstrations, experimentation, audio-visual aids and regularly assigned homework. Calculators/computers will be used when appropriate. Course may be taught as face-to-face, media-based, hybrid or online course. graphics calculator is required. A TI-83/84 will be used for instructional purposes.
X. Methods of Evaluating Student Progress
(To be completed by instructor.)
Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or small group projects and a final exam
| 677.169 | 1 |
MATH 175:
INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY
T. KYLE PETERSEN
"That student is taught the best who is told the least."
–R. L. Moore
1. Introduction
1.1. About the method. If you're reading this, you're probably a
good teacher. (At the very least, you have a non-vanishing interest
in teaching.) Did you ever have the sneaking suspicion that your stu-
dents, even the "good" ones, who get the best grades on exams, don't
really know the material you've been trying to teach them? What
percentage of your last calculus class would you say could recite that
d
dx
[xn ] = nxn−1 ? What percentage could tell you why? My answers
to these questions would be about 99 and about 15, respectively. If
your numbers are higher, congratulations, but I'd wager anyone with
an answer of more than 25 to the second question is an outlier.
Most students are led to believe mathematics consists of memoriza-
tion of facts and simple algorithmic exercises. Inquiry-based learning
(IBL, or the "modified Moore method", after R. L. Moore) seeks to
counteract this tendency. The pitfalls of the shallow view include the
inability to assess the correctness of a written solution, the belief that
there is one "right way" to solve a problem, and the idea that all prob-
lems can be addressed in just a few minutes. With an inquiry-based
approach, students learn that many worthwhile questions have answers
that can take hours, or even days (weeks!) to conquer, they see that
a solution can often come from several different directions, and they
develop a sharp eye for logical flaws in an argument. In short, IBL
tries to makes students think like mathematicians. Once students have
traced on their own all the steps and missteps1 leading to the claim
d
" dx [xn ] = nxn−1 ", they understand the statement in a way that is sim-
ply not possible from memorization alone. The need for memorization
of further facts falls by the wayside as students realize that so many
1And there are lots of steps! What is a limit? What is a derivative? The
definitions of a function and of continuity probably also crop up. . .
1
2 T. K. PETERSEN
ideas follow from true knowledge of the rules of the game and how to
apply them.
But how do we get students to reach this point? R. L. Moore adopted
a Socratic approach. There is no textbook, but rather the instructor
gives students a list of problems and some statements of definitions and
theorems, but with no exposition and no proofs. The course consists
of students doing the problems and attempting to prove the theorems.
During class meetings students present their findings at the board while
the other students ask questions. The instructor largely lurks in the
background, acting as moderator and cheerleader, but rarely, if ever,
as judge. There are many variations on the theme, almost a spectrum,
from "hard-core Moore"2 on one extreme to, at the other extreme,
something much closer to a typical lecture-style course, with written
homework, exams, and even textbooks. The specific structure of Math
175 is discussed in the next section.
There are several possible reasons why more courses are not taught
in the IBL style. One reason is that this method requires different
skills than lecturing does, and it can be easy for things to go very
wrong—more about this in the "Difficulties and Advice" section. Even
when done properly some still criticize the method; the main reason
given is lack of coverage. It does seem to be generally true that the list
of topics students see in a one-semester IBL course is shorter than the
same list for a course taught in the lecture style. One counter-argument
I have heard is that the learning curve for IBL students is exponential,
whereas the curve for lecture style students is linear. So while after one
semester the lecture class may be ahead, by the end of two semesters
the IBL class will have overtaken them.
I prefer the following analogy. The main theorems and definitions
from a course are like flowers. In a lecture course students pluck the
flowers one by one and put them in a pretty vase to admire. In an IBL
class, the students get down in the dirt to plant seeds, water them, and
watch the flowers grow. A year later, the flowers in the vase will have
wilted and died. With a little care, though, the IBL students will still
have a flower garden.
1.2. About this document. My aim with this note is to give an idea
of how this course has been run for the past couple of years, along with
some general advice about my version of the IBL method. It is not
an instruction manual. It is not a detailed syllabus. While it contains
2One rumor—almost surely false—is that he once brought a revolver to class as
extra motivation for a particularly recalcitrant group of students: "Today someone
will prove Theorem X."
MATH 175: INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY 3
information about the the structure of the course and the running of
day-to-day operations, you will find little here that is specific to num-
ber theory or cryptography. (You can find that in the worksheets.)
Difficulties in teaching this course are more likely to come from unfa-
miliarity with the method than from content.
For me, there is something paradoxical about trying to teach some-
one how to teach a course in which the guiding principle is that students
teach themselves. Shouldn't I just wish you luck and let you go figure
it out for yourself? Maybe. But maybe you can learn something from
my experience and opinions as well. (Really, the best thing I can rec-
ommend for someone interested in teaching an IBL course is to attend
a workshop, or to sit in on a class taught by an experienced IBLer.)
My point is that whatever I say, you need to make the material your
own before you put it into practice. To be sure, I hope that the ad-
vice in this note saves you headaches and wasted time, but your own
experiments and mistakes will teach you better than I ever could, and
ultimately will make you a better teacher.
Good Luck!
2. History and Structure of Math 175
Math 175 was originally conceived by Phil Hanlon in the late 1980s
as a "problems course" for honors freshmen. He gave students a list
of fifty or so problems, usually discrete, but with no obvious unifying
theme. He would lecture on various topics, and every few days a student
would present a solution to a problem from the list. Grades were based
purely on the number of solutions presented. This was classic Moore
method.
While some students relished the open-ended nature of the course,
many of their classmates disliked the fact there was no specific content
for the course. With this in mind, Hanlon tried to tie the problems
to some specific content. First he tried graph theory, then cryptology,
which stuck. Prodded by student interest, he and several collaborators
later developed an entire "coursepack" with some historical motivation
and exposition on cryptographic methods and related mathematical
topics.
Hanlon taught the course each year through the late 1990s and in-
termittently thereafter. (He took a job in the Provost's office.) From
1999–2005 several people taught the course, in several different for-
mats. At one point a hardcover textbook, Invitation to Cryptology,
was added to the required course materials. In general, the course lost
almost all connection to the Moore method.
4 T. K. PETERSEN
When I was hired in 2006, it was with the understanding that I would
help revive the IBL character of Math 175. In the fall of that year,
a
Kirsten Eisentr¨ger and I designed and co-taught the course. We still
had the textbook and coursepack that fall, but in 2007 and 2008 those
materials were dropped in favor of the materials contained in this folder.
Otherwise, the structure, grading procedures, and content is largely un-
changed from 2006, including, notably, the co-teaching model. In 2007
undergraduate teaching assistant Thomas Fai attended class meetings
c
and helped to answer student questions. In 2008, Fran¸ois Dorais and
I co-taught the course.
Math 175 is a "freshman honors seminar," which means that it is
a small class intended for first-year students in the honors program.
Each section is capped at 20 students. I have had between 15 and 19
students in the four sections I've taught. The students are generally
from the LSA honors program, though there are usually a few from
Engineering and from general LSA. Very few students have a desire
to major or minor in mathematics before taking the course. Part of
the aim of the course is to get students excited about mathematics.
Hopefully some of them will go on to take further math courses.
Students not in the honors program are required to have instructor
approval to enroll in Math 175. I never turned away an interested
freshman, but I always declined requests from upperclassmen. I think
it is important that the class be fairly homogeneous. Students should
feel as equals with their classmates and thus be unafraid to express their
opinions. With this in mind, I think it is also important to identify and
gently nudge out students who are too good. For example, in fall 2008
there were three students in one section of Math 175 who were also
taking math 295 ("super honors" calculus). They were good students
but they upset the egalitarian dynamic of the classroom.
The course meets four days a week for fifty minutes. Monday, Tues-
day, and Wednesday class is held in a seminar room with individual
desks and several chalkboards. Thursday meetings are held in a com-
puter lab. Attendance is absolutely mandatory. I've used a very effec-
tive carrot-and-stick approach. As reward for coming to class, partic-
ipation makes up a full 20% of their final grade. The punishment for
missing class is severe. Each student gets three "free" absences. Each
subsequent absence results in the final grade dropping by a full letter,
e.g., an A student with five unexcused absences receives a C.
2.1. Group work. On a typical class day, we randomly arrange stu-
dents in groups of two or three, and hand out one of the worksheets.
MATH 175: INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY 5
Students stay with their group until completion of the worksheet; of-
ten three or four class meetings. These worksheets are meant to be
done (only) in class. The pace of the course overall is dictated by stu-
dent progress through the worksheets. When one worksheet is finished,
there is usually some sort of "wrap up" discussion and new groups are
formed to begin a new worksheet. It is a real luxury that Math 175
is not a prerequisite for any subsequent course. This means you can
really wallow in a topic if it seems to be the right thing for the students.
As students dig into the worksheets, we circulate to listen to student
ideas, and to ask and answer questions.3 Students are periodically
invited to the board to present solutions to the problems on the work-
sheets. Usually one or two students will be selected to present in the
second half of the class period. Be sure to allow at least ten minutes
for a presentation; fifteen or twenty is better. Too often in my first
year I found myself rushing students through their presentations. This
is frustrating for everybody. Keeping an eye on the clock is any easy
solution to this problem. More on answering student questions, mo-
tivating students when stuck, and managing student presentations is
discussed in the "Difficulties and Advice" section.
The design of the worksheets is as follows. Like a section of a text-
book, a given worksheet usually has one main idea. A "goal theorem",
say. The worksheet builds gradually toward this goal theorem, in-
troducing definitions as necessary. There is a mix of numerical and
abstract problems, all of which are meant to guide students to the idea
of the goal theorem.
My approach for designing such a worksheet is straightforward. Be-
ginning with the goal theorem, I first write my own proof. Then I
ask, "what would a student need to know to understand and construct
this proof?" First off, they probably need a lemma or two. Now, what
would they need to be able to prove these lemmas? Is it possible to
guide students (with examples) to the idea of the lemma before they've
seen its statement? There are also some definitions that should prob-
ably appear along the way, and they too should be motivated with
examples. In the end, a typical goal theorem will come at the end of a
sequence of fifteen or more problems. Along the way there is no such
thing as a problem that's "too small" for the students.
If you plan to teach this course you should go through the worksheets
and modify them to suit your own tastes. If you prefer a different path
3Don't give them any free answers! I like to use the psychiatrist's old trick of
answering a question with a question. Student: "There are infinitely many primes,
right?" Instructor: "Do you think there are infinitely many primes?"
6 T. K. PETERSEN
to a particular goal theorem, map it out! If there is a topic omitted
that you really like (Pollard's ρ method for instance), make a new
worksheet!
The students should keep notes on the worksheet problems in a sepa-
rate folder, or in a composition notebook. This will be their "textbook"
for the course and helpful when it is time to do homework or study for
exams.
2.2. Computer lab. The computer lab is generally fun for everyone.
Students get into groups of two or three to complete a day's task.
Sometimes the goal is very narrow ("decode this message"), other times
it is wide open ("find the largest integer you can with the following
properties. . . "). Often the lab activities are phrased in terms of a
competition, with bonus points for the winning team. Whereas the
homeworks and in-class worksheets encourage students to think deeply
and methodically, the lab activities often reward speed and following
hunches—different kinds of problem solving skills.
Sometimes the lab topics are closely related to the worksheets from
earlier in the week, e.g., implementing the Euclidean algorithm. Other
times the lab has little to do with the classwork. In either case the
topic should be engaging and most students should be able to finish
within an hour. Students find the labs a nice respite from the hard
work they are putting in on the class worksheets.
Maple is the default program for most of these activities, though
there are some web-based activities as well. An added benefit of using
software like Maple is that students can begin to use it when working
on homework problems.
The computer lab activities have changed much more from year to
year when compared with the worksheets. Dorais is working to redesign
the computer labs (making them more cohesive) for fall 2009.
2.3. Homework and exams. In some IBL courses there is no home-
work and there are no exams. Grades are based solely the number
and quality of solutions presented, for example. In other IBL courses,
there is written homework, but no exams, and presentations make up a
large part of a student's grade. Math 175 has both written homework
and exams, and we don't grade presentations. One advantage of this
approach is that it makes grading straightforward for the instructor.
No different from a typical lecture course, really. Also, it feels more
"normal" for the students. The class is different enough for them al-
ready, and if they were to be graded on presentations, that would only
add anxiety to a situation they already find stressful. I have considered
MATH 175: INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY 7
dropping the final exam in favor of some sort of final project, but for
now this is a vague idea.
During the semester the students have nine homework assignments,
two midterms, and a final exam. Students are encouraged to work
together on the homework, though they must acknowledge their col-
laborators and write up their own solutions. The way the homeworks
and exams are currently written reflects the timing of the most recent
semester's students. If you find your class moving faster or slower, you
may need to move some problems accordingly or change due dates to
match the pace of the worksheets.
The homeworks have two parts. The first contains problems and
exercises based on material presented in the worksheets. The second,
called "outside the box" (OTB) questions, are often quite challenging.
The exams are meant to be fairly straightforward, with problems drawn
from worksheet material and of difficulty comparable to the first part
of the homework.
The purpose of the OTB questions is to help students develop their
problem solving skills. These problems may or may not (more often
not) be related to the worksheets. Often they have many layers so that
students can see progress without necessarily reaching the final answer.
Usually a student can receive half credit or more on these problems for
some carefully worked out examples and a nice conjecture. Rarely will
a student be able to tackle all the OTB questions on a homework (and
they are not required to do so).
Apart from developing good problem solving skills, the homework
can help students develop their skill at communicating complex ideas.
Thus the standard for written homework is very high. As is to be
expected, their writing is generally horrible at the beginning of the
semester. But they do improve! Early and often, you can show them
what good mathematics writing looks like, and cheerfully encourage
them to achieve that goal. They need to be told that yes, complete
sentences in proper English are required, and no, three examples do not
prove a universal statement. Then they need to be told again. And
again. But if you are patient, and encourage them to talk about it with
one another, they get it eventually.
Each year I am struck by the quality of written work at the end of the
semester compared to that of the beginning. While still not perfect, I
would compare it favorably to the writing found in a junior-level linear
algebra class.
8 T. K. PETERSEN
3. Difficulties and Advice
Run well, this course can be the most fun you've ever had in a
classroom. (Certainly that has been my experience.) However, there
are many places where it can go off the rails if you're not careful. The
results can be painful for everyone involved.
3.1. Marketing the method. One of the best ways to ensure a suc-
cessful semester has nothing to do with mathematics. Here is a terrific
quote from a former student, when asked what he would tell future
students taking the class:
You may think that Professor Petersen does not lecture
because he does not know what he's doing, or is a bad
teacher. This is false. I learned some of the best critical,
logical thinking skills from him because of the specific
way in which this class is taught.
Consider the first sentence. If you don't convince the students other-
wise, this is their most common assumption. You're lazy, a bad teacher,
you don't know what you're doing. Before you have even given them
the first handout they are skeptical of the method or worse.
First impressions matter. On the first day of class try to tackle the
"perception problem" head-on. Explain to them why you think the
class is taught as it is: that they will learn the material better, that
they will have ownership of the ideas, that they will experience the joy
of discovery of new ideas, and so forth.
Analogies can also help. Ask the students what their hobbies and
extracurricular interests are. Any basketball players? Any cellists? Ask
them how they became proficient. Did you become a good basketball
player by watching your coach dribble around and do lay-up drills?
by watching Michael Jordan? No. Did you learn to play the cello by
watching your teacher do scales? by listening to Yo-Yo Ma? Of course
not.
To become good at something you need to do it yourself. This makes
sense to students. In this class you, the instructor, will play the role of
coach.
If you hit the students early and often with these ideas—I probably
bring it up in one way or another at least once a week for the first
month—you can convince them that at least there is a good philosophy
behind the structure of the course. This gets you as far as the second
sentence in the student quote above. Bringing each student all the way
to the final sentence is subtler, and, perhaps, not always possible.
MATH 175: INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY 9
The problem is that unlike playing basketball or playing music,
most students don't inherently derive joy from "playing" mathemat-
ics. Therefore the hard work involved in getting better and learning
will tend to feel like work for them. It is good to remember this point
of view throughout the semester so that, whenever possible, you show
students what a great game this math stuff can be!
3.2. Developing a positive culture. One of the simplest ways to
get students to enjoy themselves while working hard is to get them
to enjoy coming to class. It is easy for students to be excited about
the days in the computer lab. On days spent in the classroom with
the worksheet it takes more effort. In general the time spent in class
should be friendly and open so that students feel comfortable offering
their opinions without fear of looking foolish. Students need to make
mistakes and discuss the dead ends to get the most out of class time.
If they are too shy or embarrassed to speak openly everyone loses out.
A certain passiveness or apathy in the mathematics classroom is
something that, for many students, has been reinforced for years. The
standard model has them sit quietly at desks listening to a lecture and
passively taking notes. Few are engaged mentally. They are rarely, if
ever, challenged to think in the moment. Part of the difficulty early in
the semester is to overcome their habits.
In a similar vein, consider Schoenfeld's observation [?] that U.S. high
school students average about two minutes of thinking per homework
problem. Two minutes! You either get it immediately or it's hope-
less. To the average student, working on the same problem for fifteen
minutes is an eternity. This is probably tied to the notion that math-
ematical ability is something innate, rather than something attained
through hard work. They are shocked when I tell them that I, as a
research mathematician, am stuck more than 95% of the time. I have
no idea what the answer is or how to get there. What do I do then?
Work more examples. Ask a narrower question. Ask a broader ques-
tion. Change the parameters and do even more examples. These ideas
don't occur naturally to most students. So tell them. They need to
learn that it is the struggle that matters, and that the struggle is often
a necessary precursor to that five percent of insight and progress.
What is rewarded in the classroom is the struggle, not only the so-
lution. Every attempt is to be applauded. Most of the students are
likely to be unsure of themselves in the beginning. For these students
the first few experiences should always end on a positive note, even if
what the student says is nonsense mathematically. Thank the student
for speaking up. Smile. Locate the kernel of truth in what the student
10 T. K. PETERSEN
said and point out its brilliance to the rest of their group or to the
class.
It's also fun to point out that while some approaches are "incorrect
solutions", they are theorems themselves, and the students are still
creating mathematics! Say students analyze a certain function and find
f (1) = 2, f (2) = 4, f (3) = 8, f (4) = 16. At this point the conjecture
f (n) = 2n emerges and students spend a good deal time and effort to
proving the conjecture, to no avail. Finally, someone, for lack of any
better ideas, works out the case n = 5 and finds f (5) = 31. Most
students will despair—they don't even have a good conjecture now!
Suppose class is ending and you want to end on a positive note. You
can take the chalk and write the following on the board (the group of
students is Sarah, Jimmy, and Eva):
Theorem 1 (Sarah, Jimmy, Eva). We have f (n) = 2n for n = 1, 2, 3, 4,
and f (5) = 31.
Corollary 1. The function f (n) is not generally equal to 2n .
This is progress! Make them believe it!
3.3. Presentations at the board. Over the course of the semester all
the students should spend roughly the same amount of time presenting
at the board. While walking around the classroom, identify which
groups "get it" and which groups are having more trouble. Anywhere
from ten to thirty minutes from the end of class ask a particular student
to go to the board and present a solution to a particular problem. In
the beginning especially, I like to pick students who seem to have a
good handle on the problem. For students who seem more shy or less
confident, I pick an easier problem to help their chances for a positive
experience.
When the student has written their solution on the board, call the
class to attention, "All right, now we have Eva presenting her solution
to problem 3," and take a seat at the back of the classroom. (Phys-
ically moving to the back of the room and sitting down removes you
from a position of authority and places Eva, at the chalkboard, in that
position.) When Eva has finished her explanation, there will be si-
lence. Probably the class will turn in their seats to look to you for
approval/disapproval. Smile. Say nothing yet of your thoughts of the
solution. Ask if there are questions for the speaker. Once any questions
are answered, if you think the presentation was complete and correct,
say so—"Great job, Eva! I especially like the part where. . . "—and give
the speaker a round of applause.
MATH 175: INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY 11
What if a student presents a solution and there is an obvious flaw in
the argument? You ask, "Does anyone have a question for Eva?" and
you wait. Don't. . . say. . . anything. Wait! Don't say anything. Wait
longer! Two minutes of silence is not unusual. It is very likely that
someone in class sees the error but is too shy or too polite to point
it out. Eventually someone will speak up, and then it is your job to
facilitate discussion. It is not your job to point out the mistake, and it is
certainly not your job to show them how to fix it. This is where the cool
stuff happens, because, believe it or not, they will figure things out for
themselves. You "helping" here just steals the thunder from someone
who could have thought of the idea for themselves. The confidence
that students gain at this time is invaluable.
3.4. When students are stuck. It is possible there will be times that
nobody but you sees the fatal flaw in an argument. You've asked for
questions, waited two full minutes, and still nothing but blank stares.
What to do? Hint at it. The more oblique the suggestion, the better. I
like starting this approach by having the presenter read their solution
aloud again. Then I ask for questions and wait again. Still nothing? I
focus in a bit more. "Could you please read the second paragraph once
more?" Still nothing? "Could you please read that paragraph one more
time? There's still something that I don't quite understand." You can
also ask someone in the audience to describe their approach. "Anna,
could you tell us how this compares to your group's solution?" Still
nothing? (I can't actually think of time when I got this far and there
were still no fruitful comments from the audience.) Well, have them
read it again: "Okay, one more time, from the top. . . ." It's sort of like
the the shampoo algorithm: Lather. Rinse. Repeat as necessary.
But of course you don't have unlimited time and students don't have
unlimited patience and determination. Sometimes you really are beat-
ing a dead horse, or it's nearly the end of the hour and you want to end
on an upbeat note. This is a very delicate situation. I would argue that
it's okay to leave a problem on the board unresolved, provided that you
can cast off any air of defeat before dismissing the class. "Okay, Jimmy,
unfortunately we're near the end of the hour, so we'll have to pause
here and begin again tomorrow. I think we made some real progress
today, though! This must just be a real tough nut to crack. . . We'll all
sleep on it and see what we can come up with tomorrow. Remember
it took two hundred years to prove Fermat's last theorem!"
Managing situations like this require the most skill on the part of
the instructor. First you need to realize that time is running away and
12 T. K. PETERSEN
nobody is going to have answer. Then you need to disengage everyone
in a way that doesn't feel like giving up. It's not easy.
Students can also use help before getting to the chalkboard. When
stuck during group work the "Read it. Read it again." approach isn't
usually appropriate. There are many other suggestions that you can
give students to get them past a hurdle though. Prompt them without
giving away too much. "Which examples have you tried? Hmm. . . what
about an example where n is prime?" Sometimes students throw up
their hands and ask a question that in essence says "Can you tell us
the answer please?" These include gems like "I don't get it," and "I
don't know what I'm supposed to do." My favorite approach to these
questions is to answer with my own question: "What part of the prob-
lem don't you get?" or "What do you think you should do here? Did
you try an example?" Also, "Do you understand all the words in the
statement of the problem?" (This can be a legitimate concern!)
In general, just remember that the goal is to have the students iden-
tify and correct mistakes without your help. The less you say to get
them to do that, the better. Once they've done it, go bananas! "That
is so awesome! That's the most incredible thing I've ever seen!" It re-
ally is exciting to watch when it works well, so chances are your praise
will be genuine. If not, fake it.
4. Some Reading
The Legacy of R. L. Moore Project website [?] is a good resource for
all things inquiry-based, and can put you in touch with a large network
of practitioners and proponents of the method. They have an annual
meeting in Austin, Texas. Paul Halmos' article [?] is great reading and
makes a compelling argument for teaching what he calls a "problems
course". For convenience it is included in this folder. Alan Schoenfeld
is a leading math education researcher and proponent of inquiry-based
methods. The article cited below [?], and included in this folder, points
out several problems arising in lecture-based courses that he feels are
corrected in an inquiry-based environment.
References
[H] P. R. Halmos, What is Teaching? Amer. Math. Monthly 101 (1994),
848–854.
[RLM] The Legacy of R. L. Moore Project,
[S] A. H. Schoenfeld, When Good Teaching Leads to Bad Results: The
Disasters of 'Well-Taught' Mathematics Courses, Educational Psy-
chologist, 23 (1988), 145–166
| 677.169 | 1 |
The difference between precalculus and trigonometry?
OK at the 2 year college here, they offer ONLY trig , and you take that after college algebra, and before you take calculus, and the counselors at the 2 year college all say that, trig and precalculus mean the same thing there, which is weird, because, then if you look at the classes offered at another nearby 2 year college, strangely, they offer trig AND precalculus, so what's the difference between the two?
The difference between precalculus and trigonometry?
This is all I could agree on about trigonometry since I've never taken it before.
However, for Precalculus, I can say that it includes only the "essentials" of trigonometry, such as graphs of all six functions and the inverse functions, right-triangle trig., analytic trigonometry, the very basics of vector analysis, and the very basics of Analytic Geometry. Also, the other material that is discussed that pretty much has nothing to do with trig. includes functions and their graphs, linear, absolute-value, quadratic, polynomial, exponential, logarithmic and rational functions, sequences and series, matrices, conics, and an introduction to limits. All the material needed to get you ready for the world of Calculus.
Jurrasic
#5
Apr16-11, 03:16 PM
P: 101
Quote by frozenguy
At my 2 year, they have trig and pre-calculus separate. Trig was straight trig. Functions, identities, graphing, deriving, etc. Pre calculus if I remember correctly was mainly analyzing functions and their graphs. Exponential, logarithmic, polynomial, rational, trig functions mainly. Touch on conic sections and vectors as well I think. Maybe some complex numbers.
That explains quite a bit. Thanks :)
Chunkysalsa
#6
Apr16-11, 05:58 PM
P: 311
at my school Precalculus = college algebra + trig. Though trig usually only has like a couple of sections while precalc and algebra have millions.
QuarkCharmer
#7
Apr16-11, 06:19 PM
P: 1,035
Check the syllabus for the course and see what is included?
Jurrasic
#8
May4-11, 12:04 AM
P: 101
Quote by Chunkysalsa
at my school Precalculus = college algebra + trig. Though trig usually only has like a couple of sections while precalc and algebra have millions.
Yeah thanks that's really helpful. They actually have the same thing at this school with hardly any trig classes but tons of college algebra, and about 4 different calculus classes.
Jurrasic
#9
May4-11, 12:06 AM
P: 101
Quote by QuarkCharmer
Check the syllabus for the course and see what is included?mege
#10
May4-11, 12:34 AM
P: 192
Quote by JurrasicIs there a Course Catalog/Bulletin which has descriptions seperately from the Course Schedule? (there should be, the bulletin/catalog usually is good for a year or more, whereas the schedule is only good for the single term)
| 677.169 | 1 |
...
Show More helps readers master the big ideas in each chapter through Concept Checks and Conceptual Problems, as well as Concept Explorations and Strategy Problems that challenge students to think step by step and not rush for a numerical answer
| 677.169 | 1 |
Calculus is more than just about applying formulae and rules to solve problems. It is, in my view, one of the most diverse topics in mathematics. The concept in itself is beautiful and, of course, useful. The course aims at making the reader understand actual concept of calculus, introduce him/her to the concept of limits, functions, and practice problems that would open up his/her mind to more diverse applications of calculus, like trigonometry and co-ordinate geometry. Prior knowledge of linear equations will be helpful, though not compusory.
| 677.169 | 1 |
Homeschool Connections has created a brand new 6-week course to focus solely on trigonometry. It is designed to help Algebra II students prepare for Advanced Mathematics, give Advanced Mathematics students a review for Calculus, or give a refresher for students preparing for their ACT or SAT test.
Introduction to Trigonometry Dates: Mondays, May 5 to June 9, 2014 Time: 4:00 pm Eastern (3:00 Central; 2:00 Mountain; 1:00 Pacific) Number of classes: 6 Prerequisites: Algebra 2 Suggested high school credit: 1/2 semester Math Instructor: Jean Hoeft, MS Course description: This course will polish students' Algebra 2 skills and prepare them for Pre-calculus / Advanced Mathematics. We will study the trigonometric functions and their inverses, polar and rectangular coordinates, the calculations of a triangle, vectors and more. Students are expected to do homework sets which are provided free by the instructor. There is no text book necessary, reference tables and notes will be provided. Students will have a working knowledge of trigonometric functions and their properties at the conclusion of the course. Course materials: None, all course materials provided Free by the instructor. Topics covered: Trigonometric functions, changing degrees to radians, recriprocal identities, arc lengths, writing the equations of sine and cosine functions of sinusoid graphs, graphs of secant and cosecant, simplifying trig identities, solving equations involving trigonometric identities, reference triangles, solving triangles for their angles and side lengths, and complex numbers with the complex coordinate plane. Homework: Students should expect to spend 3-4 hours on homework a week to complete the assigned work. Fee: $75 for all 6 classes
It's time again for Homeschool Connections Annual Refresh Conference. This is an online conference for Catholic homeschooling parents. It is designed to help you get through the winter months refreshed and ready for all that homeschooling has in store for you and your family.
Attendance is limited. If it fills up, you will be placed on a wait list. All webinars are recorded and made available for free viewing within 24 hours.
Meet Our Presenters:
Andrew Pudewa
Andrew Pudewa is the director of the Institute for Excellence in Writing and a homeschooling father of seven. Presenting throughout North America, he addresses issues relating to teaching, writing, thinking, spelling, and music with clarity, insight, practical experience, and humor. His seminars for parents, students and teachers have helped transform many a reluctant writer and have equipped educators with powerful tools to dramatically improve students' skills. Although he is a graduate of the Talent Education Institute in Japan, and holds a Certificate of Child Brain Development from the Institutes for the Achievement of Human Potential in Philadelphia, Pennsylvania, his best endorsement is from a young Alaskan boy who called him "the funny man with the wonderful words." He and his beautiful, heroic wife Robin currently teach their three youngest at home in Atascadero, California.
Ginny Seuffert
Mrs. Virginia (Ginny) Seuffert, a native New Yorker and mother of 12, has been homeschooling for over 20 years! While in New York, Mrs. Seuffert lectured, debated, and wrote a number of articles for the Pro-Life movement. After moving to Illinois, she became a founding member of the Network of Illinois Catholic Home Educators, helped establish the "Round Table" (a Catholic homeschool leadership discussion group), and became a founder and officer of the Catholic Home School Network of America.
In addition to appearing on EWTN, she has been a guest on numerous radio shows, lectured at Catholic family conferences all over the United States and Canada, and has authored several articles on such topics as home education, teaching children the virtues, and household management. The Seton Magazine regularly features her columns, and recently Seton Press published her first two books of a series, Ginny's Gems: Home Management Essentials and Ginny's Gems: 10 Essentials for Teaching Your Preschooler at Home.
Mary Ellen Barrett
Mary Ellen is a homeschooling mother of eight children. She is a longtime columnist for The Long Island Catholic (Life in Our Domestic Church) and speaks on a variety of topics at Catholic conferences and parishes around the United States. Mary Ellen is currently working on two books, on about mothering a large family and the other is an Advent Books of Days. She can be found blogging at Tales from the Bonny Blue Houseand during the Advent season at O Night Divine. Besides writing and blogging, Mary Ellen enjoys cooking, sewing, photography, and studying theology.
Katie Moran
Dr. Moran and her husband reside in Niles, OH with their five children, including two who were adopted from the Ukraine. Dr. Moran has her Bachelor of Science in General Studies from Kent State University, her Master of Science in Education from Breyer State University, and her Doctor of Philosophy in Education from University St. John of the Cross –Universidad San Juan del la Cruz.
Dr. Moran is host of the Homeschool Lifeline talk show on Radio Maria, She brings to our conference 23 years of homeschooling experience, in addition to her experience as a private tutor and homeschool consultant. She has been a guest speaker on the History Channel, served on the board of Northern Ohio Adoption Services, and is Secretary/Treasurer of the Blue Army of Our Lady of Fatima (Byzantine Chapter). Additionally, she is the president of CHSNA (Catholic Home School Network of America), member of the Round Table, a national organization of Catholic Home Schooling Leaders, founder and past leader of the Ohio Educators' Catholic Home Schooling Network , member of CHSNA delegation to Pope John Paul II, various congregations and curias, 1995, 1997, and again in 2006 to Pope Benedict XVI.
Dr. Katie Moran is the author of Doorway to Heaven, The Unique Learner – Homeschooling Children with Learning Disabilities, Philip's Fast – 40 Days of Advent Meditations According to the Byzantine Rite, The Story of the Church Workbook with Answer Key and Study Guide, based on the textbook, The Story of Church, and a DVD on Fatima and the Holy Angels. Her latest book still in the editing and writing stage: Home Schooling for Heaven, not Harvard.
Maria Rioux
Maria began her undergraduate studies at Thomas Aquinas College. There she met her husband, Jean, Homeschool Connections' philosophy instructor and chair of the philosophy department at Benedictine College (where Maria is a theology major slowly completing her degree). Together they have been homeschooled their nine children for more than 20 years. In those early days of homeschooling there were not many resources available. As a consequence, they developed their own curriculum which reflects their love for classical education as well as their affection for Charlotte Mason.
Maria is owner and co-moderator of the yahoo group The History Place. She loves to write and is a regular contributor to mater et magistra magazine. She is also a reviewer for Love2Learn Literature Alive!
Rachel Watkins
Rachel Watkins is wife to Matthew, homeschooling mom to 11 great kids, creator/writer of the Little Flowers Girls Club (ages 5 and up) and Honor Guard (ages 12 and up) Contributor to Ave Maria Radio's More 2 Life with Dr. Greg and Lisa Popcak and their companion blog Exceptional Marriages. In the midst of life, she has found some time to be published in a number of Catholic publications and websites. Her life could be defined as a daily attempt to fulfill the words of Jesus who assures us that He came so that our joy would be full! She doesn't always succeed but the efforts have been surprising.
NOTE: All talks are recorded and available within 24 hours. They can be found, along with talks from past conferences, here: Homeschool Connections Free Webinars. You'll need to "Login as a guest".
Homeschool Connections writing program, Aquinas Writing Advantage, is a complete online program for you and your student. It is designed to help students become skilled writers and be prepared for their futures. Aquinas Writing Advantage graduates are ready for college and beyond.
Parents often asked us, "Where do I start?" To answer that question, we offer the following scope and sequence, based on your student's grade level in the fall. Whether your child is starting with Homeschool Connections in 7th grade or 12th grade, we can help you. Our live, interactive classes provide grading and feedback, giving you ease of mind and freeing your time. We also offer recorded, independent-learning classes, providing you with yet another homeschool option.To learn more, please visit our website at or email us at [email protected].
SUGGESTED SCOPE AND SEQUENCE
For the Student Beginning in the 12th Grade 12th GRADE
Fall
How to Be an Excellent Student (short course) Elements of Writing for High School: Punctuation and Grammar / Simplified Writing for High School Vocabulary and Writing I Spring Advance Writing and Rhetoric Advanced Research Writing Vocabulary and Writing II SUGGESTED SCOPE AND SEQUENCE For the Student Beginning in the 11th Grade 11th GRADE Fall Elements of Writing for High School: Punctuation and Grammar / Simplified Writing for High School Vocabulary and Writing I Spring How to Be an Excellent Student (short course) High School Writing Essentials: Excellent Paragraph and Essay/Test Writing Vocabulary and Writing II 12th GRADE Fall Advanced Writing and Rhetoric The Hero's Journey and Mythic Structure for Writers 1: Archetypes Spring Advanced Research Writing The Hero's Journey and Mythic Structure for Writers 2: Form SUGGESTED SCOPE AND SEQUENCE For the Student Beginning in the 10th Grade
10th GRADE Fall
How to Be an Excellent Student (short course) Elements of Writing for High School: Punctuation and Grammar / Simplified Writing for High School Vocabulary and Writing I Spring Vocabulary and Writing II Fiction Writing Series 9th Grade
9th GRADE Fall
How to Be an Excellent Student (or in the spring) Fiction Writing Series Spring Fiction Writing Series
10th GRADE Fall
Elements of Writing for High School: Punctuation and Grammar/Simplified Writing for High School Vocabulary and Writing I Spring Vocabulary and Writing II 8th Grade
How to Be an Excellent Student Middle School Writing II Spring Fiction Writing Series
10th GRADE Fall
Elements of Writing for High School: Punctuation and Grammar / Simplified Writing for High School Voc 7th Grade
Elements of Writing for High School: Punctuation and Grammar / Simplified Writing for High School 10th GRADE Fall
VocHave you ever wondered what it is like to be a subscriber with Homeschool Connections? To get a free look click on this link! After clicking on the link, please login as a Guest.
If you would like to have access to all 120+ courses then simply click on the Subscribe button in the right margin. For only $1 for the first 7 days and $30 a month thereafter you have access to the best instruction money can buy.
Please let us know if you have any questions by emailing us at [email protected].
Build Your Teen's College Skill Set Are you and your high school student(s) planning for college? If so, there are certain skill sets that are particularly important to acquire:
Study Skills: Students need to know how to manage their time and meet deadlines. The brightest student can still flounder if these skills are not learned. The successful college student also needs good note taking and basic study skills so that they can get the most out of their classes and homework. After completing HSC's Study Skills and Note Taking course, students will put these skills into practice through their high school years and will therefore be better prepared for college.
Communication Skills: Strong communication skills will greatly benefit your student in any college major or career field. HSC offers a course to help students learn and practice good communications. In the Leadership and Communications Skills course, students learn speaking skills, listening skills, conflict management, and more.
Leadership Skills: The most successful students are often the ones who are also leaders. As Catholics, it is important that our students become people who are a positive influence at school and in the world. HSC's Leadership and Communications Skills course will encourage them to be people of service, show them how to be a faith-filled leader, and more.
Writing Skills: It's not enough to learn lessons taught in school, students need to be able to communicate the lessons learned in writing. Strong writing skills are vital for college success. HSC offers a strong writing program (Aquinas Writing Advantage) that will take your student from the basics (grammar, punctuation, vocabulary) to the advanced (rhetoric, research, academic papers). Your student will be ready for college writing after successfully completing these writing courses.
Critical Thinking Skills: Education should not be about cramming facts into children's heads. It should be about giving them a love for learning and the ability to think. We highly recommend formal logic and philosophy to help your student think critically and therefore succeed in all their school subjects. Logic and Philosophy are not electives — they are vital to a core curriculum. HSC offers a variety of courses that teach your student critical thinking skills, while at the same time raising their hearts to God and finding the beauty of their Catholic faith.
ACT/SAT Test Skills: To help your student get into the college of his choice, and get the best scholarship possible, we offer courses on preparing for the ACT and SAT tests. Your student will learn how to prepare for the test, what to expect, manage time, and more for success. Latin studies should also be considered, for a variety of reasons including the evidence that Latin studies increase ACT and SAT scores.
Most Importantly — How to Evaluate Ideas through a Catholic Lens: In college your student will encounter many new ideas and assumptions. Some of them will be potentially damaging. We want to give your student the necessary tools to recognize and understand the worldviews they encounter and know how to articulate their own beliefs effectively and convincingly. All of HSC instructors are Catholic and teach their courses through a Catholic lens, thus demonstrating to your student how God is evident in everything. Our theology courses will specifically prepare your student to defend his faith when he goes out into the world, as well as help him build a solid foundation of faith for his life.
How to Use Technology in Education: In HSC's online courses students become familiar with the same, or similar, technology they'll encounter in college. They learn how to be engaged participants in a live, interactive webinar and gain experience using online tools to collaborate with their instructor and fellow students from all across the country and the world. This is a skill set that will help them advance in higher education as well as the business place.
Recommended Homeschool Connections College Skill Set Courses Note: We offer a wide variety of courses and this recommend scope and sequence can easily be adjusted to fit your student's needs. Of course, you'll also want to include history, science, and moth.
9th Grade How to be an Excellent Student: Note Taking, Test Taking, and How to Get an A (4 weeks)
We are very happy to announce, thrilled in fact, that Professor Carol will be teaching music and art appreciation for Homeschool Connections in the fall semester. Yes, THE Professor Carol! We hope you'll join us in the adventure of art and music through history …
Class dates: Fridays, September 13 to December 13, 2013. No class October 11 and November 29 Total classes: 12 classes plus recorded lectures
Starting time: 2:30 PM Eastern (1:30 PM Central) Duration: 1 hour Prerequisite: None. No musical background is necessary. Suggested grade level: 9th to 12th grade Suggested high school credit: 1 full semester Music/Art Appreciation Fee: $175 if you register on or before August 1, 2013. $195 after Aug. 1st for all 12 classes Instructor: Carol Reynolds, Ph.D. (Professor Carol)
Course description: Journey with Professor Carol through Western History, using music as the focal point but weaving in visual art (painting, sculpture), dance, theater, architecture, and literature. The study of music and the Fine Arts supports the understanding of history, geography, and culture. Elements of science, technology, and language are included in the course as well. Sessions will focus on the years between 1600 and World War One, but will present an overview of Medieval/Renaissance Sacred Music.
Course materials: 1. Discovering Music online curriculum by Professor Carol will be made available to students for half of the regular price ($30 for four months subscription). 2. Music selections assigned by the instructor. These can be accessed in one of four ways. Choose the one that best suits your family: a) Free by searching your public library or YouTube; b) Classical Archives ($8 per month); c) Naxos ($20 per year); OR d) purchase 3-CD set from the instructor (HSC discounted price $34.95).
Homework: This is not a course for the faint of heart. We'll have a lot of fun as we discover music together, but students should expect a good amount of work outside of the classroom in that discovery. Homework will entail: 1. Viewing recorded classes in advance to the live classes. 2. Viewing assigned artwork and listening to music. 3. Interactive quizzes. 4. A midterm and a final exam (fill-in-blank, short essays, long essays, with answers/suggested answers). 5. Unit projects to be determined. Due to the nature of the medium, we encourage students more than ever to share their learning experience and the resources used in this course with the rest of their family.
There are a lot of different ways you can use Homeschool Connections' recorded classes (aka Unlimited Access) to keep learning alive and fun over the summer. Here are ten ideas to get you started.
10. Take school with you. All you need for recorded classes is a power source, internet, and a computer. You should add ear buds or a headset to the list if you need privacy. We've had students take classes from hotel rooms, Grandma's house, the library, and even the beach. Though we don't recommend taking your laptop anywhere near sand!
9. Plug the computer into the television. This is a really fun way to learn together as a family. Pick a subject that everyone is interested in learning. It may be Catholic Apologetics or Civil War or Lord of the Rings or something completely different. Make some popcorn and watch together. You may need an HDMI cable and a newer TV (Mac users will need a converter). Do what I do and have a teen set it up for you.
8. Pick a time that works best for you. Recorded classes are available 24/7. You could watch classes first thing in the morning, getting them done early so the rest of the day can be spent outdoors. Perhaps, you could would prefer to watch classes during lunch or just before bed in the evening. Pick the time that is going to help you keep up on your work throughout the whole of summer.
7. Audit a course. Watch a lecture each day and forgo the homework. For example, instead of taking 12 weeks for World History: 12 Inventions that Changed the World, watch the lectures over 12 days. When auditing, pick a subject that is easy for you.
6. Buckle down on tough subjects. Really need help with algebra? Struggled with science last year? If so, buckle down and get to work. Set aside time each and every day (Sundays off!) and stick to the schedule. Complete all of the homework before moving to the next recorded lecture. If you want extra help, sign up for the optional grading support (Instructor Access).
5. Catch up on subjects for September. Planning on taking Latin II next year but not quite ready? Perhaps illness or something else kept you from finishing Latin I this year. Whether you simply need a refresher or need to make up for lost time, there are a number of "Bootcamps" available in recording (math, Latin, and more).
4. Ask yourself, "What do I love?" Perhaps you love to read. If so, choose a literature course on a book you love. Reread The Hobbit as you watch Dr. Russell'sHobbit lectures over a couple of weeks. Or Screwtape Letters, or Space Trilogy, or The Man Who Was Thursday. You can choose from over 20 literature courses.
3. Summer is a great time to hone your writing skills Writing is a key skill for success in all other school subjects. Focusing on writing skills over summer will help you do better in history, literature, and more when fall arrives. Other courses that help you succeed in core subjects include: Note Taking Skillsand How to Use Microsoft Word.
2. Keep a schedule and stick to it. How many times have we all laid out grand plans, only to forget about them as the excitement wore off? Write out a reasonable schedule on a white board or print it and post it. Program your computer or smart phone to remind you each day. Do something tangible to keep you on schedule.
1. Keep it simple. You don't need a complicated schedule to be effective. Pick just one or two subjects. For example, maybe you weren't able to make time for philosophy in the fall and spring, but you know it would help you a lot to learn it and it sounds interesting. Focus just on philosophy courses for summer.
Bonus. Unlimited Access means just that! You have unlimited access to over 100 courses for your entire family. Yes, it's true! You can't beat the price ($30 per month!!!) and you can't beat the convenience. Middle school, high school, and adult students can easily learn year round with this independent learning program. It can be as easy or as complicated as you want to make it. It's YOUR program.
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Starting at $4Kaplan SAT Math Workbook
Kaplan SAT Math Workbook 3rd edition
Summary
The complete test preparation tool that contains tips, strategies, and practice for students who want to score higher on the math section of the SAT!As colleges across the country grow increasingly selective in their admissions standards, students seek out SAT prep in an effort to get a top score and stand out in the college applicant pool. No other products on the market can match the quality and experience behind Kaplanrs"s SAT guides.Kaplan SAT Math Workbookprovides everything students need to conquer the Quantitative Reasoning section of the exam. This targeted guide includes in-depth coverage of all pertinent math skills and information, as well as effective score-raising strategies for building speed and accuracy from math experts. Not only does this tool contain everything a student needs to conquer all the math included in the test, it also provides key information about the SAT in general, such as Kaplanrs"s methods for answering multiple-choice questions and more.Kaplan SAT Math Workbookcontains many essential and unique features to help improve test scores, including:Two realistic math tests with detailed answer explanations covering all parts of the SAT math section The top 100 SAT math concepts Effective score-raising methods and strategies for building speed and accuracy Proven strategies for avoiding common math errorsKaplan SAT Math Workbookprovides students with everything they need to improve their scores-guaranteed. Kaplanrs"sKaplan SAT Math Workbookis the must-have preparation tool for every student looking to score higher!
Author Biography
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Algebra textbook is a college-level, introductory textbook that covers the important subject of Algebra -- one of the basic building blocks of studies in higher mathematics. Boundless works with subject matter experts to select the best open educational resources available on the web, review the content for quality, and create introductory, college-level textbooks designed to meet the study needs of university students.This textbook covers:The Building Blocks of Algebra -- Real Numbers, Exponents, Scientific Notation, Order of Operations, Working with Polynomials, Factoring, Rational Expressions, Radical Notation and Exponents, Basics of Equation SolvingGraphs, Functions, and Models -- Graphing, Functions: An Introduction, Modeling Equations of Lines, Functions Revisited, Algebra of Functions, TransformationsFunctions, Equations, and Inequalities -- Linear Equations and Functions, Complex Numbers, Quadratic Equations, Functions, and Applications, Graphs of Quadratic Functions, Further Equation Solving, Working with Linear InequalitiesPolynomial and Rational Functions -- Polynomial Functions and Models, Graphing Polynomial Functions, Polynomial Division; The Remainder and Factor Theorems, Zeroes of Polynomial Functions and Their Theorems, Rational Functions, Inequalities, Variation and Problem SolvingExponents and Logarithms -- Inverse Functions, Graphing Exponential Functions, Graphing Logarithmic Functions, Properties of Logarithmic Functions, Growth and Decay; Compound InterestSystems of Equations and Matrices -- Systems of Equations in Two Variables, Systems of Equations in Three Variables, Matrices, Matrix Operations, Inverses of Matrices, Determinants and Cramer's Rule, Systems of Inequalities and Linear Programming, Partial FractionsConic Sections -- The Parabola, The Circle and the Ellipse, The Hyperbola, Nonlinear Systems of Equations and InequalitiesSequences, Series and Combinatorics -- Sequences and Series, Arithmetic Sequences and Series, Geometric Sequences and Series, Mathematical Inductions, Combinatorics, The Binomial Theorem, Probability Calculus textbook is a college-level, introductory textbook that covers the fascinating subject of Calculus. Boundless works with subject matter experts to select the best open educational resources available on the web, review the content for quality, and create introductory, college-level textbooks designed to meet the study needs of university students.This textbook covers:Building Blocks of Calculus -- Precalculus Review, Functions and Models, LimitsDerivatives and Integrals -- Derivatives, Applications of Differentiation, Integrals, Applications of IntegrationInverse Functions and Advanced Integration -- Inverse Functions: Exponential, Logarithmic, and Trigonometric Functions, Techniques of Integration, Further Applications of IntegrationDifferential Equations, Parametric Equations, and Sequences and Series -- Differential Equations, Parametric Equations and Polar Coordinates, Infinite Sequences and SeriesAdvanced Topics in Single-Variable Calculus and an Multivariable Calculus -- Vectors and the Geometry of Space, Vector Functions, Partial Derivatives, Multiple Integrals, Vector Calculus, Second-Order Linear EquationsA Closer Look at Tests of Significance -- Which Test?, A Closer Look at Tests of Significance Algebra I Second Edition is a clear presentation of algebra for the high school student. Volume 1 includes the first 6 chapters and covers the following topics: Equations and Functions, Real Numbers, Equations of Lines, Graphs of Equations and Functions, Writing Linear Equations, and Linear Inequalities.'
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Mathematical Applications in Agriculture
Summary
Invaluable in any area of agriculture or as a hands-on learning tool in introductory math courses, the 2nd Edition of MATHEMATICAL APPLICATIONS IN AGRICULTURE demonstrates industry-specific methods for solving real-world problems using applied math and logic skills students already have.
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The student workbook is 669 pages with 119 lessons, while the four CD-ROMs provide step-by-step audiovisual solutions to every homework and test problem. The CD-ROM's digital gradebook grades answers as soon as they are entered and calculates percentages for each assignment; a softcover answer booklet is also provided. Windows 2000. Teaching Textbooks Grade 4.
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Algebra I Essentials For Dummies by Mary Jane Sterling
Just the critical concepts you need for cramming, homework help, and reference
Whether you're cramming, you're studying new material, or you just need a refresher, this compact guide gives you a concise, easy-to-follow review of the most important concepts covered in a typical Algebra I course. Free of review and ramp-up materials, it lets you skip right to the parts where you need the most help. It's that easy!
Set the scene — get the lowdown on everything you'll encounter in algebra, from words andsymbols to decimals and fractions
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GeoGebra is a dynamic mathematics software that
joins geometry, algebra, and calculus. Two views
are characteristic of GeoGebra: an expression in
the algebra window corresponds to an object in the
geometry window and vice versa
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263003 / ISBN-13: 9781904263005
Useful Mathematical and Physical Formulae
A compact volume of mathematical and physical formulae presented in a concise manner for general use. Collected in this book are commonly used ...Show synopsisA compact volume of mathematical and physical formulae presented in a concise manner for general use. Collected in this book are commonly used formulae for studies such as quadratics, calculus and trigonometry; in addition are simplified explanations of Newton's Laws of Gravity and Snell's Laws of Refraction. A glossary, a table of mathematical and physical constants, and a listing of Imperial and Metric conversions is also included
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Algebra and Trig.: Graphs and Models - Text - 5th edition
Summary: The Graphs and Models series by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students ''see the math'' through its focus on visualization and technology. These books continue to maintain the features that have helped students succeed for years: focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications. This package contains134.85177.45202.28 +$3.99 s/h
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1-19-12 Hardback 5
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Mathematics eBooks
Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. eBookMall offers math eBooks on the subjects of in calculus, geometry, research, reference, and more.
Humans have been aware of mathematics ever since they began to count objects but the ancient Greeks were the first to start a systematic study of mathematics. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory.
There are over 200 eBooks in the category Mathematics. Use our eBook search to find a specific book or author.
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Graph theory applications
This text offers an introduction to the theory of graphs and its application in engineering and science. The first part covers the main graph theoretic topics: connectivity, trees, traversability, planarity, coloring, covering, matching, digraphs, networks, matrices of a graph, graph theoretic algorithms, and matroids. In the second part, these
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Schaum's Outlines present all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
Suitable for an introductory combinatorics course lasting one or two semesters, this book includes an extensive list of problems, ranging from routine exercises to research questions. It walks the reader
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More About
This Textbook
Overview
This third edition of Arem's CONQUERING MATH ANXIETY workbook presents a comprehensive, multifaceted treatment approach to reduce math anxiety and math avoidance. The author offers tips on specific strategies, as well as relaxation exercises. The book's major focus is to encourage students to take action. Hands-on activities help readers explore both the underlying causes of their problem and viable solutions. Many activities are followed by illustrated examples completed by other students. The free accompanying CD contains recordings of powerful relaxation and visualization exercises for reducing math anxiety.
Related Subjects
Meet the Author
Cynthia A. Arem is Chair of the Social Sciences department at Pima Community College. She received her Ph.D. in Educational Psychology from the University of Arizona, and was Math and Sciences Counselor at Pima Community College from 1982 to 1998. She is President of National League of American Pen Women, Tucson Branch
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The Common Core State Standards for Mathematics are notable for raising the rigor of student language demands during math instruction. Students are expected to understand complex problems, engage in constructive classroom conversations about math, and clearly support their reasoning with evidence. In this course teachers will be provided with a range of practical tools for gathering and analyzing language samples that show how students learn and what supports they need in elementary math classrooms.
This course on Division and Multiplication of Whole Numbers introduces a learning trajectory approach to students' multiplicative reasoning, exploring a stronger conceptual basis for multiplicative reasoning, so that, eventually, multiplication and division of fractions is an extension of multiplication and division of whole numbers, instead of a new and mystifying monster of its own.
This course offers participants an opportunity to engage in a community of learners using an inquiry cycle focusing on math formative assessments as a strategy for implementing CCSS in math. It focuses on the implementation of a Classroom Challenge: a 1 – 2 day lesson developed by the Mathematics Assessment Project (MAP) based on formative assessment and the CCSSM.
M2O2C2 provides a first taste of multivariable differential calculus. By introducing the machinery of linear algebra, this course provides helpful tools for understanding the derivative of a function of many variables.
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Linear Algebra Syllabus
Course Description: Linear algebra is a fundamental branch of
mathematics dealing with the
solution of linear equations. We will consider systems of linear equations,
properties of matrices and
determinants, vector spaces, linear transformations, inner products,
orthogonality, eigenvectors and
eigenvalues, and the canonical representation of linear transformations.
Office Hours: 10am MTWF, 2pm MTW. Other times by appointment. My
schedule and office
hours are also listed on the webpage.
Practice Problems: Once material has been covered in class it is
expected that you will work
through problems in the relevant section of the text. This daily homework is the
absolute minimum
work required to succeed in the course.
Homework: Regular assignments and their due date will be announced in
class. These assignments
will be graded, and are due at the beginning of the relevant class.
Exams: Exams will be held in class on Monday February 2nd, Monday
March 2nd, and Monday
April 6th. The Final Exam will be held on Monday May 4th, 9:00am - 11:00am.
Attendance: Students are expected to be present at every class.
Success in this course requires
regular attendance.
Grading: Grades will be based on 3 one-hour exams (a total of 300
points), homework assignments
(equally weighted and scaled to a total of 100 points), a final project (100
points) and a final
comprehensive exam (150 points). A total of 650 points are available, and the
cut-o s for the final
letter grade are as follows:
A
85%
B
70%
C
60%
D
50%
B+
80%
C+
67%
D+
57%
F
Below 50%
Makeup Exams: Departmental policy dictates that make-up exams are to
be given under extenuating circumstances only. No make-up quizzes will be given.
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World of Math
2000 Math is a universal language that fundamentally connects all parts of the world we live in. It is a governing force of the new Information Age and the computer science behind it. It is becoming increasingly important in the modern world that students not only learn arithmetic skills, but that they delve beyond into the more advance branches of mathematics. Our website was founded with this purpose in mind. Enter The World of Math to better your own understanding of the art of math and prove your mathematical mettle in our online competition. Visit our comprehensive classroom tutorials. Participate in our extensive chat room and message board discussions. Compete with others in real time and in our problem-of-the-week. The World of Math combines all of the essential elements of high school math into a single place. It is an expansive website dedicated to the advancement and spreading of mathematical knowledge. We hope not only that you will visit our World, but also that you participate actively in our numerous interactive environments. Learn with the World of Math Explore with the World of Math. Teach through the World of Math. From arithmetic to calculus, linear algebra and beyond, the World waits at your fingertips
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foundation for algebrayear 2 answers national math and science initiative home recent posts the ins outs of a rigorous lesson how to cultivate deep content knowledge posted 1 days ago for quite long while the term rigorous has sign that's what equals means falkner i see adam, would you say that again? [adam repeats his explanation other children, considering adam class lesson: while,
foundation for algebrayear 2 answers the jackie robinson foundation provides comprehensive scholarships and support services to minority students enrolled at institutions of higher education 3 course is designed fulfill all requirements delineated by the ap course audit can i teach physics 1 in one year? we recommend that schools
foundation for algebrayear 2 answers calcchat calculus solutions precalculus solutions is a moderated chat forum that provides interactive calculus help college precalculus and more dear parent/guardian student: soon students will be participating in the ace algebra i end-of-instruction oklahoma core curriculum test this test designed to help, solutions,
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their maths studies. 1 TYPES OF BEAMS A beam is a structure, which is loaded transversely (sideways). ... programmes for solving beamproblems. The Archon Engineering web site has many such programmes. WORKED EXAMPLE No.1
Teacher guide Solving Geometry Problems: Floodlights T-1 Solving Geometry Problems: Floodlights MATHEMATICAL GOALS This lesson unit is intended to help you assess how well students are able to identify and use
Finite deformation beam models and triality theory in dynamical post-buckling analysis1 ... In statical frictional contact problems, if the beam is supported on a rigid obstacle, and the shape of the obstacle is described by a strictly concave /(x) ...
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Solutions of Mechanical (or) Electrical problems involving discontinuous force functions (R.H.S function ) (or) Periodic functions other than and are obtained easily. The Laplace Transformation is a very powerful technique, that it replaces operations of calculus by operations of ...
Solving Structural Dynamic Problems Using DCALC p.7-1 Chapter 7: Solving Structural Dynamic Problems Using DCALC By Karl Hanson, S ... The above frame shows a modeled representation of the beam in the previous problem. As before, we will prepare this analysis running the following order of DCALC ...
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2.3 The Loaded Beam ... endpoint problems and we will also exemplify the need for such generalisations to ... Calculus of Variation An Introduction To Isoperimetric Problems, 2013. http: // ...
challenging Olympiad problems, several surprising applications, ... build a simple machine which applies a gradually increasing force to the centre of the beam while it is ... runs a maths competition for schools in the Cape Town area, and directs a nationwide Mathematical Talent Search, ...
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Use geometric reasoning to solve problems A ... 45° Ground Narrow Beam Ladder Ladder It is built on sloping ground. The beam, AB, is parallel to the ground. The support posts, AE and BD, are vertical. The support post, AE, makes an angle of 80º with the ground.
radiographers sometimes use X-ray beam filters and need to be able to quantify the impact of filtration on the intensity and quality of the resulting images, as well as on patient exposure. Once the images are processed, radiographers' next
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to the beam's curvature which is assumed to equal the second derivative of the out-of-plane displacement w with respect to x. However, ... In statics problems it is often more convenient to formulate the governing equations using
Two distinct problems are considered: the first is where the stress is assumed continuous across the boundary ... There, the solution is simplified by assumingthat the turning angle α throughwhich the beam is bent is specified,
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If you do a search on "from arithmetic to algebra" as a verbatim phrase, you'll get about 600 hits, with the ones from Google Books reaching back into the nineteenth century. About three out of every four will be about helping students make the transition from arithmetic to algebra -- it has been known for a very long time that that's where we lose many people who are never able to advance much further in math.
As I noted before, 25 years ago RAND surveyed the then-nascent field of educational software and found many effective arithmetic teaching programs and practically nothing that taught any of the important aspects of algebra (abstract relations, strategy, fundamental concepts and so on). Even back in 1988, it was clearly understood that arithmetic training programs should not be the model for developing algebra educational software because arithmetic is taught as procedural training. When you teach the quadratic formula, polynomial factoring or Cramer's Rule as if they were mere complex recipes like long division, you miss the fundamental concepts that are the whole point of studying algebra.
Depressingly, my survey of algebra-teaching software revealed that 25 years later the situation remains the same. Plenty of programs will drill a student on algebraic procedures, but most do not even attempt to teach any sort of insight, strategy or deeper understanding. Even the best merely offer supporting text or "guess the next step," the same wrong-headed approach that the pioneering math educator Mary Everest Boole identified about the arithmetic-to-algebra transition in 1909.
Proceduralism is about performing tasks (now write this number here and do this ...), but conceptualism is the heart of mathematics (how are these numbers connected or related?). In the leap from "what do I do?" to "what is it?" we're losing many students who might otherwise have gained not only the higher incomes, but the much better understanding of the world, to which mathematics is the gateway.
Now, there may be an educational software design company out there right now about to fix this problem, but probably there's not. And parents and teachers who need to get a seventh-to-ninth grader across the gap right now can't very well wait until he or she is halfway through college, or longer, for algebra teaching software that actually teaches algebra.
And yet there is a piece of instructional software right on your computer that can be used to teach all levels of algebra to all levels of student, in a fully conceptual way. It's the spreadsheet.
You can find plenty of discussion and advice about how to do this from excellent teachers like Tom Button, Sue Johnston-Wilder and David Pimm, Teresa Rojano and Ros Sutherland, but let's just quickly hit the highlights of how exploring spreadsheets, and then exploring with spreadsheets, can provide a conceptual doorway into algebra. If you're interested, you'll find all but limitless resources for this.
Consider, to begin with, that variables and parameters in spreadsheets are very similar to what they are in ordinary algebra. For that matter, Microsoft Excel notation (and most of the Open Office software notation) is either algebra notation outright, or so close that only simple explanations need to be given ("in algebra the multiplication asterisk is understood, in Excel you have to put it in," "what we call a function in algebra is what a formula is in Excel," etc.).
A basic insight of algebra is that a function can be thought of as a rule OR a table OR a graph. (I'm capitalizing because it's the Boolean logical OR rather than ordinary English "or.") In fact, they are three different ways of looking at the same thing. Similarly, a spreadsheet formula can be used to generate a table of data, and the spreadsheet's graphing features can be used to turn it into a graph.
I found in teaching elementary algebra to disadvantaged adult learners that the progression from table to graph and then to formula/function/equation might have been the most powerful tool for "selling" algebra I ever encountered. Anyone can see intuitively that for many problems, if you just make a table big enough, trying out all the possible values will lead to a solution. From there, it's a short step to, but what if there are millions of values? Then they're ready to graph it and the answers are right there at the intersections. From there it's just the step to, but what if you need an answer more exact than the line you can draw, or more dimensions than two? Well, by then, they're used to the idea of formula/function/equation as description, and if a point satisfies more than one description, it's a solution. And they've crossed over to doing algebra.
The spreadsheet provides a natural bridge from arithmetic procedure to formula/function. At first, students will just input numbers, as if the spreadsheet were a calculator. Then they see that if they input variables, they don't have to type nearly so much, and then that this means having not just this answer this time, but all the answers to all problems of this type, all the time.
It's a wide and easy-to-cross bridge from the specific to the general, and from procedure to concept.
One of the big changes in mathematics in the last 30 years has been the idea of experimental math, i.e., of exploring how numbers work by setting up numerical processes and looking at the results; it's at the heart of chaos research, for example. Just as the computer has become the equivalent of the telescope or microscope for mathematicians, Excel can be used as an amateur "scope" for exploring numbers, in a way very much analogous to the way countless students have gotten a handle on science by finding a planet in the sky or exploring the ecology of pond water. Among other things, I've used Excel to teach how every fraction is a division, and division is equivalent to multiplying by the inverse. It could easily be used for many other projects beginning even from a very early age in arithmetic.
Spreadsheet algebra is such an effective and intuitive idea that it has been re-invented several times in the last 20 years, and some Googling around will turn up immense amounts about it. (Caution: "spreadsheet algebra" is also a term used in advanced mathematics research for a kind of non-linear matrix algebra, so your Googling may very well turn up an article or two that's a bit beyond you. Don't worry, just keep looking!)
Although there still needs to be a human being there to guide the student in exploring and using the spreadsheet, as a teaching device for actual algebra (as opposed to a drilling device for standardized tests) the spreadsheet still beats out thousands of purpose-designed
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Print Book
Key Features
@bul:* Includes a thematic presentation of linear algebra * Provides a systematic integration of Mathematica * Encourages students to appreciate the benefits of mathematical rigor * All exercises can be solved with Mathematica
Description
Linear Algebra: An Introduction With Mathematica uses a matrix-based presentation and covers the standard topics any mathematician will need to understand linear algebra while using Mathematica. Development of analytical and computational skills is emphasized, and worked examples provide step-by-step methods for solving basic problems using Mathematica. The subject's rich pertinence to problem solving across disciplines is illustrated with applications in engineering, the natural sciences, computer animation, and statistics.
Readership
For researchers, librarians, professionals, and the general public who want to enhance their knowledge of linear algebra and Mathematica.
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The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential... more...
Malliavin calculus provides an infinite-dimensional differential calculus in the context of continuous paths stochastic processes. This book, demonstrating the relevance of Malliavin calculus for Mathematical Finance, starts with an exposition from scratch of this theory. Greeks (price sensitivities) are interpreted in terms of Malliavin calculus. more...
Offers a systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. This book covers some basic properties of metric and Banach spaces. It also provides background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. more...
Master pre-calculus from the comfort of home!
Want to "know it ALL" when it comes to pre-calculus? This book gives you the expert, one-on-one instruction you need, whether you're new to pre-calculus or you're looking to ramp up your skills. Providing easy-to-understand concepts and thoroughly explained exercises, math whiz Stan Gibilisco... more...
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Discrete Mathematics with Applications, 3rd Edition
Susanna Epp's DISCRETE MATHEMATICS, THIRD concepts experience.
Cengage Learning reserves the right to remove content from eBooks at any time if subsequent rights restrictions require it.
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About the Author
Gary Haggard is Professor of Computer Science at Bucknell University. His research in data structures focuses on the implementation of effective algorithms for computing invariants for large combinatorial structures such as graphs. Dr. Haggard¿s current work is directed towards finding chromatic polynomials of large graphs.
John Schlipf is a Professor of Computer Science in the Department of Electrical and Computer Engineering and Computer Science at the University of Cincinnati. His research interests include logic programming and deductive databases, algorithms for satisfiability, computability and complexity, formal verification, and model theory.
Sue Whitesides is Professor of Computer Science at McGill University. She holds a Ph.D. from University of Wisconsin and a Masters from Stanford University. Her research interests lie within combinatorial mathematics and theoretical computer science required textbook for a course at my university. My professor pulled all the homework from the ends of each chapter. This part of the book is one of my biggest gripes. The reading sections of this book pack a large amount of material in a brief page or two for each section followed by homework exercises. The exercise sections have are about as long as the actual information sections, meaning they are packed with questions. This would be a positive for this book except the questions aren't similar, so the included CD with the odd problems solved will often be of little help because question 3 will be a completely different sort of problem than question 4. Since each problem is so unique, you'll often be left dealing with problems that are considerably more complex than anything found in the reading sections of the text. If you are using the questions of this book for homework, be prepared to use google extensively. As an example, the book may explain how to perform an operation on 2 sets of numbers. Then in the homework, it will ask you to perform the same operation on 5 sets abstract sets without ever explaining how to go about doing that.
I ended up receiving an A in the course, but that was after spending ~8 hours for each 10-14 question homework. Most of that time was spent on the internet trying to learn the material from whatever sites I could find. The reading sections of this text are an excersize in frustration. In one of the explanations for a concept in the book, the author literally uses the phrase "from [problem], it is obvious that the answer is [answer]." That was the entire explanation on the topic. A textbook should never say the phrase "from X, it is obvious that Y" if the whole section is supposed to be telling you how to find Y from X in the first place. This is an introductory text into formal logic, proofs, and set mathematics. Yet, you'll often find that the author skips steps in his solutions which may be obvious to someone familiar with the material but that is obviously not the target of this text. There is an occasional table for reference which doesn't explain what the relationship between anything on the table is (I'm looking at you, Table of Commonly Used Tautologies....). This book covers a great number of topics in a fairly small book, for a textbook that is. However, this book suffers from a lack of depth necessary to reach its potential.
If you have a choice, skip this text. If, like me, you are required to use this text.... Google everything and god help you.
1.0 out of 5 starsExtremely poor organization.Jan. 13 2014
By Dan G. - Published on Amazon.com
Format:Hardcover|Amazon Verified Purchase
This book has an extremely poor organization of information. It's like the authors just threw a bunch of information at the book without thinking about how a student has to go through learning the mathematical concepts. The only reason I have to use this book is because a professor from my university was one of the authors. Get another book on discrete mathematics if you want to really learn the material.
1 of 8 people found the following review helpful
5.0 out of 5 starsGreat TextbookSept. 7 2011
By mfox - Published on Amazon.com
Format:Hardcover|Amazon Verified Purchase
This textbook was the exact same one I needed for class and was MUCH cheaper than buying from the school store. It was even in better condition than what was advertised! I would definitely recommend this book.
| 677.169 | 1 |
This is a booklet containing 31 problem sets that involve a variety of math skills, including scientific notation, simple algebra, and calculus. Each set of problems is contained on one page. Learners will use mathematics to explore varied space...(View More) science topics including black holes, ice on Mercury, a mathematical model of the Sun's interior, sunspots, the heliopause, and coronal mass ejections, among many others
| 677.169 | 1 |
Mathematical Proofs: A Transition to Advanced Mathematics, 2/e, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets. KEY TOPICS: Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory. MARKET: For all readers interested in advanced mathematics and logic.
| 677.169 | 1 |
An anonymous reader writes "As a third-year PhD math student, I am currently taking Partial Differential Equations. I'm working hard to understand all the math being thrown at us in that class, and that is okay. The problem is, I have never taken any physics anywhere. Most of the problems in PDEs model some sort of physical situation. It would be nice to be able to have in the back of my mind where this is all coming from. We constantly hear about the heat equation, wave equation, gravitational potential, etc. I'm told I should not worry about what the equations describe and just learn how to work with them, but I would rather not follow that advice. Can anyone recommend physics books for someone in my position? I don't want to just pick up a book for undergrads. Perhaps there are things out there geared towards mathematicians?"
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Re:Books (4, Insightful)
I agree. I picked up the set a few years ago based on Surely You're Joking and I'd recommend them to anybody beginning in physics, especially to Professors of freshman physics, which is usually not so much taught as shoveled. The lectures are taken from his lessons in first year physics, so not too difficult for a math grad student with no previous physics.
Re:Books (5, Informative)
I just thought of another one. It's Mathematical Methods for Physicists by Arfken. I wouldn't necessarily recommend buying it, but find one you can flip through (most university libraries have it, as do most math/physics department libraries. and I can almost guarantee that someone you know has this book).
Re:Books (3, Informative)
I too cannot recommend "The Feynman Lectures on Physics Vol I-III" enough. This was written for first year undergrad students, but should have been aimed for 3rd year students. It is very nice in that is very detailed, at the expense of going overboard. For example, Feynman discusses the fact that solutions to differential equations are in fact the minimal energy solutions. I did not grok this until I got to grad school and studied Finite Element Methods.
Another great series is the one by Laudau and Liftshitz.
Re:Books (3, Interesting)
As a 4th-year Physics undergrad, I have to voice my opinion that I absolutely can't stand Feynman's texts.
They're nice to glance at, but approach the subject in a considerably different manner than any of the other renowned physics texts.
Similarly, his proofs were terse to the point of being difficult to follow. I'll admit that my mathematical intuition isn't the greatest, though I can't help but think that this was intentional on Feynman's part, as to weed out those with weak mathematical skills from his freshman lectures. This makes them rather frustrating to use as a general reference. Similarly, the texts are largely theoretical, and offer little advice with regard to problem-solving.
Personally, I've had good experiences with the Landau/Lifshitz series of texts, and it's hard to go wrong with Griffith's books on EM and QM. Goldstein's text on Classical Mechanics is also a well-known classic.
That's not to say that that Feynman's texts are all bad. Some sections are outright brilliant, and he actually takes the time to explain himself rather extensively in many sections, which many physics (and math) writers frequently neglect to do. I keep a copy of all 3 volumes on my bookshelf, as they are occasionally handy. However, I wouldn't dream of using them as my only reference.
Anonymous Coward | more than 5 years ago
Re:PDEs now? (5, Informative)
You both probably studied how to solve certain simple PDEs in simple geometries (like the heat, wave, and Poisson equations). At a graduate level one normally learns how to prove existence and uniqueness of solutions to PDEs, how smooth those solutions are (i.e. how many derivatives do the solutions possess), and how to define weak forms of PDEs for which non-classical solutions exist (solutions that are not necessarily even continuous). Then there is the whole area of non-linear equations which is a very active research topic... (See the Navier-Stokes Equations.)
Anonymous Coward | more than 5 years ago
Re:PDEs now? (5, Insightful)
There can be a world of difference between graduate and undergraduate PDE courses; it's not like everything that's known about PDEs can be taught in a couple of undergraduate semesters. I expect most undergrad PDE courses are geared towards showing you the methods that work for a few classes of linear PDEs; a graduate course might be concerned with the analytical underpinning of those methods, or maybe about numerical and analytic techniques that are useful in solving classes of nonlinear PDEs, etc.
That being said, though, from the way the original question is worded, it sounds like it's the first time this person has seriously encountered PDEs. Not having this happen until the third year of a PnD program does seem a little odd.
Re:PDEs now? (2, Interesting)
No. ODE's are typical of Undergrad. But, PDE's are typical of Masters. That isn't to say that PDE's are taught in Undergrad, period. Rather that PDE's in Undergrad is atypical. At least in North America. Other parts of the world either have vastly superior high-school/Undergrad or skip a lot of the, necessary for actually understanding, stuff. Germany and China are respective examples.
Re:3rd year PhD student taking PDE? (1)
I think his problems may be the result of how the questions are being given to them. They probably won't be your standard undergrad, here is an equation, give me the answer, type, but more of the here is the situation, figure out the equation, then solve it type.
Halliday or Giancoli are nice (1)
I've read through at least some of both Halliday and Giancoli, but sometimes it's nice to have someone explain things to you instead. I happened to have some very good physics professors who always explained where every equation came from (although sometimes I couldn't figure out what they were getting at until they said, "Trust me on this math here" and suddenly wrote equations on the board).
Re:Halliday or Giancoli are nice (1)
I don't recommend either Halliday/Resnick/Crane or Giancoli. They are both undergraduate texts treated at a rather simple level, light on math, and you'll never see a partial differential equation.
That's the problem. Most texts that are basic physics also assume basic maths.
Maybe you can handle Jackson Electrodynamics, which is a standard graduate level text. It won't be easy, but it doesn't really assume much foreknowledge, since it lays out the groundwork in the first few chapters (which are review for most students).
Re:Halliday or Giancoli are nice (1)
I dunno, I remember finally really "getting" pdes from H&R, though maybe that was very supplemented by lectures. I do know that as subjects go, what really made the math click was E&M: Maxwell's Equations were just so damn elegant and beautiful it all came together there for me (though coffee cups are good for boundary value problems - I seem to remember Boyce and DePrima being a good text with enough of the physics to make it work well).
Partial differential equations (0, Offtopic)
First of all, "partial differential equations (-1, Flamebait)
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Anonymous Coward | more than 5 years ago
First of all, "partial differential equations (4, Informative)
Good thing you weren't modded up. Basically nothing you said was enlightening or even correct, except for the contents of the first sentence.
You didn't even bother to correct the OP, you just sat back and decided to be a useless pedant. Yes, OP is technically incorrect, but your post is uninformative and completely worthless.
All possible partial derivatives of a point on a 3-dimensional graph fall on a tangential plane. Usually we speak of a tangent line, setting x or y constant, but if one redefines the coordinates, then any line on that plane that passes through that point is a partial derivative. So that "partial derivative plane" contains all possible partial derivatives of that point. This designation is intuitive and not particularly misleading, so there was little point in being an ass about it.
Anonymous Coward | more than 5 years ago
For EM and Quantum, even a math grad should read the advanced undergraduate books by Griffiths: Introduction to Electrodynamics Introduction to Quantum Mechanics
For thermodynamics, I don't know the best text.
For General Relativity, the standard undergrad book is Hartle's Gravity. But since you're a math PhD, you can go straight to the finest first grad level Relativity book by Sean Carroll: Spacetime and Geometry
If you're looking for intuition, the indispensable and invaluable books are Feynman's Lectures on Physics.
I can recommend mathematical physics texts, but I get the impression you want the missing background for understanding. Hope this is helpful.
Re:Some essentials (4, Informative)
I'd like to second all of these recommendations, but for Quantum Mechanics if your linear algebra is sharp, I might suggest Principles of Quantum Mechanics by Shankar.
Griffifhs' Quantum Mechanics is an excellent introduction, but it assumes relatively little math knowledge, and tends to gloss over some of the assumptions being made. This is good for a student who's going to spend most of his effort trying to learn the practical aspects of doing Quantum Mechanical calculations, but not ideal for someone who grasps the math quickly and easily, and wants to really understand how things work.
Shankar is a little more difficult mathematically (and is thus often a poor introduction for an undergrad) but it very clearly lays out the assumptions being made, and how the math relates to the physics.
I haven't actually read the Sean Carroll book, but I took a course from him, and I can't imagine the book is anything but excellent.
A survey of the best (3, Informative)
Try Quantum Chemistry by McQuarrie for quantum theory--one of my favorites. It will get you up to speed on waves. I would have never thought there could be such a thing as a gentle introduction to the Schroedinger Equation, but McQuarrie is the closest there is. You can't go wrong with Atkins's Physical Chemistry for thermodynamics. For electrodynamics, there is Jackson. The classic on Information Theory is Cover and Thomas. For gravity, read Gravity (I've never read it though)--beware that its so thick, it has its own gravitational field. But I guess you don't mean relativistic physics. Decent Newtonian mechanics books are a dime a dozen because you don't need more than calculus to learn it.
My favorites (2, Informative)
I think the best book for what you are asking (and I am 95% sure this is the right book, but I've lent it out so I had to look it up from dover) is "Vector Analysis" by Homer E. Nowell. It develops the theory of vector calculus using an intuitive approach and builds up the theory of electromagnetism simultaneously.
You might also look into the Feynman lectures. I do not normally recommend them as 'learning' material because, while excellent, I'm not aware that they come with any problem sets. But for you they may be a good supplement.
And, just to throw it out there, but it seems to me that most technical schools have enough overlap between physics degree requirements and math degree requirements that if you have a reasonable interest in the other it might not be out of the question to work that into your curriculum.
Man... (1)
I'm in the exact opposite situation: I'm in a PDE class now with little grasp of the math but understand what they describe pretty well. I would hope you learn the material though, as I'd rather be able to get a solution from a mathematician. I don't know why you're snubbing undergrad books though - there are many that start to delve in the more advanced mathematics, enough so that it sets up the context for the PDEs. I'm a junior in nuclear engineering though - what's a 3rd year math PHD doing in PDE? Were you a Spanish major before?:)
Re:Man... (1)
for exceedingly strange definitions of "opposite," of course. if we are being that liberal with words, then, good sir, I, indeed, am in the exact opposite situation, and not you. I don't know anything about undergraduate level math or physics (well, perhaps this is also straining the definition for "undergraduate," given what is sometimes taught as undergraduate math in the US these days).
Yes, stick to the mathematics. (2, Insightful)
Seriously, the discussion of mathematical models in good PDE books is crisp and clear. The discussion in physics books is woolly and imprecise. That's because physicists rarely know enough mathematics to be able to express themselves precisely. So I would say: Just stick with the explanation of physical phenomena which you find in the mathematics books. It doesn't get much clearer than that, if you read the PDE books which I used to read.
Pick a different curriculum, seriously (0)
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Anonymous Coward | more than 5 years ago
If you're uncomfortable with PDE without Physics, then your curriculum is probably Mathematics and if you can't handle PDE, change majors, seriously. A Mathematics degree alone requires theoretical and abstract thinking to be successful. Seriously, find a Math counselor and talk to them about it. You'll never find any quick tutorial on Physics, unless of course you're Einstein or Newton.
Wave phenomena are complicated to begin with.... (1)
Having taken PDE's last year as a Nuke-E undergrad for intro to quantum, I can tell you that all the physical phenomena PDE's model are generally 'wave' based in _concept_.
I also took our Physics 340 on "Heat Waves and Light" which is most of the stuff relevant to PDE's....
The textbook for that course was
"Selected Chapters from 'University Physics', Young and Freedman, 11th edition." Where selected chapters were all the ones dealing with heat, waves, light, and a teeny bit of relativity.
It's a pretty standard university physics textbook.
Anonymous Coward | more than 5 years ago
Re:What? (0)
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Anonymous Coward | more than 5 years ago
There's a huge difference between the intro PDE class that undergrads usually take - and the more advanced ones that graduate students take. My concern is that he's a third year grad student...and is asking questions like this on slashdot when he should already know the answer.
Re:What? (4, Informative)
Contrary to what most people seem to think, the material taught in most Calculus and Differential Equations courses has very little resemblance to what most Mathematicians study. These fields actually all fall under the heading of Analysis, which is just one of several major branches of mathematics. A student not interested in analysis could easily spend most of his math career working in another area.
For the most part, differential equations courses are aimed at non math majors, such as physicists, chemists, engineers, and the more analytically minded biologists and economists, so even a Math major specifically interested in analysis isn't necessarily going to take classes on partial differential equations.
I myself double majored in Physics and Math, and every single course i took about differential equations was for the Physics major rather than the math Major, so I think that Math grad student could quite easily end up with a PhD without ever dealing with differential equations unless they interested him.
Re:What? (3, Insightful)
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Anonymous Coward | more than 5 years ago
Wow, the level of ignorance here is astounding, that you would get moderated so highly. Real PDE (as mathematicians study it) is HARD, and requires a heavy background in analysis. This is not the same as undergrad "PDE" courses.
This is like the high schooler saying "Why are you taking algebra as an undergrad" to a math major studying abstract algebra. Its the same word and the topics are related, but its not even close to the same thing.
Re:Some recommendations from another Math Ph.D (1)
The OP is a graduate student in a field that isn't physics and says he never took physics anywhere. He's overestimating his abilities when he says he doesn't want to start with an undergraduate textbook because that's exactly where he should start. Unless he's cramming for an exam, he should take the time to start with college physics books and move up as he understands the material. PDE is difficult, but the basic physical concepts they represent are relatively simple to understand.
Jumping Jesus on a pogo stick, you're pointing him to The Black Death straight out of the gate? Why not give him underwear made of wolverine chow? Wheeler would have died ten years ago if not for the life-giving tears of those who opened that book unprepared. That is to say, everyone.
Seriously, dial it back a bit. First, hit the Feynman lectures (stop when you get to 'partons'.) Then, for someone coming from a mathematical bent, I'd suggest starting with Sokolnikoff's book "Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua", which covers a lot of ground besides GR. Due to the absence of a just and loving god it is out of print, but surely one of the profs in a math department with a PhD program has a copy (or at minimum the library.) And there's always copies on Alibris.
And, seconding suggestions from other posters, Kittel and Kroemer's "Thermal Physics" is a good starting point on thermo, As for quantum, in the absence of all knowledge in the field I'd start with Tipler's "Modern Physics", with the goal of ramping up to Cohen-Tannoudji, Diu, and Laloe's "Quantum Mechanics".The material he is describing is what is covered in the undergrad PDE course. Its frequently given as both an undergrad course number and a graduate course number: same book, just more work for the grad level class.
not bitter (0)
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Anonymous Coward | more than 5 years ago
Not to sound bitter or anything, but you took a Ph.D. spot that a qualified student was rejected for.
The fact that you are even asking the question you asked, means you are nowhere near where you should be for *entry* into a Math Ph.D. program. It's a serious deficiency. not only to just be getting to PDE's, but to never have studied physics. How did you get a math undergrad without physics, and at what institution?
Physics/Astronomy Graduate student perspective (3, Informative)
Off the top of my head I would say...
Introduction to Partial Differential Equations Applications - E. C. Zachmanoglou & Thoe; mostly math already, but has applications.
For introduction to the wave equation try The Physics of Vibrations and Waves - Pain.
The Shrodinger equation is explained well in Quantum Mechanics - Griffiths.
Road to reality (4, Informative)
An excellent Physics book that is very math heavy but assumes no prereqs is Penrose's Road to Reality. This pretty much covers all of the main theory/formulas in cosmology, and he has 350 pages of math (much of it graduate level) to get there.
The Feynman Lectures on Physics (4, Informative)
I can not recommend these books enough. Feynman does a brilliant job of bringing the concepts of physics to life.
All together, they are quite extensive, but the individual topics are brief enough to digest in one sitting. Wether you only have a passing interest in physics, or a graduate degree in the field, you will find that there is much to appreciate in these lectures.
Even for those simply taking physics as requirement, I think that these would give you a real appreciation of the field, and probably make the classes a lot easier at that.
They're All Targeted for Mathematicians (5, Informative)
I've a couple of degrees in Physics, and I assure you, half the print in the _vast_ majority of Physics books is equations. Most physics texts seem to assume a math minor. Most Physics majors first see partial differential equations, special functions, and group theory as undergraduates. A couple of friends took partial diffeq for fun. Yeah, that's one way to know you're a nerd.
I suggest a library or a used bookstore, as these things are expensive. Here are some of the typical texts you see around on various physics topics (by author's name, because the titles are useless):
Electromagnetism:
Griffiths is a really great undergrad book, which is easy to read.
Jackson is the classic first semester grad-school book. Math Methods of Physics:
Arfken is a classic.
Cantrell is an up and coming variant. Thermodynamics:
Kittel is an oldie, but a goodie. Someone else prolly has a better suggestion. General Undergrad Phenomonology:
The World Wide Web - Invented at CERN, y'know.
Halliday & Resnic is probably the easiest book to find.
Serway is newer. Relativity:
Rindler is the standard. Mechanics:
Goldstein is pretty easy to find. Quantum:
Landau (yep, the same) and Lifshitz is a solid text that
hits on Shcrodinger's equation well.
Griffiths is easier to read, as is Eisberg & Resnick. Modern Physics:
Less of an obvious choice, but it'll be a good source for more sexy topics.
A lot of partial diffeq is used in mechanics. IIRC, partial diffeq was invented to describe mechanical systems, so many of the examples are very intuitive (for you of course, not for 99.9% of the population.)
i DO recommend an undergrad physics book... (1)
as a recently graduated engineering student, and having taken my share of advanced calc and physics, i would actually recommend an undergrad physics book geared towards engineers. this is probably the best place to start in understanding how the equations you mentioned apply...
Don't be an ass. Oops, sorry, too late... (2, Informative)
A 4- or 6-year degree in math or science should include both math and science. If not, you are NOT receiving the education you need to really understand your field. Regardless of how you feel, mathematics actually relates to (and is constrained by) our physical universe. If you do not understand that, then you are not well versed in either.
A degree in mathematics, from a responsible university, should include at least some physics. And of course a degree in physics requires a certain minimum of math, or you will not understand the subject.
What I was getting at is that it actually does work both ways. An understanding of our real world (physics), often constrains what real mathematicians do once they leave the university. You will not make it very far as an actuary, for example, if you do not understand at least the basic physics of what happens when someone experiences an automobile crash or a myocardial infarction.
Psychology adds to a broad education, but that is not even remotely related to what I was saying. Nor philosophy, nor accounting. I was not suggesting a educational free-for-all, just that physics and mathematics often go hand-in-hand.
I would not require it, but I do believe that it would benefit most people if they did have at least a little of each. I have. More than a little, actually.
But all that aside: math and physics are closely related "hard sciences". Philosophy, psychology, and accounting (we might as well include sociology and art history here), are all valuable education (at least I think they are), but they are NOT hard sciences, nor are they related to the subject at hand. In future, please stick to the matter under discussion.
a few suggestions... (1)
Since you want intuition, an introductory undergrad book might actually be a good idea. Higher level books will often assume you have seen the subject before.
Quantum Chemistry by McQuarrie is a good first book for quantum mechanics and the Schrodinger equation. Dirac's book is more advanced but also good (much harder to read). Much different focus though.
For electricity and magnetism a good first book is Griffiths Introduction to Electrodynamics. Here you'll see applications of the Poisson and Wave equations. Jackson is the classical "second" course textbook. (Upper level undergrad, beginning grad).
A good introduction to applications of the diffusion (i.e. heat) equation is Random Walks in Biology by Howard Berg. One benefit is that it is a very short book too!
For nonlinear equations there are too many references to know where to begin... There are millions of books on just the Navier-Stokes equations... Generally I'd just poke around Amazon and browse some of the books with good reviews.
Anyways if the original poster wants references for a specific PDE or area of physics please post a followup...
Mathematical Methods for Engineers and Scientists (0)
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Anonymous Coward | more than 5 years ago
There are three of them is the series and it is a little pricy but I have never seen anything explained this well. The author K.T. Tang has a constant named after him, an equation and an office at the Max Plank institute. He teaches at a small liberal arts school in tacoma, washington. I don't know why. But I was lucky enough to be given print offs of the book, for his class, before it was published.
Not to bring you down or anything, but.... (0, Flamebait)
I have not yet finished college.. forced to take night classes, and have no where near as much campus time/experience as you and many others have, but it only took me about... oh, 20 seconds to Google for some good sites, and has links to pretty much all you mentioned. The links there point to other links for further reading. Note that in the reference section of wikipedia articles are links or information to books and such. I believe they're called citations. (citation needed)
As a third-year PhD math student.....
I'd think you would already have tried Google or Wikipedia. Your browser should have them on speed dial. So, really, what is your question?
Re:Not to bring you down or anything, but.... (0)
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Anonymous Coward | more than 5 years ago
Do you have any idea how many books there are out there? We need guidance from people in the know as to which ones are the most suitable for us. This person's question was legitimate. Googling `Partial Differential Equations' is not the answer.
I'm sorry but, WHAT? (1)
What do you mean you are a third year PHD candidate in mathematics and you are only now taking PDE!? I took that sophomore year in my undergraduate engineering program, before we got into any of the serious engineering classes. If I remember correctly, it was the same time as we studied relativity in physics. What have you been doing all this time...
Vector Analysis (2, Insightful)
is where to start when it comes to deriving PDEs. The heat equation and the wave equation fall easily out of vector analysis, as do a number of other familiar PDEs. I'd start with a vector analysis book.
3rd year Math PHD and only NOW learnin Partial Dif (1)
My god, I had to learn that crap as a freshman UNDERGRAD!!! Now grant it I was an electrical/computer engineering major at the time, but still, I can't believe that a third year math PHD candidate would not have had partial diffs... I mean, seriously, it is the only way to do some stuff, especially anything in the real world (hence all the physics basis on the questions).
Re:3rd year Math PHD and only NOW learnin Partial (1)
The difference between engineering and math is that engineering focusses on real-world problems and the bit of math required to solve them. Because there are too many other things to learn - and engineering centers on practical applications. A lot of math appears to be intellectual masturbation unless you have proper training - and lacks any trivial practical application. Until suddenly, someone might find use for it to describe something in physics. Or not. A lot of the riddles you solve as a geek are applied math. Think topology. Why would an engineer have to bother with abstract algebra? Or why should he be able to derive about everything in math from aimple set of axioms?:)
Engineers don't know math. Much.
(Disclaimer: Here speaks a CS guy who used to date a lovely Math PHD. And I thought MY mind was warped...)
Anonymous Coward | more than 5 years ago
Another good supplement is The Variational Principles of Mechanics by Cornelius Lanczos of functional analysis fame (
However, you will also want something on thermal physics and I have no awesome suggestions for that. But in classical mechanics you should get a lot of nice PDEs (such as the wave equation) which will be covered by the sources I mention. In electrodynamics you will get Laplace's equation (which will also show up in gravitation in classical mechanics). There are no really good books on QM that have been published, so I would just not worry about getting the physics behind the SchrÃdinger equation.
thermodynamics (1)
The wave equation and diffusion equation are technically partial differential equations because of the 3 space dimensions and time, but these are simple PDEs because the three space dimensions are basically the same and the derivatives usually only appear as the Del operator, which treats each direction equally, and the boundary conditions are usually such that the constant of integration is just zero.
In thermodynamics, you actually have serious PDEs which involve variables that aren't all the same, and the constant of integration must be found by matching arbitrary functions to each other and boundary conditions.
This probably isn't a book for someone new to physics, but it does use some PDEs.
Good PDE book with relations to Physics (1)
I am currently taking a pde course as an undergrad and am using Partial Differential Equations: An Introduction by Walter A. Strauss. While this book does have some faults it does an excellent job of relating pdes to their physical interpretation.
To all the people suggesting Griffiths QM.... (0)
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Anonymous Coward | more than 5 years ago
That book is terrible. He should have stopped after his masterpiece on Electrodynamics. Griffiths will simply not have enough math. To reiterate, Griffiths Quantum Mechanics book is bad, his Electrodynamics book is genius.
road to reality (1)
I can recommend "The road to reality - a complete guide to the laws of the universe" by Roger Penrose. The guy undoubtedly knows what he's talking about (being a famous physician himself) and the book is very math-centric. First the mathematical concepts are explained, then based on that the physics of our universe.
Anonymous Coward | more than 5 years ago
learning by applying (1)
I hope some math professors are reading this. They always seemed to think that they only needed to teach the "how", as "why" would already be obvious or would become clear. It didn't, not for me. More like that was the excuse, because actually "how" alone was much easier to teach. I studied PDEs in calculus classes, but never used them for anything. When they did come up with example uses, they were pretty contrived, and often could be solved with plain old algebra. Or they were so small that hand application of numerical methods could pin down the answer. Took only a few iterations of the Bisection method to get that zero, or you'd hack up a quick and dirty program to push some data into a linear algebra library function and get back results, something like that. And what's a student to think on hearing that although faster, Newton's Method, which is based on calculus, isn't as reliable as Bisection, which is simple algebra. Not good examples when trying to show students how useful and valuable calculus is.
Books? There's more than books alone out there. Lots of material on the web. Lots of combined material. Here are some books associated with Sage. Are you making use of mathematical software: Sage, Matlab, Mathematica, Maple, or some such? Or are you at least able to code up something in a general purpose language if needed? Much math is to the point where you can't advance without computers. Maybe I'm a bit behind. These days, I suppose all math students use such software.
I've noticed also that people with backgrounds in pure math don't have a good basic understanding of Computer Science. You know all about Fourier Transforms, you've heard of the Fast Fourier Transform, you've heard of big O, but you don't see what the big deal is about the FFT-- to you FFT is just one of many ways to do a Fourier Transform, one specific to computers which a person would not use if working out such a transform on paper. Do you have an appreciation of the algorithmic complexities of the math problems you are encountering? The way multiplication is done in grade school is just fine for relatively few small numbers, but when you want to do millions of multiplications of large numbers (1000 digits, say), you'd better use a computer, and you'd better program the computer to use FFT. A textbook on Numerical Methods could be worth checking out.
E&M (0)
Anonymous Coward | more than 5 years ago
If you're curious about E&M, I suggest you look at Purcell's "Electricity and Magnetism". The book starts at a basic level (physics-wise, not math-wise) and works its way up.
You start with monopoles, derive the field from the inverse square law, move onto lines and sheets of charge, then dipoles, voltage & current, electronic circuits (resistors, capacitors, inductors, DC, AC, calculating V and I with diff eq, etc.).
Then you combine special relativity with the electric field and get...magnetism! Next you go through dipoles, electromagnetic radiation, induction, derive Maxwell's equations from scratch, and learn about how E&M fields interact with matter at the atomic through macroscopic scales.
The problems aren't your standard "Find X given Y using equation 5" problems. These actually make you think. Some examples off the top of my head: -Find a resistor equivalent to an infinite repeating pattern of small resistors -Prove that no magnetic field surrounds a torroidal electromagnet using Gauss's law -Calculate the capacitance of two concentric hollow spheres
500 pages of physics and math. If you can understand half of it, you'll be well grounded. (No pun intended.)
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Introduction to Bessel Functions
Introduction to Bessel Functions
A full, clear introduction to the properties and applications of Bessel functions, this self-contained text is equally useful for the classroom or for independent study. Topics include Bessel functions of zero order, modified Bessel functions, definite integrals, asymptotic expansions, and Bessel functions of any real order. More than 200 problems throughout.
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theor... read more
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General Topology by Stephen Willard Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.
The Laplace Transform by David V. Widder This volume focuses on the Laplace and Stieltjes transforms, offering a highly theoretical treatment. Topics include fundamental formulas, the moment problem, monotonic functions, and Tauberian theorems. 1941 edition.
Complex Analysis with Applications by Richard A. Silverman The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.
Foundations of Modern Analysis by Avner Friedman Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Detailed analyses. Problems. Bibliography. Index.
Undergraduate Topology by Robert H. Kasriel This introductory treatment is essentially self-contained and features explanations and proofs that relate to every practical aspect of point set topology. Hundreds of exercises appear throughout the text. 1971 edition.
Point Set Topology by Steven A. Gaal Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.
Introduction to Topology: Third Edition by Bert Mendelson Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.
Product Description:
theorems and counter examples, provides a valuable reference. From explorations of topological space, convergence, and separation axioms, the text proceeds to considerations of sup and weak topologies, products and quotients, compactness and compactification, and complete semimetric space. The concluding chapters explore metrization, topological groups, and function spaces. Each subject area is supplemented with examples, problems, and exercises that progress to increasingly rigorous levels. All examples and problems are classified as essential, optional, and advanced.
Reprint of the Ginn and Company, Waltham, Massachusetts, 1970
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Alg linear appsDocument Transcript
PrefaceHere are my online notes for my Algebra course that I teach here at Lamar University, although Ihave to admit that it's been years since I last taught this course. At this point in my career Imostly teach Calculus and Differential Equations.Despite the fact that these are my "class notes", they should be accessible to anyone wanting tolearn Algebra or needing a refresher for algebra. I've tried to make the notes as self contained aspossible and do not reference any book. However, they do assume that you've had someexposure to the basics of algebra at some point prior to this. While there is some review ofexponents, factoring and graphing it is assumed that not a lot of review will be needed to remindyou how these topics work.Here are a couple of warnings to my students who may be here to get a copy of what happened ona day that you missed.1. Because I wanted to make this a fairly complete set of notes for anyone wanting to learnalgebra I have included some material that I do not usually have time to cover in classand because this changes from semester to semester it is not noted here. You will need tofind one of your fellow class mates to see if there is something in these notes that wasn'tcovered in class.2. Because I want these notes to provide some more examples for you to read through, Idon't always work the same problems in class as those given in the notes. Likewise, evenif I do work some of the problems in here I may work fewer problems in class than arepresented here.3. Sometimes questions in class will lead down paths that are not covered here. I try toanticipate as many of the questions as possible in writing these up, but the reality is that Ican't anticipate all the questions. Sometimes a very good question gets asked in classthat leads to insights that I've not included here. You should always talk to someone whowas in class on the day you missed and compare these notes to their notes and see whatthe differences are.4. This is somewhat related to the previous three items, but is important enough to merit itsown item. THESE NOTES ARE NOT A SUBSTITUTE FOR ATTENDING CLASS!!Using these notes as a substitute for class is liable to get you in trouble. As already notednot everything in these notes is covered in class and often material or insights not in thesenotes is covered in class.
Application of Linear EquationsWe now need to discuss the section that most students hate. We need to talk about applications tolinear equations. Or, put in other words, we will now start looking at story problems or wordproblems. Throughout history students have hated these. It is my belief however that the mainreason for this is that students really don't know how to work them. Once you understand how towork them, you'll probably find that they aren't as bad as they may seem on occasion. So, we'llstart this section off with a process for working applications.Process for Working Story/Word Problems1. READ THE PROBLEM.2. READ THE PROBLEM AGAIN. Okay, this may be a little bit of overkill here.However, the point of these first two steps is that you must read the problem. This step isthe MOST important step, but it is also the step that most people don't do properly.You need to read the problem very carefully and as many times as it takes. You are onlydone with this step when you have completely understood what the problem is asking youto do. This includes identifying all the given information and identifying what you beingasked to find.Again, it can't be stressed enough that you've got to carefully read the problem.Sometimes a single word can completely change how the problem is worked. If you justskim the problem you may well miss that very important word.3. Represent one of the unknown quantities with a variable and try to relate all the otherunknown quantities (if there are any of course) to this variable.4. If applicable, sketch a figure illustrating the situation. This may seem like a silly step,but it can be incredibly helpful with the next step on occasion.5. Form an equation that will relate known quantities to the unknown quantities. To do thismake use of known formulas and often the figure sketched in the previous step can beused to determine the equation.6. Solve the equation formed in the previous step and write down the answer to all thequestions. It is important to answer all the questions that you were asked. Often you willbe asked for several quantities in the answer and the equation will only give one of them.7. Check your answer. Do this by plugging into the equation, but also use intuition to makesure that the answer makes sense. Mistakes can often be identified by acknowledgingthat the answer just doesn't make sense.Let's start things off with a couple of fairly basic examples to illustrate the process. Note as wellthat at this point it is assumed that you are capable of solving fairly simple linear equations and sonot a lot of detail will be given for the actual solution stage. The point of this section is more onthe set up of the equation than the solving of the equation.
Example 1 In a certain Algebra class there is a total of 350 possible points. These points comefrom 5 homework sets that are worth 10 points each and 3 hour exams that are worth 100 pointseach. A student has received homework scores of 4, 8, 7, 7, and 9 and the first two exam scoresare 78 and 83. Assuming that grades are assigned according to the standard scale and there are noweights assigned to any of the grades is it possible for the student to receive an A in the class andif so what is the minimum score on the third exam that will give an A? What about a B?SolutionOkay, let's start off by defining p to be the minimum required score on the third exam.Now, let's recall how grades are set. Since there are no weights or anything on the grades, thegrade will be set by first computing the following percentage.actual pointsgrade percentagetotal possible points=Since we are using the standard scale if the grade percentage is 0.9 or higher the student will getan A. Likewise if the grade percentage is between 0.8 and 0.9 the student will get a B.We know that the total possible points is 350 and the student has a total points (including the thirdexam) of,4 8 7 7 9 78 83 196p p+ + + + + + + = +The smallest possible percentage for an A is 0.9 and so if p is the minimum required score on thethird exam for an A we will have the following equation.1960.9350p+=This is a linear equation that we will need to solve for p.( )196 0.9 350 315 315 196 119p p+ = = Þ = - =So, the minimum required score on the third exam is 119. This is a problem since the exam isworth only 100 points. In other words, the student will not be getting an A in the Algebra class.Now let's check if the student will get a B. In this case the minimum percentage is 0.8. So, tofind the minimum required score on the third exam for a B we will need to solve,1960.8350p+=Solving this for p gives,( )196 0.8 350 280 280 196 84p p+ = = Þ = - =So, it is possible for the student to get a B in the class. All that the student will need to do is getat least an 84 on the third exam.
Example 2 We want to build a set of shelves. The width of the set of shelves needs to be 4times the height of the set of selves and the set of shelves must have three shelves in it. If thereare 72 feet of wood to use to build the set of shelves what should the dimensions of the set ofshelves be?SolutionWe will first define x to be the height of the set of shelves. This means that 4x is width of the setof shelves. In this case we definitely need to sketch a figure so we can correctly set up theequation. Here it is,Now we know that there are 72 feet of wood to be used and we will assume that all of it will beused. So, we can set up the following word equation.length of length of72vertical pieces horizontal piecesæ ö æ ö+ =ç ÷ ç ÷è ø è øIt is often a good idea to first put the equation in words before actually writing down the equationas we did here. At this point, we can see from the figure there are two vertical pieces; each onehas a length of x. Also, there are 4 horizontal pieces, each with a length of 4x. So, the equation isthen,( ) ( )4 4 2 7216 2 7218 724x xx xxx+ =+ ===So, it looks like the height of the set of shelves should be 4 feet. Note however that we haven'tactually answered the question however. The problem asked us to find the dimensions. Thismeans that we also need the width of the set of shelves. The width is 4(4)=16 feet. So thedimensions will need to be 4x16 feet.Pricing ProblemsThe next couple of problems deal with some basic principles of pricing.Example 3 A calculator has been marked up 15% and is being sold for $78.50. How much didthe store pay the manufacturer of the calculator?SolutionFirst, let's define p to be the cost that the store paid for the calculator. The stores markup on thecalculator is 15%. This means that 0.15p has been added on to the original price (p) to get theamount the calculator is being sold for. In other words, we have the following equation0.15 78.50p p+ =
that we need to solve for p. Doing this gives,78.501.15 78.50 68.260871.15p p= Þ = =The store paid $68.26 for the calculator. Note that since we are dealing with money we roundedthe answer down to two decimal places.Example 4 A shirt is on sale for $15.00 and has been marked down 35%. How much was theshirt being sold for before the sale?SolutionThis problem is pretty much the opposite of the previous example. Let's start with defining p tobe the price of the shirt before the sale. It has been marked down by 35%. This means that 0.35phas been subtracted off from the original price. Therefore, the equation (and solution) is,0.35 15.000.65 15.0015.0023.07690.65p ppp- === =So, with rounding it looks like the shirt was originally sold for $23.08.Distance/Rate ProblemsThese are some of the standard problems that most people think about when they think aboutAlgebra word problems. The standard formula that we will be using here isDistance Rate Time= ´All of the problems that we'll be doing in this set of examples will use this to one degree oranother and often more than once as we will see.Example 5 Two cars are 500 miles apart and moving directly towards each other. One car ismoving at a speed of 100 mph and the other is moving at 70 mph. Assuming that the cars startmoving at the same time how long does it take for the two cars to meet?SolutionLet's let t represent the amount of time that the cars are traveling before they meet. Now, weneed to sketch a figure for this one. This figure will help us to write down the equation that we'llneed to solve.From this figure we can see that the Distance Car A travels plus the Distance Car B travels mustequal the total distance separating the two cars, 500 miles.
Here is the word equation for this problem in two separate forms.Distance Distance500of Car A of Car BRate of Time of Rate of Time of500Car A Car A Car B Car B used the standard formula here twice, once for each car. We know that the distance a cartravels is the rate of the car times the time traveled by the car. In this case we know that Car Atravels at 100 mph for t hours and that Car B travels at 70 mph for t hours as well. Plugging theseinto the word equation and solving gives us,100 70 500170 5005002.941176 hrs170t ttt+ === =So, they will travel for approximately 2.94 hours before meeting.Example 6 Repeat the previous example except this time assume that the faster car will start 1hour after slower car starts.SolutionFor this problem we are going to need to be careful with the time traveled by each car. Let's let tbe the amount of time that the slower travel car travels. Now, since the faster car starts out 1 hourafter the slower car it will only travel for 1t - hours.Now, since we are repeating the problem from above the figure and word equation will remainidentical and so we won't bother repeating them here. The only difference is what we substitutefor the time traveled for the faster car. Instead of t as we used in the previous example we willuse 1t - since it travels for one hour less that the slower car.Here is the equation and solution for this example.( )100 1 70 500100 100 70 500170 6006003.529412 hrs170t tt ttt- + =- + === =In this case the slower car will travel for 3.53 hours before meeting while the faster car will travelfor 2.53 hrs (1 hour less than the faster car…).
Example 7 Two boats start out 100 miles apart and start moving to the right at the same time.The boat on the left is moving at twice the speed as the boat on the right. Five hours after startingthe boat on the left catches up with the boat on the right. How fast was each boat moving?SolutionLet's start off by letting r be the speed of the boat on the right (the slower boat). This means thatthe boat to the left (the faster boat) is moving at a speed of 2r. Here is the figure for this situation.From the figure it looks like we've got the following word equation.Distance Distance100of Boat B of Boat Aæ ö æ ö+ =ç ÷ ç ÷è ø è øUpon plugging in the standard formula for the distance gives,Rate of Time of Rate of Time of100Boat B Boat B Boat A Boat Aæ öæ ö æ öæ ö+ =ç ÷ç ÷ ç ÷ç ÷è øè ø è øè øFor this problem we know that the time each is 5 hours and we know that the rate of Boat A is 2rand the rate of Boat B is r. Plugging these into the work equation and solving gives,( )( ) ( )( )100 5 2 5100 5 10100 520r rr rrr+ =+ ===So, the slower boat is moving at 20 mph and the faster boat is moving at 40 mpg (twice as fast).Work/Rate ProblemsThese problems are actually variants of the Distance/Rate problems that we just got doneworking. The standard equation that will be needed for these problems is,Portion of job Work Time Spentdone in given time Rate Workingæ ö æ ö æ ö= ´ç ÷ ç ÷ ç ÷è ø è ø è øAs you can see this formula is very similar to the formula we used above.
Example 8 An office has two envelope stuffing machines. Machine A can stuff a batch ofenvelopes in 5 hours, while Machine B can stuff a batch of envelopes in 3 hours. How longwould it take the two machines working together to stuff a batch of envelopes?SolutionLet t be the time that it takes both machines, working together, to stuff a batch of envelopes. Theword equation for this problem is,Portion of job Portion of job1 Jobdone by Machine A done by Machine BWork Rate Time Spent Work Rate Time Spent1of Machine A Working of Machine B know that the time spent working is t however we don't know the work rate of each machine.To get these we'll need to use the initial information given about how long it takes each machineto do the job individually. We can use the following equation to get these rates.Work Time Spent1 JobRate Workingæ ö æ ö= ´ç ÷ ç ÷è ø è øLet's start with Machine A.( ) ( )11 Job Work Rate of A 5 Work Rate of A5= ´ Þ =Now, Machine B.( ) ( )11 Job Work Rate of B 3 Work Rate of B3= ´ Þ =Plugging these quantities into the main equation above gives the following equation that we needto solve.1 11 Multiplying both sides by 155 33 5 158 15151.875 hours8t tt ttt+ =+ === =So, it looks like it will take the two machines, working together, 1.875 hours to stuff a batch ofenvelopes.Example 9 Mary can clean an office complex in 5 hours. Working together John and Mary canclean the office complex in 3.5 hours. How long would it take John to clean the office complexby himself?SolutionLet t be the amount of time it would take John to clean the office complex by himself. The basicword equation for this problem is,
Portion of job Portion of job1 Jobdone by Mary done by JohnWork Rate Time Spent Work Rate Time Spent1of Mary Working of JohnThis time we know that the time spent working together is 3.5 hours. We now need to find thework rates for each person. We'll start with Mary.( ) ( )11 Job Work Rate of Mary 5 Work Rate of Mary5= ´ Þ =Now we'll find the work rate of John. Notice however, that since we don't know how long it willtake him to do the job by himself we aren't going to be able to get a single number for this. Thatis not a problem as we'll see in a second.( ) ( )11 Job Work Rate of John Work Rate of Johntt= ´ Þ =Notice that we've managed to get the work rate of John in terms of the time it would take him todo the job himself. This means that once we solve the equation above we'll have the answer thatwe want. So, let's plug into the work equation and solve for the time it would take John to do thejob by himself.( ) ( )( )( )1 13.5 3.5 1 Multiplying both sides by 553.5 3.5 5 517.5 1.517.511.67 hrs1.5ttt ttt t+ =+ === Þ =So, it looks like it would take John 11.67 hours to clean the complex by himself.Mixing ProblemsThis is the final type of problems that we'll be looking at in this section. We are going to belooking at mixing solutions of different percentages to get a new percentage. The solution willconsist of a secondary liquid mixed in with water. The secondary liquid can be alcohol or acidfor instance.The standard equation that we'll use here will be the following.Amount of secondary Percentage of Volume ofliquid in the water Solution Solutionæ ö æ ö æ ö= ´ç ÷ ç ÷ ç ÷è ø è ø è øNote as well that the percentage needs to be a decimal. So if we have an 80% solution we willneed to use 0.80.
Example 10 How much of a 50% alcohol solution should we mix with 10 gallons of a 35%solution to get a 40% solution?SolutionOkay, let x be the amount of 50% solution that we need. This means that there will be 10x +gallons of the 40% solution once we're done mixing the two.Here is the basic work equation for this problem.( ) ( ) ( )Amount of alcohol Amount of alcohol Amount of alcoholin 50% Solution in 35% Solution in 40% SolutionVolume of Volume of Volume of0.5 0.35 0.450% Solution 35% Solution 40% Soæ ö æ ö æ ö+ =ç ÷ ç ÷ ç ÷è ø è ø è øæ ö æ ö+ =ç ÷ ç ÷è ø è ø lutionæ öç ÷è øNow, plug in the volumes and solve for x.( ) ( )0.5 0.35 10 0.4 100.5 3.5 0.4 40.1 0.50.55gallons0.1x xx xxx+ = ++ = +== =So, we need 5 gallons of the 50% solution to get a 40% solution.Example 11 We have a 40% acid solution and we want 75 liters of a 15% acid solution. Howmuch water should we put into the 40% solution to do this?SolutionLet x be the amount of water we need to add to the 40% solution. Now, we also don't how muchof the 40% solution we'll need. However, since we know the final volume (75 liters) we willknow that we will need 75 x- liters of the 40% solution.Here is the word equation for this problem.Amount of acid Amount of acid Amount of acidin the water in 40% Solution in 15% Solutionæ ö æ ö æ ö+ =ç ÷ ç ÷ ç ÷è ø è ø è øNotice that in the first term we used the "Amount of acid in the water". This might look a littleweird to you because there shouldn't be any acid in the water. However, this is exactly what wewant. The basic equation tells us to look at how much of the secondary liquid is in the water. So,this is the correct wording. When we plug in the percentages and volumes we will think of thewater as a 0% percent solution since that is in fact what it is. So, the new word equation is,( ) ( ) ( )Volume Volume of Volume of0 0.4 0.15of Water 40% Solution 15% Solutionæ ö æ ö æ ö+ =ç ÷ ç ÷ ç ÷è ø è ø è ø
Do not get excited about the zero in the first term. This is okay and will not be a problem. Let'snow plug in the volumes and solve for x.( )( ) ( )( ) ( )( )0 0.4 75 0.15 7530 0.4 11.2518.75 0.418.7546.875 liters0.4x xxxx+ - =- === =So, we need to add in 46.875 liters of water to 28.125 liters of a 40% solution to get 75 liters of a15% solution.
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Calculus for the Utterly Confused - 2nd edition
Summary: Whether you're a science major, an engineer, or a business graduate, calculus can be one of the most intimidating subjects around. Fortunately, Calculus for the Utterly Confused is your formula for success. Written by two experienced teachers who have taken the complexity out of calculus for thousands of students, this book breaks down tough concepts into easy-to-understand chunks.
Calculus for the Utterly Confused shows you how to apply calculus concepts to p...show moreroblems in business, medicine, sociology, physics, and environmental science. You'll get on the road to higher grades and greater confidence, and go from utterly confused to totally prepared in no time!
Inside, you'll learn about
Calculus problems with applications to business and economics
How to use spreadsheets for business analysis
Growth and decay models including exponential and logarithmic models for biology
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Students in need of experience constructing and interpreting statistical graphs will find this exercise useful. The lesson uses data from past presidential elections; students will construct a variety of graphs (bar...
This online course includes elements from an undergraduate seminar on mathematical problem solving. The material will help students develop their mathematical and problem solving skills. A few topics that are covered...
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Algebra Glencoe Lesson BIGIDEA: NUMBERS, OPERATIONS AND EXPRESSIONS Students work with integer exponents, scientific notation, and radicals, and use variables and expressions to solve problems from purely mathematical as well as applied contexts.
Algebra: BIGIDEA2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals. Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties.
BigIdea: The place values to the right of the decimal point in the base-ten system names numbers less than one. EQ: ... MG 2.1* MG 2.2* Algebra and Functions ⅔** AF 2.1* prescription for determining a second number when a first number is given.
BigIdea2: Develop an understanding of and use formulas to determine surface areas and volumes of three-dimensional shapes. ... Supporting Idea: Algebra Supporting Idea: Geometry and Measurement Supporting Idea: Number and Operations
Hear about the big ideas behind this book. Do several key activities: fractions ... that remove the abstraction from algebra and give it meaning. Topics will be from algebra 1& 2, trigonometry, & pre-calculus. Modeling With Geometry and the 8 Mathematical ... A Unifying Idea = The Equal Sign
... with their college and career goals for 5 years as part of a non-profit program she developed called, TeenSpace. The idea to ... Carol previously taught Algebra2, ... Big Brothers Big Sisters of Athens County, OUCTM, and the National Hands on Network. Scanlon, Rick (540)720-4100 Math ...
Participants will consider the alternative energy as a means for exploration and the math concepts that such an idea will entail. ... Developing Big Ideas in Algebra thru ... We have examples for use in Algebra 1 & 2, geometry, and Calculus that we have copied ...
... for GOAL SETTING purposes and represent a suggestion of how long it should take students to acquire a specific content idea or ... using inspection, long division, or a computer algebra system for more complex ... · Major understandings are the big generalizations for the topic ...
GLE captures the bigidea (conceptual understanding) of magnitude of numbers. CCSS is ... a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a ... -- Use appropriate representations to solve problems or to portray, clarify, or extend a mathematical idea.
JASPER PRE-ALGEBRA WORKING SMART X All 3 episodes help students see the power of ... A CAPITAL IDEA ACI involves a sample within a ... It involves discover a mutual interest in finding a way to 2 sampling methods and 1 extrapolation to the carry on funding for the 9th grade school trip to
But perhaps the most provocative idea is the proposal for adopting rule 137, ... NCAA football ratings determine which schools get to play for the big money in postseason bowl games. ... Progress in Commutative Algebra2 : ...
... take the DSAT Exam and look over the CST "Released Questions" prior to planning your lessons so that you have a good idea of the level of teaching that needs to be ... How Big is 1 Million? 8A 12A 16A Expanded Notation 18A ... ALGEBRA & FUNCTIONS AF1.2...Expressions with Parenthesis ...
... How Big is 1,000? Problem Solving: Number ... take the DSAT Exam and look over the CST "Released Questions" prior to planning your lessons so that you have a good idea of the level of teaching that needs ... ALGEBRA & FUNCTIONS...CLUSTER 3 NUMBER SENSE... CLUSTER 2 NUMBER SENSE ...
This session will focus on meaningful algebra activities that are concrete ... lesson, including the NJ Standards, will be discussed. See an idea today - use it in your ... This session will focus on a curriculum organized around the "big ideas" of Algebra and help your students ...
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self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities. less
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This Student Reference Book can be used to look up and review topics in mathematics. It has the following sections: 1) A Table of Contents that lists the sections and shows how the book is organized. 2) Essays within each section. 3) Directions on how to play some of the mathematical games you may have played before. 4) A Data Bank with posters, maps, and other information. 5) A Glossary of mathematical terms. 6) An Answer Key and 7) An Index to help you locate information quickly.
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Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
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The most helpful favorable review
The most helpful critical review
23 of 23 people found the following review helpful
5.0 out of 5 starsPhenomenal resource for math competition coaches and students...
3.0 out of 5 starsSomewhat Disappointed...
would find in a Math Counts or AMC contest. You will learn some new tricks (they were new to me at least) that helps solve problems much more quickly. I recommend it to new coaches who have caught the math competition bug but don't know where to get materials, or even experienced coaches who want another outstanding resource for their library. For someone still trying to learn all of the ins and outs of middle school math contests, this has vaulted into a spot as one of my go-to resources, along with the Art of Problem Solving series and old Math Counts problems.
This is an impressive collection of competition math problems that are explained very well! The book addresses multiple levels of ability and is a wonderful source of interesting mathematics. As a high school math coach of many years I can say that this book is NOT just for Middle School! It's a great high school math book. Math teachers everywhere need to be challenging students to think. "Competition Math for Middle School" is just what they need. I recommend this book to math teachers teaching everything from Algebra 1 to Calculus. Topics in the book include Number Theory, Geometry and Combinatorics. It's a treat!
We bought this for my son to help him study for the Math Counts competition - and just as a resource to supplement his math curriculum. He loved the book and found it VERY helpful. Would highly recommend it.
I use this book as a supplement to my daughter's school math. I like this book because it explains how simple mathematical concepts can be applied in competition level. This book provides with many practice questions that students can practice until they get familiar with similar questions. My daughter is smart but sometimes, can be scared of these competition math questions. This book is not too difficult that both average and smart students can learn from it. The explanation is simple but comprehensive. This book is not filled with those arrogant questions that can make kids feel defeatism in math. I gave the questions in the probability section to my daughter after she learned probability at the school. She learned how school math can be expanded and applied to the competition level from this book. Not all kids who are interested in math are genius. This book is for those students. I highly recommend this book.
I'm doing Mathcounts in my school, and wanted some resources to help me perform better in the chapter and state competitions. I was on and online course at artofproblemsolving.com for advanced Mathcounts/AMC 8, and in the previous years I had taken a course on Johns Hopkins CTY. I bought this book on Artofproblemsolving.com because it was meant for contest "mathletes" like me. Instantly, I focused areas on my weak sections of math, like probability/counting, and geometry. I reviewed the probability section for a few days and in what seems like an instant, it became my best subject. This book teaches the reader through the concepts first, with a few worked examples, then lets you do it on your own. The problems are challenging, fun, and serve as an excellent resource for sharpening skills on weak areas. Now, I'm working on the geometry section. Also, this book shows slick methods for hard problems, like "How many different rectangles can be formed on an 8x8 chessboard?" Overall, I think this is an excellent resource for one who is serious about competition math and wants to excel in competitions like mathcounts. A last thing I would recommend is that people who want to buy this book is that they should be somewhat confident that they will proceed to state mathcounts(or at least, have some experience).
have learnt not to spend too much time on certain problems or sections that are not properly sized.
I am in my Math Counts team in Middle School and this was a great book. It talked about a lot of interesting math-related topics. All of my team mates had gotten this book, so I decided to buy it too and it was a good decision. I will recommend this book to everyone who needs some math competition help in middle school.
This is a very good book for middle schoolers who are looking to learn more math and want to be challenged.
This is my son's first math book - other than his school text books. The concepts are taught by working through the example problems. The problems in the book are generally tougher and more advanced than the ones in the middle school text books. He finished the book this summer and he loved working through the problems on his own. Kids need to be challenged and taught to think on their own. This book helped him do that.
Love the book. Good examples and plenty of practice. We are not into competition Math. We only bought this book to challenge my son who is very good at Math, we use it as "daily challenge problem." The questions are not boring, explanations are very well worded. My son has a lot of fun with it. I suggest that you purchase this at Algebra level. We are doing pre-algebra, so it's still a bit hard, but manageable only because my son loves Math.
Apparently there is a 50 percent attrition rate for American students taking their first college calculus course. Considering that a lot of these students didn't get into these schools by being underqualified, what is the problem? Who are the ones who succeed?
It seems the absence of real mathematical problem solving as a regular feature of a middle school and high school curriculum is contributing to the problem mentioned. The reasons such programs are not common appear a mix of culture and politics and sadly it misleads students tremendously. Differently, experience with problem solving seems to contribute much to those who truly understand mathematics as an activity and consequently succeed in the undergraduate setting and beyond.
If one would like to fill this void somehow, Batterson's book is an excellent segway into higher mathematics. Maybe the title is a good marketing device, but a misnomer nonetheless -- it could be called a "Problem Solving Primer." Olympiad books require a great deal of sophistication that even a relatively successful undergraduate student might lack. Batterson, perhaps augmented with Polya, is the place to cut your teeth initially, and the transition beyond will seem more seemless.
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Elements of Partial Differential Equations [NOOK Book]
Overview
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory. Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems...
More About
This Book
Overview
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.
Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent study will particularly appreciate the worked examples that
| 677.169 | 1 |
Mathematics for Elementary Teachers: A Conceptual Approach
9780073519579
ISBN:
007351957X
Publisher: McGraw-Hill
Summary: Would you like to rent Mathematics for Elementary Teachers: A Conceptual Approach online from Valore Books now? If you would like to take advantage of discounted prices on pre-owned copies of this book published by McGraw-Hill, look at our selection now. Written by Albert B Bennett, Laurie J Burton and Leonard T Nelson, you can find the cheapest copies of this text book by using our site now. Buy Mathematics for Elem...entary Teachers: A Conceptual Approach online from us today and find out why so many people rent and buy books for college from us. Try our website now for the cheapest deals.
Bennett, Albert B. is the author of Mathematics for Elementary Teachers: A Conceptual Approach, published under ISBN 9780073519579 and 007351957X. Five hundred ninety four Mathematics for Elementary Teachers: A Conceptual Approach textbooks are available for sale on ValoreBooks.com, two hundred seventy one used from the cheapest price of $86.33, or buy new starting at $113 New Condition. SKU:9780071310024-1-0-15 Orders ship the same or next busin... [more].[less]
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A guide to concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. more...
Word problems are the most difficult part of any math course ?- and the most important to both the SATs and other standardized tests. This book teaches proven methods for analyzing and solving any type of math word problem. more...
Solving Word Problems for Life, Grades 6-8 offers students who struggle with math a daily opportunity to improve their skills. The book offers 180 math word problems. The first 30 focus on 6th-grade math standards, the second 30 on 7th-grade standards, and the last 30 on 8th-grade standards. There is also a section of more difficult, extra-credit problems... more...
As a result of the editors' collaborative teaching at Harvard in the late 1960s, they produced a ground-breaking work -- The Art Of Problem Posing -- which related problem posing strategies to the already popular activity of problem solving. It took the concept of problem posing and created strategies for engaging in that activity as a central theme... more...
The new edition of this classic book describes and provides a myriad of examples of the relationships between problem posing and problem solving, and explores the educational potential of integrating these two activities in classrooms at all levels. The Art of Problem Posing, Third Edition encourages readers to shift their thinking about problem... more...
Updated and expanded, this second edition satisfies the same philosophical objective as the first -- to show the importance of problem posing. Although interest in mathematical problem solving increased during the past decade, problem posing remained relatively ignored. The Art of Problem Posing draws attention to this equally important act and is... more...
Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source... more...
"Advances in Discrete Tomography and its Applications" is a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The self-contained survey chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge... more...
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Introduction to Real Analysis: An Educational Approach - 09 edition
Summary: Providing a lucid and accessible introduction to the field, Introduction to Real Analysis engages readers by beginning with an AP calculus focus, and then quickly moving to the more theoretical aspects of mathematical analysis topics. Exercises and examples throughout the book range in difficulty and are both proof oriented and computational skill-building problems. This thoroughly classroom-tested book is designed to be particularly accessible and clear for future teachers of second...show moreary mathematics as well as current teachers working towards a degree in mathematics education. ...show less
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The nation's first choice for an NSF reform high school mathematics series This new 2nd edition features a colorful lesson design; earlier development of algebraic topics; expanded use of technology; pre-requisite skills review in every lesson; Unit... (read more)
Tessellations--shapes repeated over and over to fill a plane without overlapping--have inspired beautiful art, from intricate tile work to M.C. Escher's playful graphics. Now, master origami artist Eric Gjerde has produced the same stunning kaleidoscopic... (read more)
The two volumes contain 65 chapters, which are based on talks presented by reputable researchers in the field at the Tenth International Conference on Integral Methods in Science and Engineering. The chapters address a wide variety of methodologies,
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This course is an introduction to algebraic and enumerative combinatorics. You will discover the beautiful interplay
between algebra and combinatorics, learning how to
apply algebraic techniques to solve enumeration problems, and how to use
combinatorial methods to solve questions arising in other areas of mathematics.
No prior knowledge of combinatorics is expected, but
some familiarity with linear algebra and group theory is preferable.
The homework will consist of a problem set roughly every two weeks.
Collaboration is permitted, but you are not allowed to copy someone else's
work. The solutions must be written individually. You have to mention on your
problem set the names of the students that you worked with, and also which
books or articles you used.
The final will be a take-home exam. You must work on the problems on your own. No
collaboration permitted in the exam.
The final project will consist of preparing a topic and presenting it in
class. Students can work in pairs. Here are possible topics
for the project.
Students with disabilities: Students with disabilities enrolled in this
course that may need disability-related classroom accommodations are encouraged
to make an office appointment to see me before the end of the second week of
the term. All discussions will remain confidential, although the Student
Accessibility Services office may be consulted to discuss appropriate implementation of any
accommodation requested.
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Barron's Dictionary of Mathematics Terms - 3rd edition
Summary: This quick-reference dictionary for math students, teachers, engineers, and statisticians defines more than 700 terms related to algebra, geometry, analytic geometry, trigonometry, probability, statistics, logic, and calculus. It also lists and defines mathematical symbols, includes a brief table of integrals, and describes how to derive key theorems. Filled with illustrative diagrams and equations
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TI 84/84+GuidebookDocument Transcript
TI-84 Plus and TI-84 Plus Silver Edition GuidebookNote: This guidebook for the TI-84 Plus or TI-84 Plus Silver Edition with operating system (OS)version 2.53MP. If your calculator has a previous OS version, your screens may look differentand some features may not be available. You can download the latest OS at education.ti.com.
Chapter 1:Operating the TI-84 Plus Silver EditionDocumentation ConventionsIn the body of this guidebook, TI-84 Plus refers to the TI-84 Plus Silver Edition. Sometimes, as inChapter 19, the full name TI-84 Plus Silver Edition is used to distinguish it from the TI-84 Plus.All the instructions and examples in this guidebook also work for the TI-84 Plus. All the functions ofthe TI-84 Plus Silver Edition and the TI-84 Plus are the same. The two graphing calculators differonly in available RAM memory, interchangeable faceplates, and Flash application ROM memory.Screen shots were taken using OS version 2.53MP in either MathPrint™ or Classic mode. Allfeatures are available in both modes; however, screens make look slightly different depending onthe mode setting. Many examples highlight features that are not available in previous OS versions.If your calculator does not have the latest OS, features may not be available and your screens maylook different. You can download the latest OS from education.ti.com.TI-84 Plus KeyboardGenerally, the keyboard is divided into these zones: graphing keys, editing keys, advancedfunction keys, and scientific calculator keys.Keyboard ZonesGraphing — Graphing keys access the interactive graphing features. The third function of thesekeys (t ^-a) displays the shortcut menus, which include templates for fractions, n/d,quick matrix entry, and some of the functions found on the MATH and VARS menus.Editing — Editing keys allow you to edit expressions and values.Advanced — Advanced function keys display menus that access the advanced functions.Scientific — Scientific calculator keys access the capabilities of a standard scientific calculator. Chapter 1: Operating the TI-84 Plus Silver Edition 1
TI-84 Plus Silver EditionGraphing KeysEditing KeysAdvancedFunction KeysScientificCalculator KeysUsing the Color.Coded KeyboardThe keys on the TI-84 Plus are color-coded to help you easily locate the key you need.The light colored keys are the number keys. The keys along the right side of the keyboard are thecommon math functions. The keys across the top set up and display graphs. The Œ key providesaccess to applications such as the Inequality Graphing, Transformation Graphing, Conic Graphing,Polynomial Root Finder and Simultaneous Equation Solver, and Catalog Help.The primary function of each key is printed on the keys. For example, when you press , theMATH menu is displayed.Using the y and ƒ KeysThe secondary function of each key is printed above the key. When you press the y key, thecharacter, abbreviation, or word printed above the other keys becomes active for the nextkeystroke. For example, when you press y and then , the TEST menu is displayed. Thisguidebook describes this keystroke combination as y :.Many keys also have a third function. These functions are printed above the keys in the samecolor as the ƒ key. The third functions enter alphabetic characters and special symbols aswell as access SOLVE and shortcut menus. For example, when you press ƒ and then ,the letter A is entered. This guidebook describes this keystroke combination as ƒ [A]. Chapter 1: Operating the TI-84 Plus Silver Edition 2
If you want to enter several alphabetic characters in a row, you can press y 7 to lock thealpha key in the On position and avoid having to press ƒ multiple times. Press ƒ asecond time to unlock it.Note: The flashing cursor changes to Ø when you press ƒ, even if you are accessing afunction or a menu. ƒ^-a Access shortcut y menus forAccesses the functionalitysecond function including templatesprinted above each for fractions, n/d,key. and other functions.ƒAccesses the thirdfunction printedabove each key.Turning On and Turning Off the TI-84 PlusTurning On the Graphing CalculatorTo turn on the TI-84 Plus, press É. An information screen displays reminding you that you canpress t ^ - a to display the shortcut menus. This message also displays when you resetRAM. To continue but not see this information screen again, press 1. To continue and see this information screen again the next time you turn on the TI-84 Plus, press 2.• If you previously had turned off the graphing calculator by pressing y M, the TI-84 Plus displays the home screen as it was when you last used it and clears any error. (The information screen displays first, unless you chose not to see it again.) If the home screen is blank, press } to scroll through the history of previous calculations.• If Automatic Power Down™ (APD™) had previously turned off the graphing calculator, the TI-84 Plus will return exactly as you left it, including the display, cursor, and any error. Chapter 1: Operating the TI-84 Plus Silver Edition 3
• If the TI-84 Plus is turned off and connected to another graphing calculator or personal computer, any communication activity will "wake up" the TI-84 Plus.To prolong the life of the batteries, APD™ turns off the TI-84 Plus automatically after about fiveminutes without any activity.Turning Off the Graphing CalculatorTo turn off the TI-84 Plus manually, press y M.• All settings and memory contents are retained by the Constant Memory™ function.• Any error condition is cleared.BatteriesThe TI-84 Plus uses five batteries: four AAA alkaline batteries and one button cell backup battery.The backup battery provides auxiliary power to retain memory while you replace the AAAbatteries. To replace batteries without losing any information stored in memory, follow the steps inAppendix C.Setting the Display ContrastAdjusting the Display ContrastYou can adjust the display contrast to suit your viewing angle and lighting conditions. As you changethe contrast setting, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates thecurrent level. You may not be able to see the number if contrast is too light or too dark.Note: The TI-84 Plus has 40 contrast settings, so each number 0 through 9 represents foursettings.The TI-84 Plus retains the contrast setting in memory when it is turned off.To adjust the contrast, follow these steps. Press y } to darken the screen one level at a time. Press y † to lighten the screen one level at a time.Note: If you adjust the contrast setting to 0, the display may become completely blank. To restorethe screen, press y } until the display reappears.When to Replace BatteriesWhen the batteries are low, a low-battery message is displayed when you turn on the graphingcalculator.To replace the batteries without losing any information in memory, follow the steps in Appendix C. Chapter 1: Operating the TI-84 Plus Silver Edition 4
Generally, the graphing calculator will continue to operate for one or two weeks after the low-battery message is first displayed. After this period, the TI-84 Plus will turn off automatically andthe unit will not operate. Batteries must be replaced. All memory should be retained.Note:• The operating period following the first low-battery message could be longer than two weeks if you use the graphing calculator infrequently.• Always replace batteries before attempting to install a new operating system.The DisplayTypes of DisplaysThe TI-84 Plus displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describeshow the TI-84 Plus can display a horizontally or vertically split screen to show graphs and textsimultaneously.Home ScreenThe home screen is the primary screen of the TI-84 Plus. On this screen, enter instructions toexecute and expressions to evaluate. The answers are displayed on the same screen. Mostcalculations are stored in the history on the home screen. You can press } and † to scroll throughthe history of entries on the home screen and you can paste the entries or answers to the currententry line.Displaying Entries and Answers• When text is displayed, the TI-84 Plus screen can display a maximum of 8 lines with a maximum of 16 characters per line in Classic mode. In MathPrint™ mode, fewer lines and fewer characters per line may be displayed.• If all lines of the display are full, text scrolls off the top of the display. - To view previous entries and answers, press }. - To copy a previous entry or answer and paste it to the current entry line, move the cursor to the entry or answer you want to copy and press Í. Note: List and matrix outputs cannot be copied. If you try to copy and paste a list or matrix output, the cursor returns to the input line.• If an expression on the home screen, the Y= editor (Chapter 3), or the program editor (Chapter 16) is longer than one line, it wraps to the beginning of the next line in Classic mode. In MathPrint™ mode, an expression on the home screen or Y= editor that is longer than one line scrolls off the screen to the right. An arrow on the right side of the screen indicates that you can scroll right to see more of the expression. In numeric editors such as the window screen (Chapter 3), a long expression scrolls to the right and left in both Classic and MathPrint™ modes. Press y ~ to move the cursor to the end of the line. Press y | to move the cursor to the beginning of the line. Chapter 1: Operating the TI-84 Plus Silver Edition 5
When an entry is executed on the home screen, the answer is displayed on the right side of thenext line. Entry AnswerThe mode settings control the way the TI-84 Plus interprets expressions and displays answers.If an answer, such as a list or matrix, is too long to display entirely on one line, an arrow(MathPrint™) or an ellipsis (Classic) is displayed to the right or left. Press ~ and | to display theanswer. MathPrint™ Classic Entry Entry Answer Answer Entry Entry Answer AnswerUsing Shortcut Menus t^ t_ t` ta Opens FRAC Opens FUNC Opens MTRX Opens YVAR menu. menu. menu. menu.Shortcut menus allow quick access to the following:• Templates to enter fractions and selected functions from the MATH MATH and MATH NUM menus as you would see them in a textbook. Functions include absolute value, summation, numeric differentiation, numeric integration, and log base n. Chapter 1: Operating the TI-84 Plus Silver Edition 6
• Matrix entry.• Names of function variables from the VARS Y-VARS menu.Initially, the menus are hidden. To open a menu, press t plus the F-key that corresponds tothe menu, that is, ^ for FRAC, _ for FUNC, ` for MTRX, or a for YVAR. To select a menuitem, either press the number corresponding to the item, or use the arrow keys to move the cursorto the appropriate line and then press Í.All shortcut menu items except matrix templates can also be selected using standard menus. Forexample, you can choose the summation template from three places:FUNC shortcut menuMATH MATH menuCatalogThe shortcut menus are available to use where input is allowed. If the calculator is in Classicmode, or if a screen is displayed that does not support MathPrint™ display, entries will bedisplayed in Classic display. The MTRX menu is only available in MathPrint™ mode on the homescreen and in the Y= editor.Note: Shortcut menus may not be available if t plus F-key combinations are used by anapplication that is running, such as Inequality Graphing or Transformation Graphing.Returning to the Home ScreenTo return to the home screen from any other screen, press y 5.Busy IndicatorWhen the TI-84 Plus is calculating or graphing, a vertical moving line is displayed as a busyindicator in the top-right corner of the screen. When you pause a graph or a program, the busyindicator becomes a vertical moving dotted line. Chapter 1: Operating the TI-84 Plus Silver Edition 7
Display CursorsIn most cases, the appearance of the cursor indicates what will happen when you press the nextkey or select the next menu item to be pasted as a character.Cursor Appearance Effect of Next KeystrokeEntry Solid rectangle A character is entered at the cursor; any existing $ character is overwrittenInsert Underline A character is inserted in front of the cursor __ locationSecond Reverse arrow A 2nd character is entered or a 2nd operation is Þ executedAlpha Reverse A An alpha character is entered, SOLVE is Ø executed, or shortcut menus are displayed.Full Checkerboard rectangle No entry; the maximum characters are entered at # a prompt or memory is fullMathPrint™ Right arrow The cursor moves to either the next part of the template or out of the template.If you press ƒ during an insertion, the cursor becomes an underlined A (A). If you press yduring an insertion, the underlined cursoSr becomes an underlined # (#).Note: If you highlight a small character such as a colon or a comma and then press ƒ or y,the cursor does not change because the cursor width is too narrow.Graphs and editors sometimes display additional cursors, which are described in other chapters.Interchangeable FaceplatesThe TI-84 Plus Silver Edition has interchangeable faceplates that let you customize theappearance of your unit. To purchase additional faceplates, refer to the TI Online Store ateducation.ti.com.Removing a Faceplate1. Lift the tab at the bottom edge of the faceplate away from the TI-84 Plus Silver Edition case.2. Carefully lift the faceplate away from the unit until it releases. Be careful not to damage the faceplate or the keyboard. Chapter 1: Operating the TI-84 Plus Silver Edition 8
Installing New Faceplates1. Align the top of the faceplate in the corresponding grooves of the TI-84 Plus Silver Edition case.2. Gently click the faceplate into place. Do not force.3. Make sure you gently press each of the grooves to ensure the faceplate is installed properly. See the diagram for proper groove placement.Using the ClockUse the clock to set the time and date, select the clock display format, and turn the clock on andoff. The clock is turned on by default and is accessed from the mode screen.Displaying the Clock Settings1. Press z.2. Press the † to move the cursor to SET CLOCK.3. Press Í.Changing the Clock Settings1. Press the ~ or | to highlight the date format you want. Press Í.2. Press † to highlight YEAR. Press ' and type the year.3. Press † to highlight MONTH. Press ' and type the number of the month (1-12).4. Press † to highlight DAY. Press ' and type the date.5. Press † to highlight TIME. Press ~ or | to highlight the time format you want. Press Í. Chapter 1: Operating the TI-84 Plus Silver Edition 9
6. Press † to highlight HOUR. Press ' and type the hour (a number from 1-12 or 0-23).7. Press † to highlight MINUTE. Press ' and type the minutes (a number from 0-59).8. Press † to highlight AM/PM. Press ~ or | to highlight the format. Press Í.9. To save changes, press † to highlight SAVE. Press Í.Error MessagesIf you type the wrong date for the month, for example,June 31 (June does not have 31 days), you willreceive an error message with two choices:• To quit the clock application and return to the home screen, select 1: Quit. — or —• To return to the clock application and correct the error, select 2: Goto.Turning the Clock OnThere are two options to turn the clock on. One option is through the MODE screen, the other isthrough the Catalog. Chapter 1: Operating the TI-84 Plus Silver Edition 10
Using the Mode Screen to turn the clock on1. If the clock is turned off, Press † to highlight TURN CLOCK ON.2. Press Í Í.Using the Catalog to turn the clock on1. If the clock is turned off, Press y N2. Press † or } to scroll the CATALOG until the selection cursor points to ClockOn.3. Press Í Í.Turning the Clock Off1. Press y N.2. Press † or } to scroll the CATALOG until the selection cursor points to ClockOff.3. Press Í Í.Entering Expressions and InstructionsWhat Is an Expression?An expression is a group of numbers, variables, functions and their arguments, or a combination ofthese elements. An expression evaluates to a single answer. On the TI-84 Plus, you enter anexpression in the same order as you would write it on paper. For example, pR2 is an expression.You can use an expression on the home screen to calculate an answer. In most places where avalue is required, you can use an expression to enter a value. Chapter 1: Operating the TI-84 Plus Silver Edition 11
Entering an ExpressionTo create an expression, you enter numbers, variables, and functions using the keyboard andmenus. An expression is completed when you press Í, regardless of the cursor location. Theentire expression is evaluated according to Equation Operating System (EOS™) rules, and theanswer is displayed according to the mode setting for Answer.Most TI-84 Plus functions and operations are symbols comprising several characters. You mustenter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the logof 45, you must press « 45. Do not enter the letters L, O, and G. If you enter LOG, the TI-84 Plusinterprets the entry as implied multiplication of the variables L, O, and G.Calculate 3.76 P (L7.9 + ‡5) + 2 log 45.3 Ë 76 ¥ £ Ì 7 Ë 9 Ãy C 5 ¤ ¤ à 2 « 45 ¤Í MathPrint™ ClassicMultiple Entries on a LineTo enter two or more expressions or instructions on a line, separate them with colons (ƒ [:]).All instructions are stored together in last entry (ENTRY).Entering a Number in Scientific Notation1. Enter the part of the number that precedes the exponent. This value can be an expression.2. Press y D. â is pasted to the cursor location.3. Enter the exponent, which can be one or two digits. Note: If the exponent is negative, press Ì, and then enter the exponent.When you enter a number in scientific notation, the TI-84 Plus does not automatically displayanswers in scientific or engineering notation. The mode settings and the size of the numberdetermine the display format.FunctionsA function returns a value. For example, ÷, L, +, ‡, and log( are the functions in the example on theprevious page. In general, the first letter of each function is lowercase on the TI-84 Plus. Mostfunctions take at least one argument, as indicated by an open parenthesis following the name. Forexample, sin( requires one argument, sin(value). Chapter 1: Operating the TI-84 Plus Silver Edition 12
Note: The Catalog Help App contains syntax information for most of the functions in the catalog.InstructionsAn instruction initiates an action. For example, ClrDraw is an instruction that clears any drawnelements from a graph. Instructions cannot be used in expressions. In general, the first letter ofeach instruction name is uppercase. Some instructions take more than one argument, as indicatedby an open parenthesis at the end of the name. For example, Circle( requires three arguments,Circle(X,Y,radius).Interrupting a CalculationTo interrupt a calculation or graph in progress, which is indicated by the busy indicator, press É.When you interrupt a calculation, a menu is displayed.• To return to the home screen, select 1:Quit.• To go to the location of the interruption, select 2:Goto.When you interrupt a graph, a partial graph is displayed.• To return to the home screen, press ' or any nongraphing key.• To restart graphing, press a graphing key or select a graphing instruction.TI-84 Plus Edit KeysKeystrokes Result~ or | Moves the cursor within an expression; these keys repeat.} or † Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat. Moves the cursor from term to term within an expression in MathPrint™ mode; these keys repeat. On the home screen, scrolls through the history of entries and answers.y| Moves the cursor to the beginning of an expression.y~ Moves the cursor to the end of an expression.y} On the home screen, moves the cursor out of a MathPrint™ expression. In the Y=editor, moves the cursor from a MathPrint™ expression to the previous Y-var.y† In the Y=editor, moves the cursor from a MathPrint ™ expression to the next Y-var.Í Evaluates an expression or executes an instruction.' On a line with text on the home screen, clears the current line. On a blank line on the home screen, clears everything on the home screen. In an editor, clears the expression or value where the cursor is located; it does not store a zero. Chapter 1: Operating the TI-84 Plus Silver Edition 13
Keystrokes Result{ Deletes a character at the cursor; this key repeats.y6 Changes the cursor to an underline (__); inserts characters in front of the underline cursor; to end insertion, press y 6 or press |, }, ~, or †.y Changes the cursor to Þ; the next keystroke performs a 2nd function (displayed above a key and to the left); to cancel 2nd, press y again.ƒ Changes the cursor to Ø; the next keystroke performs a third function of that key (displayed above a key and to the right), executes SOLVE (Chapters 10 and 11), or accesses a shortcut menu; to cancel ƒ, press ƒ or press |, }, ~, or †.y7 Changes the cursor to Ø; sets alpha-lock; subsequent keystrokes access the third functions of the keys pressed; to cancel alpha-lock, press ƒ. If you are prompted to enter a name such as for a group or a program, alpha-lock is set automatically." Pastes an X in Func mode, a T in Par mode, a q in Pol mode, or an n in Seq mode with one keystroke.Setting ModesChecking Mode SettingsMode settings control how the TI-84 Plus displays and interprets numbers and graphs. Modesettings are retained by the Constant 'Memory™ feature when the TI-84 Plus is turned off. Allnumbers, including elements of matrices and lists, are displayed according to the current modesettings.To display the mode settings, press z. The current settings are highlighted. Defaults arehighlighted below. The following pages describe the mode settings in detail.Normal Sci Eng Numeric notationFloat 0123456789 Number of decimal places in answersRadian Degree Unit of angle measureFunc Par Pol Seq Type of graphingConnected Dot Whether to connect graph pointsSequential Simul Whether to plot simultaneouslyReal a+bi re^qi Real, rectangular complex, or polar complexFull Horiz G-T Full screen, two split-screen modesMathPrint Classic Controls whether inputs and outputs on the home screen and in the Y= editor are displayed as they are in textbooksn/d Un/d Displays results as simple fractions or mixed fractionsAnswers: Auto Dec Frac Controls the format of the answers Chapter 1: Operating the TI-84 Plus Silver Edition 14
GoTo Format Graph: No Yes Shortcut to the Format Graph screen (y .)StatDiagnostics: Off On Determines which information is displayed in a statistical regression calculationSet Clock Sets the time and dateChanging Mode SettingsTo change mode settings, follow these steps.1. Press † or } to move the cursor to the line of the setting that you want to change.2. Press ~ or | to move the cursor to the setting you want.3. Press Í.Setting a Mode from a ProgramYou can set a mode from a program by entering the name of the mode as an instruction; forexample, Func or Float. From a blank program command line, select the mode setting from themode screen; the instruction is pasted to the cursor location.Normal, Sci, EngNotation modes only affect the way an answer is displayed on the home screen. Numeric answerscan be displayed with up to 10 digits and a two-digit exponent and as fractions. You can enter anumber in any format.Normal notation mode is the usual way we express numbers, with digits to the left and right of thedecimal, as in 12345.67.Sci (scientific) notation mode expresses numbers in two parts. The significant digits display withone digit to the left of the decimal. The appropriate power of 10 displays to the right of å, as in1.234567â4.Eng (engineering) notation mode is similar to scientific notation. However, the number can haveone, two, or three digits before the decimal; and the power-of-10 exponent is a multiple of three, asin 12.34567â3.Note: If you select Normal notation, but the answer cannot display in 10 digits (or the absolutevalue is less than .001), the TI-84 Plus expresses the answer in scientific notation.Float, 0123456789Float (floating) decimal mode displays up to 10 digits, plus the sign and decimal. Chapter 1: Operating the TI-84 Plus Silver Edition 15
0123456789 (fixed) decimal mode specifies the number of digits (0 through 9) to display to the rightof the decimal for decimal answers.The decimal setting applies to Normal, Sci, and Eng notation modes.The decimal setting applies to these numbers, with respect to the Answer mode setting:• An answer displayed on the home screen• Coordinates on a graph (Chapters 3, 4, 5, and 6)• The Tangent( DRAW instruction equation of the line, x, and dy/dx values (Chapter 8)• Results of CALCULATE operations (Chapters 3, 4, 5, and 6)• The regression equation stored after the execution of a regression model (Chapter 12)Radian, DegreeAngle modes control how the TI-84 Plus interprets angle values in trigonometric functions andpolar/rectangular conversions.Radian mode interprets angle values as radians. Answers display in radians.Degree mode interprets angle values as degrees. Answers display in degrees.Func, Par, Pol, SeqGraphing modes define the graphing parameters. Chapters 3, 4, 5, and 6 describe these modes indetail.Func (function) graphing mode plots functions, where Y is a function of X (Chapter 3).Par (parametric) graphing mode plots relations, where X and Y are functions of T (Chapter 4).Pol (polar) graphing mode plots functions, where r is a function of q (Chapter 5).Seq (sequence) graphing mode plots sequences (Chapter 6).Connected, DotConnected plotting mode draws a line connecting each point calculated for the selected functions.Dot plotting mode plots only the calculated points of the selected functions.Sequential, SimulSequential graphing-order mode evaluates and plots one function completely before the nextfunction is evaluated and plotted.Simul (simultaneous) graphing-order mode evaluates and plots all selected functions for a singlevalue of X and then evaluates and plots them for the next value of X. Chapter 1: Operating the TI-84 Plus Silver Edition 16
Note: Regardless of which graphing mode is selected, the TI-84 Plus will sequentially graph all statplots before it graphs any functions.Real, a+bi, re^qiReal mode does not display complex results unless complex numbers are entered as input.Two complex modes display complex results.• a+bi (rectangular complex mode) displays complex numbers in the form a+bi.• re^qi (polar complex mode) displays complex numbers in the form re^qi.Note: When you use the n/d template, both n and d must be real numbers. For example, you canenter (the answer is displayed as a decimal value) but if you enter , a data type errordisplays. To perform division with a complex number in the numerator or denominator, use regulardivision instead of the n/d template.Full, Horiz, G-TFull screen mode uses the entire screen to display a graph or edit screen.Each split-screen mode displays two screens simultaneously.• Horiz (horizontal) mode displays the current graph on the top half of the screen; it displays the home screen or an editor on the bottom half (Chapter 9).• G-T (graph-table) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9).MathPrint™, ClassicMathPrint™ mode displays most inputs and outputs the way they are shown in textbooks, such as 21 3-- + -- and x 2 dx . - -2 4 1Classic mode displays expressions and answers as if written on one line, such as 1/2 + 3/4.Note: If you switch between these modes, most entries will be preserved; however matrixcalculations will not be preserved. Chapter 1: Operating the TI-84 Plus Silver Edition 17
n/d, Un/dn/d displays results as a simple fraction. Fractions may contain a maximum of six digits in thenumerator; the value of the denominator may not exceed 9999.Un/d displays results as a mixed number, if applicable. U, n, and d must be all be integers. If U is anon-integer, the result may be converted U … n/d. If n or d is a non-integer, a syntax error isdisplayed. The whole number, numerator, and denominator may each contain a maximum of threedigits.Answers: Auto, Dec, FracAuto displays answers in a similar format as the input. For example, if a fraction is entered in anexpression, the answer will be in fraction form, if possible. If a decimal appears in the expression,the output will be a decimal number.Dec displays answers as integers or decimal numbers.Frac displays answers as fractions, if possible.Note: The Answers mode setting also affects how values in sequences, lists, and tables aredisplayed. Choose Dec or Frac to ensure that values are displayed in either decimal or fractionform. You can also convert values from decimal to fraction or fraction to decimal using the FRACshortcut menu or the MATH menu.GoTo Format Graph: No, YesNo does not display the FORMAT graph screen, but can always be accessed by pressingy ..Yes leaves the mode screen and displays the FORMAT graph screen when you press Í sothat you can change the graph format settings. To return to the mode screen, press z.Stat Diagnostics: Off, OnOff displays a statistical regression calculation without the correlation coefficient (r) or thecoefficient of determination (r2).On displays a statistical regression calculation with the correlation coefficient (r), and thecoefficient of determination (r2), as appropriate.Set ClockUse the clock to set the time, date, and clock display formats. Chapter 1: Operating the TI-84 Plus Silver Edition 18
• Although most variables can be archived, system variables including r, T, X, Y, and q cannot be archived (Chapter 18)• Apps are independent applications.which are stored in Flash ROM. AppVars is a variable holder used to store variables created by independent applications. You cannot edit or change variables in AppVars unless you do so through the application which created them.Storing Variable ValuesStoring Values in a VariableValues are stored to and recalled from memory using variable names. When an expressioncontaining the name of a variable is evaluated, the value of the variable at that time is used.To store a value to a variable from the home screen or a program using the ¿ key, begin on ablank line and follow these steps.1. Enter the value you want to store. The value can be an expression.2. Press ¿. ! is copied to the cursor location.3. Press ƒ and then the letter of the variable to which you want to store the value.4. Press Í. If you entered an expression, it is evaluated. The value is stored to the variable.Displaying a Variable ValueTo display the value of a variable, enter the name on a blank line on the home screen, and thenpress Í.Archiving Variables (Archive, Unarchive)You can archive data, programs, or other variables in a section of memory called user data archivewhere they cannot be edited or deleted inadvertently. Archived variables are indicated by asterisks(ä) to the left of the variable names. Archived variables cannot be edited or executed. They canonly be seen and unarchived. For example, if you archive list L1, you will see that L1 exists inmemory but if you select it and paste the name L1 to the home screen, you won't be able to see itscontents or edit it until it is unarchived. Chapter 1: Operating the TI-84 Plus Silver Edition 20
Recalling Variable ValuesUsing Recall (RCL)To recall and copy variable contents to the current cursor location, follow these steps. To leaveRCL, press '.1. Press y K. RCL and the edit cursor are displayed on the bottom line of the screen.2. Enter the name of the variable in one of five ways. • Press ƒ and then the letter of the variable. • Press y 9, and then select the name of the list, or press y [Ln]. • Press y >, and then select the name of the matrix. • Press to display the VARS menu or ~ to display the VARS Y-VARS menu; then select the type and then the name of the variable or function. • Press t a to display the YVAR shortcut menu, then select the name of the function. • Press |, and then select the name of the program (in the program editor only). The variable name you selected is displayed on the bottom line and the cursor disappears.3. Press Í. The variable contents are inserted where the cursor was located before you began these steps. Note: You can edit the characters pasted to the expression without affecting the value in memory.Scrolling Through Previous Entries on the Home ScreenYou can scroll up through previous entries and answers on the home screen, even if you havecleared the screen. When you find an entry or answer that you want to use, you can select it andpaste it on the current entry line.Note: List and matrix answers cannot be copied and pasted to the new entry line. However, youcan copy the list or matrix command to the new entry line and execute the command again todisplay the answer. Chapter 1: Operating the TI-84 Plus Silver Edition 21
Press } or † to move the cursor to the entry or answer you want to copy and then press Í. TThe entry or answer that you copied is automatically pasted on the current input line at the cursor location. Note: If the cursor is in a MathPrint™ expression, press y } to move the cursor out of the expression and then move the cursor to the entry or answer you want to copy. Press u or { to delete an entry/answer pair. After an entry/answer pair has been deleted, it cannot be displayed or recalled again.ENTRY (Last Entry) Storage AreaUsing ENTRY (Last Entry)When you press Í on the home screen to evaluate an expression or execute an instruction,the expression or instruction is placed in a storage area called ENTRY (last entry). When you turnoff the TI-84 Plus, ENTRY is retained in memory.To recall ENTRY, press y [. The last entry is pasted to the current cursor location, whereyou can edit and execute it. On the home screen or in an editor, the current line is cleared and thelast entry is pasted to the line.Because the TI-84 Plus updates ENTRY only when you press Í, you can recall the previousentry even if you have begun to enter the next expression.5Ã7Íy[Accessing a Previous EntryThe TI-84 Plus retains as many previous entries as possible in ENTRY, up to a capacity of 128bytes. To scroll those entries, press y [ repeatedly. If a single entry is more than 128 bytes,it is retained for ENTRY, but it cannot be placed in the ENTRY storage area.1 ¿ƒ AÍ2¿ƒ BÍy[If you press y [ after displaying the oldest stored entry, the newest stored entry is displayedagain, then the next-newest entry, and so on.y[ Chapter 1: Operating the TI-84 Plus Silver Edition 22
Executing the Previous Entry AgainAfter you have pasted the last entry to the home screen and edited it (if you chose to edit it), youcan execute the entry. To execute the last entry, press Í.To execute the displayed entry again, press Í again. Each subsequent execution displays theentry and the new answer.0 ¿ƒ N̓ N à 1 ¿ƒ Nƒ ã:䊃ÄN ¡ ÍÍÍMultiple Entry Values on a LineTo store to ENTRY two or more expressions or instructions, separate each expression orinstruction with a colon, then press Í. All expressions and instructions separated by colonsare stored in ENTRY.When you press y [, all the expressions and instructions separated by colons are pasted tothe current cursor location. You can edit any of the entries, and then execute all of them when youpress Í.Example: For the equation A=pr 2, use trial and error to find the radius of a circle that covers 200square centimeters. Use 8 as your first guess.8 ¿ ƒ R ƒ ã :äyB ƒ R ¡Íy[y | 7 y 6 Ë 95ÍContinue until the answer is as accurate as you want.Clearing ENTRYClear Entries (Chapter 18) clears all data that the TI-84 Plus is holding in the ENTRY storage area.Using Ans in an ExpressionWhen an expression is evaluated successfully from the home screen or from a program, the TI-84Plus stores the answer to a storage area called Ans (last answer). Ans may be a real or complexnumber, a list, a matrix, or a string. When you turn off the TI-84 Plus, the value in Ans is retained inmemory. Chapter 1: Operating the TI-84 Plus Silver Edition 23
You can use the variable Ans to represent the last answer in most places. Press y Z to copy thevariable name Ans to the cursor location. When the expression is evaluated, the TI-84 Plus uses thevalue of Ans in the calculation.Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield per squaremeter if the plot produces a total of 147 tomatoes.1Ë7¯4Ë2Í147 ¥ y ZÍContinuing an ExpressionYou can use Ans as the first entry in the next expression without entering the value again orpressing y Z. On a blank line on the home screen, enter the function. The TI-84 Plus pastesthe variable name Ans to the screen, then the function.5¥2ͯ9Ë9ÍStoring AnswersTo store an answer, store Ans to a variable before you evaluate another expression.Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius5 meters and height 3.3 meters, and then store the result in the variable V.yB 5 ¡Í¯3Ë3Í¿ƒ VÍTI-84 Plus MenusUsing a TI-84 Plus MenuYou can access most TI-84 Plus operations using menus. When you press a key or keycombination to display a menu, one or more menu names appear on the top line of the screen.• The menu name on the left side of the top line is highlighted. Up to seven items in that menu are displayed, beginning with item 1, which also is highlighted. Chapter 1: Operating the TI-84 Plus Silver Edition 24
• A number or letter identifies each menu item's place in the menu. The order is 1 through 9, then 0, then A, B, C, and so on. The LIST NAMES, PRGM EXEC, and PRGM EDIT menus only label items 1 through 9 and 0.• When the menu continues beyond the displayed items, a down arrow ($) replaces the colon next to the last displayed item.• When a menu item ends in an ellipsis (...), the item displays a secondary menu or editor when you select it.• When an asterisk (ä) appears to the left of a menu item, that item is stored in user data archive (Chapter 18).Displaying a MenuWhile using your TI-84 Plus, you often will need toaccess items from its menus.When you press a key that displays a menu, thatmenu temporarily replaces the screen where you areworking. For example, when you press , theMATH menu is displayed as a full screen.After you select an item from a menu, the screenwhere you are working usually is displayed again.Moving from One Menu to AnotherSome keys access more than one menu. When youpress such a key, the names of all accessible menusare displayed on the top line. When you highlight amenu name, the items in that menu are displayed.Press ~ and | to highlight each menu name.Note: FRAC shortcut menu items are also found on theMATH NUM menu. FUNC shortcut menu items arealso found on the MATH MATH menu.Scrolling a MenuTo scroll down the menu items, press †. To scroll up the menu items, press }. Chapter 1: Operating the TI-84 Plus Silver Edition 25
To page down six menu items at a time, press ƒ †. To page up six menu items at a time,press ƒ }.To go to the last menu item directly from the first menu item, press }. To go to the first menu itemdirectly from the last menu item, press †.Selecting an Item from a MenuYou can select an item from a menu in either of two ways.• Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen.• Press † or } to move the cursor to the item you want, and then press Í.After you select an item from a menu, the TI-84 Plustypically displays the previous screen.Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items 1 through 9 and 0 arelabeled in such a way that you can select them by pressing the appropriate number key. To movethe cursor to the first item beginning with any alpha character or q, press the key combination forthat alpha character or q. If no items begin with that character, the cursor moves beyond it to thenext item.Example: Calculate 3‡27.†††Í27 ÍLeaving a Menu without Making a SelectionYou can leave a menu without making a selection in any of four ways.• Press y 5 to return to the home screen.• Press ' to return to the previous screen.• Press a key or key combination for a different menu, such as or y 9.• Press a key or key combination for a different screen, such as o or y 0. Chapter 1: Operating the TI-84 Plus Silver Edition 26
2. Select the type of variable, such as 2:Zoom from the VARS menu or 3:Polar from the VARS Y-VARS menu. A secondary menu is displayed.3. If you selected 1:Window, 2:Zoom, or 5:Statistics from the VARS menu, you can press ~ or | to display other secondary menus.4. Select a variable name from the menu. It is pasted to the cursor location.Equation Operating System (EOS™)Order of EvaluationThe Equation Operating System (EOS™) defines the order in which functions in expressions areentered and evaluated on the TI-84 Plus. EOS™ lets you enter numbers and functions in a simple,straightforward sequence.EOS evaluates the functions in an expression in this order.Order Number Function 1 Functions that precede the argument, such as ‡, sin(, or log( 2 Functions that are entered after the argument, such as 2, M1, !, ¡, r, and conversions 3 x Powers and roots, such as 25 or 5 32 4 Permutations (nPr) and combinations (nCr) 5 Multiplication, implied multiplication, and division 6 Addition and subtraction 7 Relational functions, such as > or 8 Logic operator and 9 Logic operators or and xorNote: Within a priority level, EOS™ evaluates functions from left to right. Calculations withinparentheses are evaluated first.Implied MultiplicationThe TI-84 Plus recognizes implied multiplication, so you need not press ¯ to expressmultiplication in all cases. For example, the TI-84 Plus interprets 2p, 4sin(46), 5(1+2), and (2…5)7 asimplied multiplication.Note: TI-84 Plus implied multiplication rules, although like the TI-83, differ from those of the TI-82.For example, the TI-84 Plus evaluates 1à2X as (1à2)…X, while the TI-82 evaluates 1à2X as 1à(2…X)(Chapter 2). Chapter 1: Operating the TI-84 Plus Silver Edition 28
ParenthesesAll calculations inside a pair of parentheses are completed first. For example, in the expression4(1+2), EOS first evaluates the portion inside the parentheses, 1+2, and then multiplies the answer,3, by 4.NegationTo enter a negative number, use the negation key. Press Ì and then enter the number. On theTI-84 Plus, negation is in the third level in the EOS™ hierarchy. Functions in the first level, such assquaring, are evaluated before negation.Example: MX2, evaluates to a negative number (or 0). Use parentheses to square a negativenumber.Note: Use the ¹ key for subtraction and the Ì key for negation. If you press ¹ to enter a negativenumber, as in 9 ¯ ¹ 7, or if you press Ì to indicate subtraction, as in 9 Ì 7, an error occurs. Ifyou press ƒ A Ì ƒ B, it is interpreted as implied multiplication (A…MB).Special Features of the TI-84 PlusFlash – Electronic UpgradabilityThe TI-84 Plus uses Flash technology, which lets you upgrade to future software versions withoutbuying a new graphing calculator.As new functionality becomes available, you can electronically upgrade your TI-84 Plus from theInternet. Future software versions include maintenance upgrades that will be released free ofcharge, as well as new applications and major software upgrades that will be available forpurchase from the TI Web site: education.ti.com. For details, refer to Chapter 19.1.5 Megabytes of Available Memory1.5 MB of available memory are built into the TI-84 Plus Silver Edition, and 0.5 MB for theTI-84 Plus. About 24 kilobytes (K) of RAM (random access memory) are available for you tocompute and store functions, programs, and data. Chapter 1: Operating the TI-84 Plus Silver Edition 29
About 1.5 M of user data archive allow you to store data, programs, applications, or any othervariables to a safe location where they cannot be edited or deleted inadvertently. You can also freeup RAM by archiving variables to user data. For details, refer to Chapter 18.ApplicationsMany applications are preloaded on your TI-84 Plus and others can be installed to customize theTI-84 Plus to your needs. The 1.5 MB archive space lets you store up to 94 applications at onetime on the TI-84 Plus Silver Edition. Applications can also be stored on a computer for later use orlinked unit-to-unit. There are 30 App slots for the TI-84 Plus. For details, refer to Chapter 18.ArchivingYou can store variables in the TI-84 Plus user data archive, a protected area of memory separatefrom RAM. The user data archive lets you:• Store data, programs, applications or any other variables to a safe location where they cannot be edited or deleted inadvertently.• Create additional free RAM by archiving variables.By archiving variables that do not need to be edited frequently, you can free up RAM forapplications that may require additional memory. For details, refer to:Chapter 18.Other TI-84 Plus FeaturesThe TI-84 Plus guidebook that is included with your graphing calculator has introduced you tobasic TI-84 Plus operations. This guidebook covers the other features and capabilities of the TI-84Plus in greater detail.GraphingYou can store, graph, and analyze up to 10 functions, up to six parametric functions, up to six polarfunctions, and up to three sequences. You can use DRAW instructions to annotate graphs.The graphing chapters appear in this order: Function, Parametric, Polar, Sequence, and DRAW.For graphing details, refer to Chapters 3, 4, 5, 6, 8.SequencesYou can generate sequences and graph them over time. Or, you can graph them as web plots oras phase plots. For details, refer to Chapter 6.TablesYou can create function evaluation tables to analyze many functions simultaneously. For details,refer to Chapter 7. Chapter 1: Operating the TI-84 Plus Silver Edition 30
Split ScreenYou can split the screen horizontally to display both a graph and a related editor (such as the Y=editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically todisplay a graph and its table simultaneously. For details, refer to Chapter 9.MatricesYou can enter and save up to 10 matrices and perform standard matrix operations on them. Fordetails, refer to Chapter 10.ListsYou can enter and save as many lists as memory allows for use in statistical analyses. You canattach formulas to lists for automatic computation. You can use lists to evaluate expressions atmultiple values simultaneously and to graph a family of curves. For details, refer to:Chapter 11.StatisticsYou can perform one- and two-variable, list-based statistical analyses, including logistic and sineregression analysis. You can plot the data as a histogram, xyLine, scatter plot, modified or regularbox-and-whisker plot, or normal probability plot. You can define and store up to three stat plotdefinitions. For details, refer to Chapter 12.Inferential StatisticsYou can perform 16 hypothesis tests and confidence intervals and 15 distribution functions. Youcan display hypothesis test results graphically or numerically. For details, refer to Chapter 13.ApplicationsPress Πto see the complete list of applications that came with your graphing calculator.Documentation for TI Flash applications are on the product CD. Visit education.ti.com/guides foradditional Flash application guidebooks. For details, refer to Chapter 14.CATALOGThe CATALOG is a convenient, alphabetical list of all functions and instructions on the TI-84 Plus.You can paste any function or instruction from the CATALOG to the current cursor location. Fordetails, refer to Chapter 15.ProgrammingYou can enter and store programs that include extensive control and input/output instructions. Fordetails, refer to Chapter 16. Chapter 1: Operating the TI-84 Plus Silver Edition 31
ArchivingArchiving allows you to store data, programs, or other variables to user data archive where theycannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variablesthat may require additional memory.Archived variables are indicated by asterisks (ä) to theleft of the variable names.For details, refer to Chapter 16.Communication LinkThe TI-84 Plus has a USB port using a USB unit-to-unit cable to connect and communicate withanother TI-84 Plus or TI-84 Plus Silver Edition. The TI-84 Plus also has an I/O port using an I/Ounit-to-unit cable to communicate with a TI-84 Plus Silver Edition, a TI-84 Plus, a TI-83 Plus SilverEdition, a TI-83 Plus, a TI-83, a TI-82, a TI-73, CBL 2™, or a CBR™ System.With TI Connect™ software and a USB computer cable, you can also link the TI-84 Plus to apersonal computer.As future software upgrades become available on the TI Web site, you can download the softwareto your PC and then use the TI Connect™ software and a USB computer cable to upgrade yourTI-84 Plus.For details, refer to: Chapter 19Error ConditionsDiagnosing an ErrorThe TI-84 Plus detects errors while performing these tasks.• Evaluating an expression• Executing an instruction• Plotting a graph• Storing a valueWhen the TI-84 Plus detects an error, it returns an error message as a menu title, such asERR:SYNTAX or ERR:DOMAIN. Appendix B describes each error type and possible reasons for theerror. Chapter 1: Operating the TI-84 Plus Silver Edition 32
• If you select 1:Quit (or press y 5 or '), then the home screen is displayed.• If you select 2:Goto, then the previous screen is displayed with the cursor at or near the error location.Note: If a syntax error occurs in the contents of a Y= function during program execution, then theGoto option returns to the Y= editor, not to the program.Correcting an ErrorTo correct an error, follow these steps.1. Note the error type (ERR:error type).2. Select 2:Goto, if it is available. The previous screen is displayed with the cursor at or near the error location.3. Determine the error. If you cannot recognize the error, refer to Appendix B.4. Correct the expression. Chapter 1: Operating the TI-84 Plus Silver Edition 33
Chapter 2:Math, Angle, and Test OperationsGetting Started: Coin FlipGetting Started is a fast-paced introduction. Read the chapter for details. For more probabilitysimulations, try the Probability Simulations App for the TI-84 Plus. You can download this App fromeducation.ti.com.Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, theprobability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is0.5.1. Begin on the home screen. Press | to display the MATH PRB menu. Press 7 to select 7:randBin( (random Binomial). randBin( is pasted to the home screen. Press 10 to enter the number of coin flips. Press ¢. Press Ë 5 to enter the probability of heads. Press ¢. Press 40 to enter the number of simulations. Press ¤.2. Press Í to evaluate the expression. A list of 40 elements is generated with the first 7 displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on.3. Press ~ or | to view the additional counts in the list. An arrow (MathPrint™ mode) or an ellipses (Classic mode) indicate that the list continues beyond the screen.4. Press ¿ y d Í to store the data to the list name L1. You then can use the data for another activity, such as plotting a histogram MathPrint™ (Chapter 12).Note: Since randBin( generates random numbers, yourlist elements may differ from those in the example. Classic Chapter 2: Math, Angle, and Test Operations 34
Keyboard Math OperationsUsing Lists with Math OperationsMath operations that are valid for lists return a list calculated element by element. If you use twolists in the same expression, they must be the same length.Addition, Subtraction, Multiplication, DivisionYou can use + (addition, Ã), N (subtraction, ¹), … (multiplication, ¯), and à (division, ¥) with realand complex numbers, expressions, lists, and matrices. You cannot use à with matrices. If youneed to input A/2, enter this as A †1/2 or A †.5.valueA+valueB valueA N valueBvalueA…valueB valueA à valueBTrigonometric FunctionsYou can use the trigonometric (trig) functions (sine, ˜; cosine, ™; and tangent, š) with realnumbers, expressions, and lists. The current angle mode setting affects interpretation. Forexample, sin(30) in radian mode returns L.9880316241; in degree mode it returns .5.sin(value) cos(value) tan(value)You can use the inverse trig functions (arcsine, y ?; arccosine, y @; and arctangent,y A) with real numbers, expressions, and lists. The current angle mode setting affectsinterpretation.sinL1(value) cosL1(value) tanL1(value)Note: The trig functions do not operate on complex numbers.Power, Square, Square RootYou can use ^ (power, ›), 2 (square, ¡), and ‡( (square root, y C) with real and complexnumbers, expressions, lists, and matrices. You cannot use ‡( with matrices.MathPrint™: valuepower value2 ‡(value) ÈClassic: value^power È Chapter 2: Math, Angle, and Test Operations 35
InverseYou can use L1 (inverse, œ) with real and complex numbers, expressions, lists, and matrices. Themultiplicative inverse is equivalent to the reciprocal, 1àx.value-1log(, 10^(, ln(You can use log( (logarithm, «), 10^( (power of 10, y G), and ln( (natural log, μ) with real orcomplex numbers, expressions, and lists.log(value) MathPrint™: 10power ln(value) Classic: 10^(power)Exponentiale^( (exponential, y J) returns the constant e raised to a power. You can use e^( with real orcomplex numbers, expressions, and lists.MathPrint™: epowerClassic: e^(power)Constante (constant, y [e]) is stored as a constant on the TI-84 Plus. Press y [e] to copy e to the cursorlocation. In calculations, the TI-84 Plus uses 2.718281828459 for e.NegationM (negation, Ì) returns the negative of value. You can use M with real or complex numbers,expressions, lists, and matrices. Chapter 2: Math, Angle, and Test Operations 36
MvalueEOS™ rules (Chapter 1) determine when negation is evaluated. For example, L42 returns anegative number, because squaring is evaluated before negation. Use parentheses to square anegated number, as in (L4)2.Note: On the TI-84 Plus, the negation symbol (M) is shorter and higher than the subtraction sign (N),which is displayed when you press ¹.Pip (Pi, y B) is stored as a constant in the TI-84 Plus. In calculations, the TI-84 Plus uses3.1415926535898 for p.MATH OperationsMATH MenuTo display the MATH menu, press .MATH NUM CPX PRB1: 4Frac Displays the answer as a fraction.2: 4Dec Displays the answer as a decimal.3: 3 Calculates the cube.4: 3 ‡( Calculates the cube root.5: x ‡ Calculates the xth root.6: fMin( Finds the minimum of a function.7: fMax( Finds the maximum of a function.8: nDeriv( Computes the numerical derivative. Chapter 2: Math, Angle, and Test Operations 37
MATH NUM CPX PRB9: fnInt( Computes the function integral.0: summation )( Returns the sum of elements of list from start to end, where start <= end.A: logBASE( Returns the logarithm of a specifed value determined from a specified base: logBASE(value, base).B: Solver... Displays the equation solver.4Frac, 4Dec4Frac (display as a fraction) displays an answer as its rational equivalent. You can use 4Frac withreal or complex numbers, expressions, lists, and matrices. If the answer cannot be simplified orthe resulting denominator is more than three digits, the decimal equivalent is returned. You canonly use 4Frac following value.value 4Frac4Dec (display as a decimal) displays an answer in decimal form. You can use 4Dec with real orcomplex numbers, expressions, lists, and matrices. You can only use 4Dec following value.value 4DecNote: You can quickly convert from one number type to the other by using the FRAC shortcutmenu. Press t ^ 4:4F3 4D to convert a value.Cube, Cube Root3 (cube) returns the cube of value. You can use 3 with real or complex numbers, expressions, lists,and square matrices.value3 (cube root) returns the cube root of value. You can use 3‡( with real or complex numbers,3‡ (expressions, and lists.3 ‡(value) Chapter 2: Math, Angle, and Test Operations 38
x‡ (Root)x ‡ (xth root) returns the xth root of value. You can use x‡ with real or complex numbers, expressions,and lists.xthrootx‡valuefMin(, fMax(fMin( (function minimum) and fMax( (function maximum) return the value at which the localminimum or local maximum value of expression with respect to variable occurs, between lower andupper values for variable. fMin( and fMax( are not valid in expression. The accuracy is controlled bytolerance (if not specified, the default is 1âL5).fMin(expression,variable,lower,upper[,tolerance])fMax(expression,variable,lower,upper[,tolerance])Note: In this guidebook, optional arguments and the commas that accompany them are enclosedin brackets ([ ]).MathPrint™ClassicnDeriv(nDeriv( (numerical derivative) returns an approximate derivative of expression with respect to variable,given the value at which to calculate the derivative and H (if not specified, the default is 1âL3).nDeriv( is valid only for real numbers. Chapter 2: Math, Angle, and Test Operations 39
MathPrint™:Classic: nDeriv(expression,variable,value[,H])nDeriv( uses the symmetric difference quotient method, which approximates the numericalderivative value as the slope of the secant line through these points. f x + – f x – f x = ----------------------------------------- - 2As H becomes smaller, the approximation usually becomes more accurate. In MathPrint™ mode,the default H is 1EM3. You can switch to Classic mode to change H for investigations.MathPrint™ClassicYou can use nDeriv( once in expression. Because of the method used to calculate nDeriv(, the TI-84Plus can return a false derivative value at a nondifferentiable point.fnInt(fnInt( (function integral) returns the numerical integral (Gauss-Kronrod method) of expression withrespect to variable, given lower limit, upper limit, and a tolerance (if not specified, the default is 1âL5).fnInt( is valid only for real numbers.MathPrint™:Classic: fnInt(expression,variable,lower,upper[,tolerance])In MathPrint™ mode, the default H is 1EM3. You can switch to Classic mode to change H forinvestigations. Chapter 2: Math, Angle, and Test Operations 40
Note: To speed the drawing of integration graphs (when fnInt( is used in a Y= equation), increasethe value of the Xres window variable before you press s.Using the Equation SolverSolverSolver displays the equation solver, in which you can solve for any variable in an equation. Theequation is assumed to be equal to zero. Solver is valid only for real numbers.When you select Solver, one of two screens is displayed.• The equation editor (see step 1 picture below) is displayed when the equation variable eqn is empty.• The interactive solver editor is displayed when an equation is stored in eqn.Entering an Expression in the Equation SolverTo enter an expression in the equation solver, assuming that the variable eqn is empty, followthese steps.1. Select B:Solver from the MATH menu to display the equation editor.2. Enter the expression in any of three ways. • Enter the expression directly into the equation solver. • Paste a Y= variable name from the YVARS shortcut menu (t a) to the equation solver. • Press y K, paste a Y= variable name from the YVARS shortcut menu, and press Í. The expression is pasted to the equation solver. The expression is stored to the variable eqn as you enter it.3. Press Í or †. The interactive solver editor is displayed. • The equation stored in eqn is set equal to zero and displayed on the top line. • Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed. Chapter 2: Math, Angle, and Test Operations 41
• The default lower and upper bounds appear in the last line of the editor (bound={L1â99,1â99}). • A $ is displayed in the first column of the bottom line if the editor continues beyond the screen.Note: To use the solver to solve an equation such as K=.5MV2, enter eqn:0=KN.5MV2 in theequation editor.Entering and Editing Variable ValuesWhen you enter or edit a value for a variable in the interactive solver editor, the new value is storedin memory to that variable.You can enter an expression for a variable value. It is evaluated when you move to the nextvariable. Expressions must resolve to real numbers at each step during the iteration.You can store equations to any VARS Y-VARS variables, such as Y1 or r6, and then reference thevariables in the equation. The interactive solver editor displays all variables of all Y= functionsrecalled in the equation.Solving for a Variable in the Equation SolverTo solve for a variable using the equation solver after an equation has been stored to eqn, followthese steps.1. Select B:Solver from the MATH menu to display the interactive solver editor, if not already displayed.2. Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press Í or †. Chapter 2: Math, Angle, and Test Operations 42
3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-84 Plus will attempt to display the solution that is closest to your guess. upper + lower The default guess is calculated as ---------------------------------------- . - 24. Edit bound={lower,upper}. lower and upper are the bounds between which the TI-84 Plus searches for a solution. This is optional, but it may help find the solution more quickly. The default is bound={L1â99,1â99}.5. Move the cursor to the variable for which you want to solve and press ƒ . • The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that the value continues beyond the screen. Note: When a number continues beyond the screen, be sure to press ~ to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent. • The values of the variables are updated in memory. • leftNrt=diff is displayed in the last line of the editor. diff is the difference between the left and right sides of the equation when evaluated at the calculated solution. A solid square in the first column next to leftNrt indicates that the equation has been evaluated at the new value of the variable for which you solved.Editing an Equation Stored to eqnTo edit or replace an equation stored to eqn when the interactive equation solver is displayed,press } until the equation editor is displayed. Then edit the equation.Equations with Multiple RootsSome equations have more than one solution. You can enter a new initial guess or new bounds tolook for additional solutions.Further SolutionsAfter you solve for a variable, you can continue to explore solutions from the interactive solvereditor. Edit the values of one or more variables. When you edit any variable value, the solid Chapter 2: Math, Angle, and Test Operations 43
squares next to the previous solution and leftNrt=diff disappear. Move the cursor to the variable forwhich you now want to solve and press ƒ .Controlling the Solution for Solver or solve(The TI-84 Plus solves equations through an iterative process. To control that process, enterbounds that are relatively close to the solution and enter an initial guess within those bounds. Thiswill help to find a solution more quickly. Also, it will define which solution you want for equationswith multiple solutions.Using solve( on the Home Screen or from a ProgramThe function solve( is available only from CATALOG or from within a program. It returns a solution(root) of expression for variable, given an initial guess, and lower and upper bounds within which thesolution is sought. The default for lower is L1â99. The default for upper is L1â99. solve( is valid onlyfor real numbers.solve(expression,variable,guess[,{lower,upper}])expression is assumed equal to zero. The value of variable will not be updated in memory. guess maybe a value or a list of two values. Values must be stored for every variable in expression, exceptvariable, before expression is evaluated. lower and upper must be entered in list format.MathPrint™ClassicMATH NUM (Number) OperationsMATH NUM MenuTo display the MATH NUM menu, press ~.MATH NUM CPX PRB1: abs( Absolute value2: round( Round3: iPart( Integer part Chapter 2: Math, Angle, and Test Operations 44
MATH NUM CPX PRB4: fPart( Fractional part5: int( Greatest integer6: min( Minimum value7: max( Maximum value8: lcm( Least common multiple9: gcd( Greatest common divisor0: remainder( Reports the remainder as a whole number from a division of two whole numbers where the divisor is not zero.A: 4n/d3 4Un/d Converts an improper fraction to a mixed number or a mixed number to an improper fraction.B: 4F3 4D Converts a decimal to a fraction or a fraction to a decimal.C: Un/d Displays the mixed number template in MathPrint™ mode. In Classic mode, displays a small u between the whole number and fraction.D: n/d Displays the fraction template in MathPrint™ mode. In Classic mode, displays a thick fraction bar between the numerator and the denominator.abs(abs( (absolute value) returns the absolute value of real or complex (modulus) numbers,expressions, lists, and matrices.Note: abs( is also found on the FUNC shortcut menu (t _ 1).abs(value)MathPrint™ClassicNote: abs( is also available on the MATH CPX menu. Chapter 2: Math, Angle, and Test Operations 45
round(round( returns a number, expression, list, or matrix rounded to #decimals (9). If #decimals is omitted,value is rounded to the digits that are displayed, up to 10 digits.round(value[,#decimals])iPart(, fPart(iPart( (integer part) returns the integer part or parts of real or complex numbers, expressions, lists,and matrices.iPart(value)fPart( (fractional part) returns the fractional part or parts of real or complex numbers, expressions,lists, and matrices.fPart(value)Note: The way the fractional result is displayed depends on the Answers mode setting. To convert from oneformat to another, use 4F3 4D on the FRAC shortcut menu (t ^ 4).int(int( (greatest integer) returns the largest integer real or complex numbers, expressions, lists, andmatrices.int(value) Chapter 2: Math, Angle, and Test Operations 46
Note: For a given value, the result of int( is the same as the result of iPart( for nonnegative numbersand negative integers, but one integer less than the result of iPart( for negative nonintegernumbers.min(, max(min( (minimum value) returns the smaller of valueA and valueB or the smallest element in list. If listAand listB are compared, min( returns a list of the smaller of each pair of elements. If list and valueare compared, min( compares each element in list with value.max( (maximum value) returns the larger of valueA and valueB or the largest element in list. If listAand listB are compared, max( returns a list of the larger of each pair of elements. If list and value arecompared, max( compares each element in list with value.min(valueA,valueB) max(valueA,valueB)min(list) max(list)min(listA,listB) max(listA,listB)min(list,value) max(list,value)Note: min( and max( also are available on the LIST MATH menu.lcm(, gcd(lcm( returns the least common multiple of valueA and valueB, both of which must be nonnegativeintegers. When listA and listB are specified, lcm( returns a list of the least common multiple of eachpair of elements. If list and value are specified, lcm( finds the least common multiple of eachelement in list and value.gcd( returns the greatest common divisor of valueA and valueB, both of which must be nonnegativeintegers. When listA and listB are specified, gcd( returns a list of the greatest common divisor ofeach pair of elements. If list and value are specified, gcd( finds the greatest common divisor of eachelement in list and value.lcm(valueA,valueB) gcd(valueA,valueB)lcm(listA,listB) gcd(listA,listB)lcm(list,value) gcd(list,value) Chapter 2: Math, Angle, and Test Operations 47
remainder(remainder( returns the remainder resulting from the division of two positive whole numbers, dividendand divisor, each of which can be a list. The divisor cannot be zero. If both arguments are lists, theymust have the same number of elements. If one argument is a list and the other a non-list, the non-list is paired with each element of the list, and a list is returned.remainder(dividend, divisor)remainder(list, divisor)remainder(dividend, list)remainder(list, list)4n/d3 4Un/d4n/d3 4Un/d converts an improper fraction to a mixed number or a mixed number to an improperfraction. You can also access 4n/d3 4Un/d from the FRAC shortcut menu (t ^ 3). Chapter 2: Math, Angle, and Test Operations 48
4F3 4D4F3 4D converts a fraction to a decimal or a decimal to a fraction. You can also access 4F3 4D fromthe FRAC shortcut menu (t ^ 4).Un/dUn/d displays the mixed number template. You can also access Un/d from the FRAC shortcutmenu (t ^ 2). In the fraction, n and d must be non-negative integers.MathPrint™ "Classicn/dn/d displays the mixed number template. You can also access n/d from the FRAC shortcut menu(t ^ 1). n and d can be real numbers or expressions but may not contain complex numbers.MathPrint™ "ClassicEntering and Using Complex NumbersComplex-Number ModesThe TI-84 Plus displays complex numbers in rectangular form and polar form. To select a complex-number mode, press z, and then select either of the two modes.• a+bi (rectangular-complex mode)• re^qi (polar-complex mode) Entering and Using Complex Numbers 49
On the TI-84 Plus, complex numbers can be stored to variables. Also, complex numbers are validlist elements.In Real mode, complex-number results return an error, unless you entered a complex number asinput. For example, in Real mode ln(L1) returns an error; in a+bi mode ln(L1) returns an answer.Real mode a+bi mode $ $Entering Complex NumbersComplex numbers are stored in rectangular form, but you can enter a complex number inrectangular form or polar form, regardless of the mode setting. The components of complexnumbers can be real numbers or expressions that evaluate to real numbers; expressions areevaluated when the command is executed.You can enter fractions in complex numbers, but the output will always be a decimal value.When you use the n/d template, a fraction cannot contain a complex number. "You can use division to compute the answer: Entering and Using Complex Numbers 50
Note about Radian Versus Degree ModeRadian mode is recommended for complex number calculations. Internally, the TI-84 Plusconverts all entered trigonometric values to radians, but it does not convert values for exponential,logarithmic, or hyperbolic functions.In degree mode, complex identities such as e^(iq) = cos(q) + i sin(q) are not generally truebecause the values for cos and sin are converted to radians, while those for e^() are not. Forexample, e^(i45) = cos(45) + i sin(45) is treated internally as e^(i45) = cos(p/4) + i sin(p/4).Complex identities are always true in radian mode.Interpreting Complex ResultsComplex numbers in results, including list elements, are displayed in either rectangular or polarform, as specified by the mode setting or by a display conversion instruction. In the examplebelow, polar-complex (re^qi) and Radian modes are set.MathPrint™:Classic:Rectangular-Complex ModeRectangular-complex mode recognizes and displays a complex number in the form a+bi, where a isthe real component, b is the imaginary component, and i is a constant equal to –1 .To enter a complex number in rectangular form, enter the value of a (real component), press à or ¹,enter the value of b (imaginary component), and press y V (constant).real component(+ or N)imaginary component iPolar-Complex ModePolar-complex mode recognizes and displays a complex number in the form re^qi, where r is themagnitude, e is the base of the natural log, q is the angle, and i is a constant equal to –1 . Entering and Using Complex Numbers 51
To enter a complex number in polar form, enter the value of r (magnitude), press y J(exponential function), enter the value of q (angle), press y V (constant), and then press ¤.magnitudee^(anglei)MathPrint™Classic Entering and Using Complex Numbers 52
imag(imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of complexnumbers.imag(a+bi) returns b.imag(re^(qi)) returns r†sin(q).MathPrint™ Classicangle(angle( returns the polar angle of a complex number or list of complex numbers, calculated as tanL1(b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in thesecond quadrant or Np in the third quadrant.angle(a+bi) returns tanL1(b/a).angle(re^(qi)) returns q, where Lp<q<p.MathPrint™ Classicabs(abs( (absolute value) returns the magnitude (modulus), , of a complex number or listof complex numbers. You can also access abs( from the FUNC shortcut menu (t _ 1).abs(a+bi) returns .abs(re^(qi)) returns r (magnitude). Entering and Using Complex Numbers 54
4Rect4Rect (display as rectangular) displays a complex result in rectangular form. It is valid only at theend of an expression. It is not valid if the result is real.complex result8Rect returns a+bi.4Polar4Polar (display as polar) displays a complex result in polar form. It is valid only at the end of anexpression. It is not valid if the result is real.complex result8Polar returns re^(qi).MATH PRB (Probability) OperationsMATH PRB MenuTo display the MATH PRB menu, press |.MATH NUM CPX PRB1: rand Random-number generator2: nPr Number of permutations3: nCr Number of combinations4: ! Factorial Entering and Using Complex Numbers 55
MATH NUM CPX PRB5: randInt( Random-integer generator6: randNorm( Random # from Normal distribution7: randBin( Random # from Binomial distribution8: randIntNoRep( Random ordered list of integers in a rangerandrand (random number) generates and returns one or more random numbers > 0 and < 1. Togenerate a list of random-numbers, specify an integer > 1 for numtrials (number of trials). Thedefault for numtrials is 1.rand[(numtrials)]Note: To generate random numbers beyond the range of 0 to 1, you can include rand in anexpression. For example, rand5 generates a random number > 0 and < 5.With each rand execution, the TI-84 Plus generates the same random-number sequence for agiven seed value. The TI-84 Plus factory-set seed value for rand is 0. To generate a differentrandom-number sequence, store any nonzero seed value to rand. To restore the factory-set seedvalue, store 0 to rand or reset the defaults (Chapter 18).Note: The seed value also affects randInt(, randNorm(, and randBin( instructions.nPr, nCrnPr (number of permutations) returns the number of permutations of items taken number at a time.items and number must be nonnegative integers. Both items and number can be lists.items nPr numbernCr (number of combinations) returns the number of combinations of items taken number at a time.items and number must be nonnegative integers. Both items and number can be lists.items nCr number Entering and Using Complex Numbers 56
Factorial! (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorialsfor each integer or multiple of .5. value must be ' L.5 and 69.value!Note: The factorial is computed recursively using the relationship (n+1)! = n…n!, until n is reducedto either 0 or L1/2. At that point, the definition 0!=1 or the definition (L1à2)!=‡p is used to completethe calculation. Hence:n!=n…(nN1)…(nN2)… ... …2…1, if n is an integer ' 0n!= n…(nN1)…(nN2)… ... …1à2…‡p, if n+1à2 is an integer ' 0n! is an error, if neither n nor n+1à2 is an integer ' 0.(The variable n equals value in the syntax description above.)randInt(randInt( (random integer) generates and displays a random integer within a range specified bylower and upper integer bounds. To generate a list of random numbers, specify an integer > 1 fornumtrials (number of trials); if not specified, the default is 1.randInt(lower,upper[,numtrials])randNorm(randNorm( (random Normal) generates and displays a random real number from a specifiedNormal distribution. Each generated value could be any real number, but most will be within theinterval [mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for numtrials(number of trials); if not specified, the default is 1.randNorm(m,s[,numtrials]) Entering and Using Complex Numbers 57
ANGLE7: P8Rx( Returns x, given R and q8: P8Ry( Returns y, given R and qEntry NotationDMS (degrees/minutes/seconds) entry notation comprises the degree symbol (¡), the minutesymbol (), and the second symbol ("). degrees must be a real number; minutes and seconds must bereal numbers ' 0.Note: DMS entry notation does not support fractions in minutes or seconds.degrees¡minutesseconds"For example, we know that 30 degrees is the same as p/6 radians, and we can verify that bylooking at the values in degree and radian modes. If the angle mode is not set to Degree, you mustuse ¡ so that the TI-84 Plus can interpret the argument as degrees, minutes, and seconds.Degree mode Radian modeDegree¡ (degree) designates an angle or list of angles as degrees, regardless of the current angle modesetting. In Radian mode, you can use ¡ to convert degrees to radians.value¡{value1,value2,value3,value4,...,value n}¡¡ also designates degrees (D) in DMS format. (minutes) designates minutes (M) in DMS format." (seconds) designates seconds (S) in DMS format.Note: " is not on the ANGLE menu. To enter ", press ƒ [ã].Radiansr (radians) designates an angle or list of angles as radians, regardless of the current angle modesetting. In Degree mode, you can use r to convert radians to degrees.valuer Entering and Using Complex Numbers 59
Degree mode8DMS8DMS (degree/minute/second) displays answer in DMS format. The mode setting must be Degreefor answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid only at the end of aline.answer8DMSR8Pr (, R8Pq(, P8Rx(, P8Ry(R8Pr( converts rectangular coordinates to polar coordinates and returns r. R8Pq( convertsrectangular coordinates to polar coordinates and returns q. x and y can be lists.R8Pr(x,y), R8Pq(x,y) Note: Radian mode is set.P8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry( converts polarcoordinates to rectangular coordinates and returns y. r and q can be lists.P8Rx(r,q), P8Ry(r,q) Note: Radian mode is set. Entering and Using Complex Numbers 60
TEST (Relational) OperationsTEST MenuTo display the TEST menu, press y :.This operator... Returns 1 (true) if...TEST LOGIC1: = Equal2: ƒ Not equal to3: > Greater than4: ' Greater than or equal to5: < Less than6: Less than or equal toÄ=, ƒ, >, ', <, Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false.valueA and valueB can be real numbers, expressions, or lists. For = and ƒ only, valueA and valueB alsocan be matrices or complex numbers. If valueA and valueB are matrices, both must have the samedimensions.Relational operators are often used in programs to control program flow and in graphing to controlthe graph of a function over specific values.valueA=valueB valueAƒvalueBvalueA>valueB valueA'valueBvalueA<valueB valueAvalueBUsing TestsRelational operators are evaluated after mathematical functions according to EOS rules(Chapter 1).• The expression 2+2=2+3 returns 0. The TI-84 Plus performs the addition first because of EOS rules, and then it compares 4 to 5.• The expression 2+(2=2)+3 returns 6. The TI-84 Plus performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3. Entering and Using Complex Numbers 61
TEST LOGIC (Boolean) OperationsTEST LOGIC MenuTo display the TEST LOGIC menu, press y : ~.This operator... Returns a 1 (true) if...TEST LOGIC1: and Both values are nonzero (true).2: or At least one value is nonzero (true).3: xor Only one value is zero (false).4: not( The value is zero (false).Boolean OperatorsBoolean operators are often used in programs to control program flow and in graphing to controlthe graph of the function over specific values. Values are interpreted as zero (false) or nonzero(true).and, or, xorand, or, and xor (exclusive or) return a value of 1 if an expression is true or 0 if an expression isfalse, according to the table below. valueA and valueB can be real numbers, expressions, or lists.valueA and valueBvalueA or valueBvalueA xor valueB valueA valueB and or xor ƒ0 ƒ0 returns 1 1 0 ƒ0 0 returns 0 1 1 0 ƒ0 returns 0 1 1 0 0 returns 0 0 0not(not( returns 1 if value (which can be an expression) is 0.not(value)Using Boolean Operations Entering and Using Complex Numbers 62
Boolean logic is often used with relational tests. In the following program, the instructions store 4into C. Entering and Using Complex Numbers 63
Chapter 3:Function GraphingGetting Started: Graphing a CircleGetting Started is a fast-paced introduction. Read the chapter for details.Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph thiscircle, you must enter separate formulas for the upper and lower portions of the circle. Then useZSquare (zoom square) to adjust the display and make the functions appear as a circle.1. In Func mode, press o to display the Y= editor. Press y C £ 100 ¹ " ¡ ¤ Í to enter the expression Y=‡(100NX 2), which defines the top half of the circle. The expression Y=L‡(100NX 2) defines the bottom half of the circle. On the TI-84 Plus, you can define one function in terms of another. To define Y2=LY1, press Ì to enter the negation sign. Press t a to display the Y-VARS shortcut menu, and then press Í to select Y1.2. Press q 6 to select 6:ZStandard. This is a quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press s. Notice that the functions appear as an ellipse in the standard viewing window. This is due to the range of values that ZStandard defines for the X-axis and Y-axis.3. To adjust the display so that each pixel represents an equal width and height, press q 5 to select 5:ZSquare. The functions are replotted and now appear as a circle on the display. Chapter 3: Function Graphing 64
4. To see the ZSquare window variables, press p and notice the new values for Xmin, Xmax, Ymin, and Ymax.Defining GraphsTI-84 Plus—Graphing Mode SimilaritiesChapter 3 specifically describes function graphing, but the steps shown here are similar for eachTI-84 Plus graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to parametricgraphing, polar graphing, and sequence graphing.Defining a GraphTo define a graph in any graphing mode, follow these steps. Some steps are not alwaysnecessary.1. Press z and set the appropriate graph mode.2. Press o and enter, edit, or select one or more functions in the Y= editor.3. Deselect stat plots, if necessary.4. Set the graph style for each function.5. Press p and define the viewing window variables.6. Press y . and select the graph format settings.Displaying and Exploring a GraphAfter you have defined a graph, press s to display it. Explore the behavior of the function orfunctions using the TI-84 Plus tools described in this chapter.Saving a Graph for Later UseYou can store the elements that define the current graph to any of 10 graph database variables(GDB1 through GDB9, and GDB0; Chapter 8). To recreate the current graph later, simply recall thegraph database to which you stored the original graph.These types of information are stored in a GDB.• Y= functions• Graph style settings• Window settings• Format settings Chapter 3: Function Graphing 65
You can store a picture of the current graph display to any of 10 graph picture variables (Pic1through Pic9, and Pic0; Chapter 8). Then you can superimpose one or more stored pictures ontothe current graph.Setting the Graph ModesChecking and Changing the Graphing ModeTo display the mode screen, press z. The default settings are highlighted below. To graphfunctions, you must select Func mode before you enter values for the window variables and beforeyou enter the functions.The TI-84 Plus has four graphing modes.• Func (function graphing)• Par (parametric graphing; Chapter 4)• Pol (polar graphing; Chapter 5)• Seq (sequence graphing; Chapter 6)Other mode settings affect graphing results. Chapter 1 describes each mode setting.• Float or 0123456789 (fixed) decimal mode affects displayed graph coordinates.• Radian or Degree angle mode affects interpretation of some functions.• Connected or Dot plotting mode affects plotting of selected functions.• Sequential or Simul graphing-order mode affects function plotting when more than one function is selected.Setting Modes from a ProgramTo set the graphing mode and other modes from a program, begin on a blank line in the programeditor and follow these steps.1. Press z to display the mode settings.2. Press †, ~, |, and } to place the cursor on the mode that you want to select.3. Press Í to paste the mode name to the cursor location.The mode is changed when the program is executed. Chapter 3: Function Graphing 66
Defining FunctionsDisplaying Functions in the Y= EditorTo display the Y= editor, press o. You can store up to 10 functions to the function variables Y1through Y9, and Y0. You can graph one or more defined functions at once. In this example,functions Y1 and Y2 are defined and selected.Defining or Editing a FunctionTo define or edit a function, follow these steps.1. Press o to display the Y= editor.2. Press † to move the cursor to the function you want to define or edit. To erase a function, press '.3. Enter or edit the expression to define the function. • You may use functions and variables (including matrices and lists) in the expression. When the expression evaluates to a nonreal number, the value is not plotted; no error is returned. • You can access the shortcut menus by pressing ƒ ^ - a. • The independent variable in the function is X. Func mode defines " as X. To enter X, press " or press ƒ [X]. • When you enter the first character, the = is highlighted, indicating that the function is selected. As you enter the expression, it is stored to the variable Yn as a user-defined function in the Y= editor.4. Press Í or † to move the cursor to the next function.Defining a Function from the Home Screen or a ProgramTo define a function from the home screen or a program, begin on a blank line and follow thesesteps.1. Press ƒ [ã], enter the expression, and then press ƒ [ã] again.2. Press ¿. Chapter 3: Function Graphing 67
3. Press ƒ a to display the YVAR shortcut menu, move the cursor to the function name, and then press Í. "expression"!YnWhen the instruction is executed, the TI-84 Plus stores the expression to the designated variableYn, selects the function, and displays the message Done.Evaluating Y= Functions in ExpressionsYou can calculate the value of a Y= function Yn at a specified value of X. A list of values returns a list.Yn(value)Yn({value1,value2,value3, . . .,value n})Selecting and Deselecting FunctionsSelecting and Deselecting a FunctionYou can select and deselect (turn on and turn off) a function in the Y= editor. A function is selectedwhen the = sign is highlighted. The TI-84 Plus graphs only the selected functions. You can selectany or all functions Y1 through Y9, and Y0.To select or deselect a function in the Y= editor, follow these steps.1. Press o to display the Y= editor.2. Move the cursor to the function you want to select or deselect.3. Press | to place the cursor on the function's = sign.4. Press Í to change the selection status.When you enter or edit a function, it is selected automatically. When you clear a function, it isdeselected. Chapter 3: Function Graphing 68
Turning On or Turning Off a Stat Plot in the Y= EditorTo view and change the on/off status of a stat plot in the Y= editor, use Plot1 Plot2 Plot3 (the topline of the Y= editor). When a plot is on, its name is highlighted on this line.To change the on/off status of a stat plot from the Y= editor, press } and ~ to place the cursor onPlot1, Plot2, or Plot3, and then press Í. Plot1 is turned on. Plot2 and Plot3 are turned off.Selecting and Deselecting Functions from the Home Screen or a ProgramTo select or deselect a function from the home screen or a program, begin on a blank line andfollow these steps.1. Press ~ to display the VARS Y-VARS menu.2. Select 4:On/Off to display the ON/OFF secondary menu.3. Select 1:FnOn to turn on one or more functions or 2:FnOff to turn off one or more functions. The instruction you select is copied to the cursor location.4. Enter the number (1 through 9, or 0; not the variable Yn) of each function you want to turn on or turn off. • If you enter two or more numbers, separate them with commas. • To turn on or turn off all functions, do not enter a number after FnOn or FnOff. FnOn[function#,function#, . . .,function n] FnOff[function#,function#, . . .,function n]5. Press Í. When the instruction is executed, the status of each function in the current mode is set and Done is displayed.For example, in Func mode, FnOff :FnOn 1,3 turns off all functions in the Y= editor, and then turnson Y1 and Y3. Chapter 3: Function Graphing 69
Setting Graph Styles for FunctionsMATH Graph Style Icons in the Y= EditorThis table describes the graph styles available for function graphing. Use the styles to visuallydifferentiate functions to be graphed together. For example, you can set Y1 as a solid line, Y2 as adotted line, and Y3 as a thick line. Icon Style Description ç Line A solid line connects plotted points; this is the default in Connected mode è Thick A thick solid line connects plotted points é Above Shading covers the area above the graph ê Below Shading covers the area below the graph ë Path A circular cursor traces the leading edge of the graph and draws a path ì Animate A circular cursor traces the leading edge of the graph without drawing a path í Dot A small dot represents each plotted point; this is the default in Dot modeNote: Some graph styles are not available in all graphing modes. Chapters 4, 5, and 6 list thestyles for Par, Pol, and Seq modes.Setting the Graph StyleTo set the graph style for a function, follow these steps.1. Press o to display the Y= editor.2. Press † and } to move the cursor to the function.3. Press | | to move the cursor left, past the = sign, to the graph style icon in the first column. The insert cursor is displayed. (Steps 2 and 3 are interchangeable.)4. Press Í repeatedly to rotate through the graph styles. The seven styles rotate in the same order in which they are listed in the table above.5. Press ~, }, or † when you have selected a style. Chapter 3: Function Graphing 70
Shading Above and BelowWhen you select é or ê for two or more functions, the TI-84 Plus rotates through four shadingpatterns.• Vertical lines shade the first function with a é or ê graph style.• Horizontal lines shade the second.• Negatively sloping diagonal lines shade the third.• Positively sloping diagonal lines shade the fourth.• The rotation returns to vertical lines for the fifth é or ê function, repeating the order described above.When shaded areas intersect, the patterns overlap.Note: When é or ê is selected for a Y= function that graphs a family of curves, such as Y1={1,2,3}X,the four shading patterns rotate for each member of the family of curves.Setting a Graph Style from a ProgramTo set the graph style from a program, select H:GraphStyle( from the PRGM CTL menu. To displaythis menu, press while in the program editor. function# is the number of the Y= function namein the current graphing mode. graphstyle# is an integer from 1 to 7 that corresponds to the graphstyle, as shown below.1 = ç (line) 5 = ë (path)2 = è (thick) 6 = ì (animate)3 = é (above) 7 = í (dot)4 = ê (below)GraphStyle(function#,graphstyle#)For example, when this program is executed in Func mode, GraphStyle(1,3) sets Y1 to é (above). Chapter 3: Function Graphing 71
Setting the Viewing Window VariablesThe TI-84 Plus Viewing WindowThe viewing window is the portion of the coordinate plane defined by Xmin, Xmax, Ymin, and Ymax.Xscl (X scale) defines the distance between tick marks on the x-axis. Yscl (Y scale) defines thedistance between tick marks on the y-axis. To turn off tick marks, set Xscl=0 and Yscl=0.Displaying the Window VariablesTo display the current window variable values, press p. The window editor above and to theright shows the default values in Func graphing mode and Radian angle mode. The windowvariables differ from one graphing mode to another.Xres sets pixel resolution (1 through 8) for function graphs only. The default is 1.• At Xres=1, functions are evaluated and graphed at each pixel on the x-axis.• At Xres=8, functions are evaluated and graphed at every eighth pixel along the x-axis.Note: Small Xres values improve graph resolution but may cause the TI-84 Plus to draw graphsmore slowly.Changing a Window Variable ValueTo change a window variable value from the window editor, follow these steps.1. Press † or } to move the cursor to the window variable you want to change.2. Edit the value, which can be an expression. • Enter a new value, which clears the original value. • Move the cursor to a specific digit, and then edit it.3. Press Í, †, or }. If you entered an expression, the TI-84 Plus evaluates it. The new value is stored.Note: Xmin<Xmax and Ymin<Ymax must be true in order to graph.Storing to a Window Variable from the Home Screen or a ProgramTo store a value, which can be an expression, to a window variable, begin on a blank line andfollow these steps. Chapter 3: Function Graphing 72
1. Enter the value you want to store.2. Press ¿.3. Press to display the VARS menu.4. Select 1:Window to display the Func window variables (X/Y secondary menu). • Press ~ to display the Par and Pol window variables (T/q secondary menu). • Press ~ ~ to display the Seq window variables (U/V/W secondary menu).5. Select the window variable to which you want to store a value. The name of the variable is pasted to the current cursor location.6. Press Í to complete the instruction.When the instruction is executed, the TI-84 Plus stores the value to the window variable anddisplays the value.@X and @YThe variables @X and @Y (items 8 and 9 on the VARS (1:Window) X/Y secondary menu; @X is alsoon the Window screen) define the distance from the center of one pixel to the center of anyadjacent pixel on a graph (graphing accuracy). @X and @Y are calculated from Xmin, Xmax, Ymin,and Ymax when you display a graph. Xmax – Xmin Ymax – Ymin X = -------------------------------------- - Y = -------------------------------------- - 94 62You can store values to @X and @Y. If you do, Xmax and Ymax are calculated from @X, Xmin, @Y,and Ymin.Note: The ZFrac ZOOM settings (Zfrac1/2, ZFrac1/3, ZFrac1/4, ZFrac1/5, ZFrac1/8, ZFrac1/10)change @X and @Y to fractional values. If fractions are not needed for your problem, you can adjust@X and @Y to suit your needs.Setting the Graph FormatDisplaying the Format SettingsTo display the format settings, press y .. The default settings are highlighted below.Note: You can also go to the Format Graph screen from the Mode screen by selecting YES at theGoTo Format Graph prompt. After you make changes, press zto return to the Mode screen.RectGC PolarGC Sets cursor coordinates.CoordOn CoordOff Sets coordinates display on or off.GridOff GridOn Sets grid off or on. Chapter 3: Function Graphing 73
AxesOn AxesOff Sets axes on or off.LabelOff LabelOn Sets axes label off or on.ExprOn ExprOff Sets expression display on or off.Format settings define a graph's appearance on the display. Format settings apply to all graphingmodes. Seq graphing mode has an additional mode setting (Chapter 6).Changing a Format SettingTo change a format setting, follow these steps.1. Press †, ~, }, and | as necessary to move the cursor to the setting you want to select.2. Press Í to select the highlighted setting.RectGC, PolarGCRectGC (rectangular graphing coordinates) displays the cursor location as rectangular coordinatesX and Y.PolarGC (polar graphing coordinates) displays the cursor location as polar coordinates R and q.The RectGC/PolarGC setting determines which variables are updated when you plot the graph,move the free-moving cursor, or trace.• RectGC updates X and Y; if CoordOn format is selected, X and Y are displayed.• PolarGC updates X, Y, R, and q; if CoordOn format is selected, R and q are displayed.CoordOn, CoordOffCoordOn (coordinates on) displays the cursor coordinates at the bottom of the graph. If ExprOffformat is selected, the function number is displayed in the top-right corner.CoordOff (coordinates off) does not display the function number or coordinates.GridOff, GridOnGrid points cover the viewing window in rows that correspond to the tick marks on each axis.GridOff does not display grid points.GridOn displays grid points.AxesOn, AxesOffAxesOn displays the axes. Chapter 3: Function Graphing 74
AxesOff does not display the axes.This overrides the LabelOff/ LabelOn format setting.LabelOff, LabelOnLabelOff and LabelOn determine whether to display labels for the axes (X and Y), if AxesOn formatis also selected.ExprOn, ExprOffExprOn and ExprOff determine whether to display the Y= expression when the trace cursor isactive. This format setting also applies to stat plots.When ExprOn is selected, the expression is displayed in the top-left corner of the graph screen.When ExprOff and CoordOn both are selected, the number in the top-right corner specifies whichfunction is being traced.Displaying GraphsDisplaying a New GraphTo display the graph of the selected function or functions, press s. TRACE, ZOOMinstructions, and CALC operations display the graph automatically. As the TI-84 Plus plots thegraph, the busy indicator is on. As the graph is plotted, X and Y are updated.Pausing or Stopping a GraphWhile plotting a graph, you can pause or stop graphing.• Press Í to pause; then press Í to resume.• Press É to stop; then press s to redraw.Smart GraphSmart Graph is a TI-84 Plus feature that redisplays the last graph immediately when you presss, but only if all graphing factors that would cause replotting have remained the same sincethe graph was last displayed.If you performed any of the following actions since the graph was last displayed, the TI-84 Plus willreplot the graph based on new values when you press s.• Changed a mode setting that affects graphs• Changed a function in the current picture• Selected or deselected a function or stat plot Chapter 3: Function Graphing 75
• Changed the value of a variable in a selected function• Changed a window variable or graph format setting• Cleared drawings by selecting ClrDraw• Changed a stat plot definitionOverlaying Functions on a GraphOn the TI-84 Plus, you can graph one or more new functions without replotting existing functions.For example, store sin(X) to Y1 in the Y= editor and press s. Then store cos(X) to Y2 andpress s again. The function Y2 is graphed on top of Y1, the original function.Graphing a Family of CurvesIf you enter a list (Chapter 11) as an element in an expression, the TI-84 Plus plots the function foreach value in the list, thereby graphing a family of curves. In Simul graphing-order mode, it graphsall functions sequentially for the first element in each list, and then for the second, and so on.{2,4,6}sin(X) graphs three functions: 2 sin(X), 4 sin(X), and 6 sin(X).{2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X) .Note: When using more than one list, the lists must have the same dimensions. Chapter 3: Function Graphing 76
Exploring Graphs with the Free-Moving CursorFree-Moving CursorWhen a graph is displayed, press |, ~, }, or † to move the cursor around the graph. When youfirst display the graph, no cursor is visible. When you press |, ~, }, or †, the cursor moves fromthe center of the viewing window.As you move the cursor around the graph, the coordinate values of the cursor location aredisplayed at the bottom of the screen if CoordOn format is selected. The Float/Fix decimal modesetting determines the number of decimal digits displayed for the coordinate values.To display the graph with no cursor and no coordinate values, press ' or Í. When youpress |, ~, }, or †, the cursor moves from the same position.Graphing AccuracyThe free-moving cursor moves from pixel to pixel on the screen. When you move the cursor to apixel that appears to be on the function, the cursor may be near, but not actually on, the function.The coordinate value displayed at the bottom of the screen actually may not be a point on thefunction. To move the cursor along a function, use r.The coordinate values displayed as you move the cursor approximate actual math coordinates,accurate to within the width and height of the pixel. As Xmin, Xmax, Ymin, and Ymax get closertogether (as in a Zoom In) graphing accuracy increases, and the coordinate values more closelyapproximate the math coordinates. Free- moving cursor appears to be on the curveExploring Graphs with TRACEBeginning a TraceUse TRACE to move the cursor from one plotted point to the next along a function. To begin atrace, press r. If the graph is not displayed already, press r to display it. The trace cursoris on the first selected function in the Y= editor, at the middle X value on the screen. The cursorcoordinates are displayed at the bottom of the screen if CoordOn format is selected. TheY= expression is displayed in the top-left corner of the screen, if ExprOn format is selected. Chapter 3: Function Graphing 77
Moving the Trace CursorTo move the TRACE cursor do this:To the previous or next plotted point, press | or ~.Five plotted points on a function (Xres press y | or y ~.affects this),To any valid X value on a function, enter a value, and then press Í.From one function to another, press } or †.When the trace cursor moves along a function, the Y value is calculated from the X value; that is,Y=Yn(X). If the function is undefined at an X value, the Y value is blank. Trace cursor on the curveIf you move the trace cursor beyond the top or bottom of the screen, the coordinate values at thebottom of the screen continue to change appropriately.Moving the Trace Cursor from Function to FunctionTo move the trace cursor from function to function, press † and }. The cursor follows the order ofthe selected functions in the Y= editor. The trace cursor moves to each function at the same Xvalue. If ExprOn format is selected, the expression is updated.Moving the Trace Cursor to Any Valid X ValueTo move the trace cursor to any valid X value on the current function, enter the value. When youenter the first digit, an X= prompt and the number you entered are displayed in the bottom-leftcorner of the screen. You can enter an expression at the X= prompt. The value must be valid forthe current viewing window. When you have completed the entry, press Í to move the cursor.Note: This feature does not apply to stat plots. Chapter 3: Function Graphing 78
Panning to the Left or RightIf you trace a function beyond the left or right side of the screen, the viewing window automaticallypans to the left or right. Xmin and Xmax are updated to correspond to the new viewing window.Quick ZoomWhile tracing, you can press Í to adjust the viewing window so that the cursor locationbecomes the center of the new viewing window, even if the cursor is above or below the display.This allows panning up and down. After Quick Zoom, the cursor remains in TRACE.Leaving and Returning to TRACEWhen you leave and return to TRACE, the trace cursor is displayed in the same location it was inwhen you left TRACE, unless Smart Graph has replotted the graph.Using TRACE in a ProgramOn a blank line in the program editor, press r. The instruction Trace is pasted to the cursorlocation. When the instruction is encountered during program execution, the graph is displayedwith the trace cursor on the first selected function. As you trace, the cursor coordinate values areupdated. When you finish tracing the functions, press Í to resume program execution.Exploring Graphs with the ZOOM InstructionsZOOM MenuTo display the ZOOM menu, press q. You can adjust the viewing window of the graph quickly inseveral ways. All ZOOM instructions are accessible from programs.ZOOM MEMORY1: ZBox Draws a box to define the viewing window.2: Zoom In Magnifies the graph around the cursor.3: Zoom Out Views more of a graph around the cursor.4: ZDecimal Sets @X and @Y to 0.1.5: ZSquare Sets equal-size pixels on the X and Y axes.6: ZStandard Sets the standard window variables.7: ZTrig Sets the built-in trig window variables.8: ZInteger Sets integer values on the X and Y axes.9: ZoomStat Sets the values for current stat lists.0: ZoomFit Fits YMin and YMax between XMin and XMax.A: ZQuadrant1 Displays the portion of the graph that is in quadrant 1 Chapter 3: Function Graphing 79
ZOOM MEMORYB: ZFrac1/2 Sets the window variables so that you can trace in increments of , if possible. Sets @X and @Y to .C: ZFrac1/3 Sets the window variables so that you can trace in increments of , if possible. Sets @X and @Y to .D: ZFrac1/4 Sets the window variables so that you can trace in increments of , if possible. Sets @X and @Y to .E: ZFrac1/5 Sets the window variables so that you can trace in increments of , if possible. Sets @X and @Y to .F: ZFrac1/8 Sets the window variables so that you can trace in increments of , if possible. Sets @X and @Y to .G: ZFrac1/10 Sets the window variables so that you can trace in increments of , if possible. Sets @X and @Y to .Note: You can adjust all window variables from the VARS menu by pressing 1:Window andthen selecting the variable from the X/Y, T/q, or U/V/W menu.Zoom CursorWhen you select 1:ZBox, 2:Zoom In, or 3:Zoom Out, the cursor on the graph becomes the zoomcursor (+), a smaller version of the free-moving cursor (+).ZBoxTo define a new viewing window using ZBox, follow these steps.1. Select 1:ZBox from the ZOOM menu. The zoom cursor is displayed at the center of the screen.2. Move the zoom cursor to any spot you want to define as a corner of the box, and then press Í. When you move the cursor away from the first defined corner, a small, square dot indicates the spot.3. Press |, }, ~, or †. As you move the cursor, the sides of the box lengthen or shorten proportionately on the screen. Note: To cancel ZBox before you press Í, press '.4. When you have defined the box, press Í to replot the graph. Chapter 3: Function Graphing 80
To use ZBox to define another box within the new graph, repeat steps 2 through 4. To cancel ZBox,press '.Zoom In, Zoom OutZoom In magnifies the part of the graph that surrounds the cursor location. Zoom Out displays agreater portion of the graph, centered on the cursor location. The XFact and YFact settingsdetermine the extent of the zoom.To zoom in on a graph, follow these steps.1. Check XFact and YFact; change as needed.2. Select 2:Zoom In from the ZOOM menu. The zoom cursor is displayed.3. Move the zoom cursor to the point that is to be the center of the new viewing window.4. Press Í. The TI-83 Plus adjusts the viewing window by XFact and YFact; updates the window variables; and replots the selected functions, centered on the cursor location.5. Zoom in on the graph again in either of two ways. • To zoom in at the same point, press Í. • To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing window, and then press Í.To zoom out on a graph, select 3:Zoom Out and repeat steps 3 through 5.To cancel Zoom In or Zoom Out, press '.ZDecimalZDecimal replots the functions immediately. It updates the window variables to preset values, asshown below. These values set @X and @Y equal to 0.1 and set the X and Y value of each pixel toone decimal place.Xmin=L4.7 Ymin=L3.1Xmax=4.7 Ymax=3.1Xscl=1 Yscl=1ZSquareZSquare replots the functions immediately. It redefines the viewing window based on the currentvalues of the window variables. It adjusts in only one direction so that @X=@Y, which makes thegraph of a circle look like a circle. Xscl and Yscl remain unchanged. The midpoint of the currentgraph (not the intersection of the axes) becomes the midpoint of the new graph. Chapter 3: Function Graphing 81
ZStandardZStandard replots the functions immediately. It updates the window variables to the standardvalues shown below.Xmin=L10 Ymin=L10 Xres=1Xmax=10 Ymax=10Xscl=1 Yscl=1ZTrigZTrig replots the functions immediately. It updates the window variables to preset values that areappropriate for plotting trig functions. Those preset values in Radian mode are shown below.Xmin=L(47à24)p (decimal equivalent) Ymin=L4Xmax=(47à24)p (decimal equivalent) Ymax=4Xscl=p/2 (decimal equivalent) Yscl=1ZIntegerZInteger redefines the viewing window to the dimensions shown below. To use ZInteger, move thecursor to the point that you want to be the center of the new window, and then press Í;ZInteger replots the functions.@X=1 Xscl=10@Y=1 Yscl=10ZoomStatZoomStat redefines the viewing window so that all statistical data points are displayed. For regularand modified box plots, only Xmin and Xmax are adjusted.ZoomFitZoomFit replots the functions immediately. ZoomFit recalculates YMin and YMax to include theminimum and maximum Y values of the selected functions between the current XMin and XMax.XMin and XMax are not changed.ZQuadrant1ZQuandrant1 replots the function immediately. It redefines the window settings so that onlyquadrant 1 is displayed. Chapter 3: Function Graphing 82
ZFrac1/2ZFrac1/2 replots the functions immediately. It updates the window variables to preset values, asshown below. These values set @X and @Y equal to 1/2 and set the X and Y value of each pixel toone decimal place.Xmin=L47/2 Ymin=L31/2Xmax=47/2 Ymax=31/2Xscl=1 Yscl=1ZFrac1/3ZFrac1/3 replots the functions immediately. It updates the window variables to preset values, asshown below. These values set @X and @Y equal to 1/3 and set the X and Y value of each pixel toone decimal place.Xmin=L47/3 Ymin=L31/3Xmax=47/3 Ymax=31/3Xscl=1 Yscl=1ZFrac1/4ZFrac1/4 replots the functions immediately. It updates the window variables to preset values, asshown below. These values set @X and @Y equal to 1/4 and set the X and Y value of each pixel toone decimal place.Xmin=L47/4 Ymin=L31/4Xmax=47/4 Ymax=31/4Xscl=1 Yscl=1ZFrac1/5ZFrac1/5 replots the functions immediately. It updates the window variables to preset values, asshown below. These values set @X and @Y equal to 1/5 and set the X and Y value of each pixel toone decimal place.Xmin=L47/5 Ymin=L31/5Xmax=47/5 Ymax=31/5Xscl=1 Yscl=1 Chapter 3: Function Graphing 83
ZFrac1/8ZDecimal replots the functions immediately. It updates the window variables to preset values, asshown below. These values set @X and @Y equal to 1/8 and set the X and Y value of each pixel toone decimal place.Xmin=L47/8 Ymin=L31/8Xmax=47/8 Ymax=31/8Xscl=1 Yscl=1ZFrac1/10ZFrac1/10 replots the functions immediately. It updates the window variables to preset values, asshown below. These values set @X and @Y equal to 1/10 and set the X and Y value of each pixel toone decimal place.Xmin=L47/10 Ymin=L31/10Xmax=47/10 Ymax=31/10Xscl=1 Yscl=1Using ZOOM MEMORYZOOM MEMORY MenuTo display the ZOOM MEMORY menu, press q ~.ZOOM MEMORY1: ZPrevious Uses the previous viewing window.2: ZoomSto Stores the user-defined window.3: ZoomRcl Recalls the user-defined window.4: SetFactors... Changes Zoom In and Zoom Out factors.ZPreviousZPrevious replots the graph using the window variables of the graph that was displayed before youexecuted the last ZOOM instruction.ZoomStoZoomSto immediately stores the current viewing window. The graph is displayed, and the values ofthe current window variables are stored in the user-defined ZOOM variables ZXmin, ZXmax, ZXscl,ZYmin, ZYmax, ZYscl, and ZXres.These variables apply to all graphing modes. For example, changing the value of ZXmin in Funcmode also changes it in Par mode. Chapter 3: Function Graphing 84
ZoomRclZoomRcl graphs the selected functions in a user-defined viewing window. The user-definedviewing window is determined by the values stored with the ZoomSto instruction. The windowvariables are updated with the user-defined values, and the graph is plotted.ZOOM FACTORSThe zoom factors, XFact and YFact, are positive numbers (not necessarily integers) greater than orequal to 1. They define the magnification or reduction factor used to Zoom In or Zoom Out around apoint.Checking XFact and YFactTo display the ZOOM FACTORS screen, where you can review the current values for XFact andYFact, select 4:SetFactors from the ZOOM MEMORY menu. The values shown are the defaults.Changing XFact and YFactYou can change XFact and YFact in either of two ways.• Enter a new value. The original value is cleared automatically when you enter the first digit.• Place the cursor on the digit you want to change, and then enter a value or press { to delete it.Using ZOOM MEMORY Menu Items from the Home Screen or a ProgramFrom the home screen or a program, you can store directly to any of the user-defined ZOOMvariables.From a program, you can select the ZoomSto and ZoomRcl instructions from the ZOOM MEMORYmenu. Chapter 3: Function Graphing 85
Using the CALC (Calculate) OperationsCALCULATE MenuTo display the CALCULATE menu, press y /. Use the items on this menu to analyze thecurrent graph functions.CALCULATE1: value Calculates a function Y value for a given X.2: zero Finds a zero (x-intercept) of a function.3: minimum Finds a minimum of a function.4: maximum Finds a maximum of a function.5: intersect Finds an intersection of two functions.6: dy/dx Finds a numeric derivative of a function.7: ‰f(x)dx Finds a numeric integral of a function.valuevalue evaluates one or more currently selected functions for a specified value of X.Note: When a value is displayed for X, press ' to clear the value. When no value is displayed,press ' to cancel the value operation.To evaluate a selected function at X, follow these steps.1. Select 1:value from the CALCULATE menu. The graph is displayed with X= in the bottom-left corner.2. Enter a real value, which can be an expression, for X between Xmin and Xmax.3. Press Í.The cursor is on the first selected function in the Y= editor at the X value you entered, and thecoordinates are displayed, even if CoordOff format is selected.To move the cursor from function to function at the entered X value, press } or †. To restore thefree-moving cursor, press | or ~. Chapter 3: Function Graphing 86
zerozero finds a zero (x-intercept or root) of a function using solve(. Functions can have more than onex-intercept value; zero finds the zero closest to your guess.The time zero spends to find the correct zero value depends on the accuracy of the values youspecify for the left and right bounds and the accuracy of your guess.To find a zero of a function, follow these steps.1. Select 2:zero from the CALCULATE menu. The current graph is displayed with Left Bound? in the bottom-left corner.2. Press } or † to move the cursor onto the function for which you want to find a zero.3. Press | or ~ (or enter a value) to select the x-value for the left bound of the interval, and then press Í. A 4 indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottom-left corner. Press | or ~ (or enter a value) to select the x-value for the right bound, and then press Í. A 3 indicator on the graph screen shows the right bound. Guess? is then displayed in the bottom-left corner.4. Press | or ~ (or enter a value) to select a point near the zero of the function, between the bounds, and then press Í.The cursor is on the solution and the coordinates are displayed, even if CoordOff format isselected. To move to the same x-value for other selected functions, press } or †. To restore thefree-moving cursor, press | or ~.minimum, maximumminimum and maximum find a minimum or maximum of a function within a specified interval to atolerance of 1âL5.To find a minimum or maximum, follow these steps.1. Select 3:minimum or 4:maximum from the CALCULATE menu. The current graph is displayed.2. Select the function and set left bound, right bound, and guess as described for zero. Chapter 3: Function Graphing 87
The cursor is on the solution, and the coordinates are displayed, even if you have selectedCoordOff format; Minimum or Maximum is displayed in the bottom-left corner.To move to the same x-value for other selected functions, press } or †. To restore the free-moving cursor, press | or ~.intersectintersect finds the coordinates of a point at which two or more functions intersect using solve(. Theintersection must appear on the display to use intersect.To find an intersection, follow these steps.1. Select 5:intersect from the CALCULATE menu. The current graph is displayed with First curve? in the bottom-left corner.2. Press † or }, if necessary, to move the cursor to the first function, and then press Í. Second curve? is displayed in the bottom-left corner.3. Press † or }, if necessary, to move the cursor to the second function, and then press Í.4. Press ~ or | to move the cursor to the point that is your guess as to location of the intersection, and then press Í.The cursor is on the solution and the coordinates are displayed, even if CoordOff format isselected. Intersection is displayed in the bottom-left corner. To restore the free-moving cursor,press |, }, ~, or †.dy/dxdy/dx (numerical derivative) finds the numerical derivative (slope) of a function at a point, withH=1âL3.To find a function's slope at a point, follow these steps.1. Select 6:dy/dx from the CALCULATE menu. The current graph is displayed.2. Press } or † to select the function for which you want to find the numerical derivative.3. Press | or ~ (or enter a value) to select the X value at which to calculate the derivative, and then press Í.The cursor is on the solution and the numerical derivative is displayed.To move to the same x-value for other selected functions, press } or †. To restore the free-moving cursor, press | or ~. Chapter 3: Function Graphing 88
‰f(x)dx‰f(x)dx (numerical integral) finds the numerical integral of a function in a specified interval. It usesthe fnInt( function, with a tolerance of H=1âL3.To find the numerical integral of a function, follow these steps.1. Select 7:‰f(x)dx from the CALCULATE menu. The current graph is displayed with Lower Limit? in the bottom-left corner.2. Press } or † to move the cursor to the function for which you want to calculate the integral.3. Set lower and upper limits as you would set left and right bounds for zero. The integral value is displayed, and the integrated area is shaded. Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that invokes Smart Graph to clear the shaded area. Chapter 3: Function Graphing 89
Chapter 4:Parametric GraphingGetting Started: Path of a BallGetting Started is a fast-paced introduction. Read the chapter for details.Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 metersper second, at an initial angle of 25 degrees with the horizontal from ground level. How far doesthe ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity.For initial velocity v o and angle q, the position of the ball as a function of time has horizontal andvertical components. 1Horizontal: X1(t)=tv 0cos(q) Vertical: Y1(t)=tv 0sin(q)N -- gt2 - 2The vertical and horizontal vectors of the ball's motion also will be graphed.Vertical vector: X2(t)=0 Y2(t)=Y1(t)Horizontal vector: X3(t)=X1(t) Y3(t)=0Gravity constant: g=9.8 m/sec21. Press z. Press † † † ~ Í to select Par mode. Press † † ~ Í to select Simul for simultaneous graphing of all three parametric equations in this example.2. Press } } } ~ Í to go to the Format Graph screen. Press † † † ~ Í to select AxesOff, which turns off the axes. Chapter 4: Parametric Graphing 90
12. Press r to obtain numerical results and answer the questions at the beginning of this section. Tracing begins at Tmin on the first parametric equation (X1T and Y1T). As you press ~ to trace the curve, the cursor follows the path of the ball over time. The values for X (distance), Y (height), and T (time) are displayed at the bottom of the screen.Defining and Displaying Parametric GraphsTI-84 Plus Graphing Mode SimilaritiesThe steps for defining a parametric graph are similar to the steps for defining a function graph.Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 detailsaspects of parametric graphing that differ from function graphing.Setting Parametric Graphing ModeTo display the mode screen, press z. To graph parametric equations, you must selectparametric graphing mode before you enter window variables and before you enter thecomponents of parametric equations.Displaying the Parametric Y= EditorAfter selecting parametric graphing mode, press o to display the parametric Y= editor.In this editor, you can display and enter both the X and Y components of up to six equations, X1Tand Y1T through X6T and Y6T. Each is defined in terms of the independent variable T. A commonapplication of parametric graphs is graphing equations over time.Selecting a Graph StyleThe icons to the left of X1T through X6T represent the graph style of each parametric equation. Thedefault in parametric mode is ç (line), which connects plotted points. Line, è (thick), ë (path),ì (animate), and í (dot) styles are available for parametric graphing. Chapter 4: Parametric Graphing 92
Defining and Editing Parametric EquationsTo define or edit a parametric equation, follow the steps in Chapter 3 for defining a function orediting a function. The independent variable in a parametric equation is T. In parametric graphingmode, you can enter the parametric variable T in either of two ways.• Press ".• Press ƒ [T].Two components, X and Y, define a single parametric equation. You must define both of them.Selecting and Deselecting Parametric EquationsThe TI-84 Plus graphs only the selected parametric equations. In the Y= editor, a parametricequation is selected when the = signs of both the X and Y components are highlighted. You mayselect any or all of the equations X1T and Y1T through X6T and Y6T.To change the selection status, move the cursor onto the = sign of either the X or Y componentand press Í. The status of both the X and Y components is changed.Setting Window VariablesTo display the window variable values, press p. These variables define the viewing window.The values below are defaults for parametric graphing in Radian angle mode.Tmin=0 Smallest T value to evaluateTmax=6.2831853... Largest T value to evaluate (2p)Tstep=.1308996... T value increment T window variables.Setting the Graph FormatTo display the current graph format settings, press y .. Chapter 3 describes the formatsettings in detail. The other graphing modes share these format settings; Seq graphing mode hasan additional axes format setting. Chapter 4: Parametric Graphing 93
Displaying a GraphWhen you press s, the TI-84 Plus plots the selected parametric equations. It evaluates the Xand Y components for each value of T (from Tmin to Tmax in intervals of Tstep), and then plotseach point defined by X and Y. The window variables define the viewing window.As the graph is plotted, X, Y, and T are updated.Smart Graph applies to parametric graphs.Window Variables and Y.VARS MenusYou can perform these actions from the home screen or a program.• Access functions by using the name of the X or Y component of the equation as a variable.• Store parametric equations.• Select or deselect parametric equations.• Store values directly to window variables.Exploring Parametric GraphsFree-Moving CursorThe free-moving cursor in parametric graphing works the same as in Func graphing.In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected,X and Y are displayed.In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q aredisplayed. Chapter 4: Parametric Graphing 94
TRACETo activate TRACE, press r. When TRACE is active, you can move the trace cursor along thegraph of the equation one Tstep at a time. When you begin a trace, the trace cursor is on the firstselected function at Tmin. If ExprOn is selected, then the function is displayed.In RectGC format, TRACE updates and displays the values of X, Y, and T if CoordOn format is on.In PolarGC format, X, Y, R, q and T are updated; if CoordOn format is selected, R, q, and T aredisplayed. The X and Y (or R and q) values are calculated from T.To move five plotted points at a time on a function, press y | or y ~. If you move the cursorbeyond the top or bottom of the screen, the coordinate values at the bottom of the screen continueto change appropriately.Quick Zoom is available in parametric graphing; panning is not.Moving the Trace Cursor to Any Valid T ValueTo move the trace cursor to any valid T value on the current function, enter the number. When youenter the first digit, a T= prompt and the number you entered are displayed in the bottom-left cornerof the screen. You can enter an expression at the T= prompt. The value must be valid for thecurrent viewing window. When you have completed the entry, press Í to move the cursor.ZOOMZOOM operations in parametric graphing work the same as in Func graphing. Only the X (Xmin,Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.The T window variables (Tmin, Tmax, and Tstep) are only affected when you select ZStandard. TheVARS ZOOM secondary menu ZT/Zq items 1:ZTmin, 2:ZTmax, and 3:ZTstep are the zoom memoryvariables for parametric graphing.CALCCALC operations in parametric graphing work the same as in Func graphing. The CALCULATEmenu items available in parametric graphing are 1:value, 2:dy/dx, 3:dy/dt, and 4:dx/dt. Chapter 4: Parametric Graphing 95
Chapter 5:Polar GraphingGetting Started: Polar RoseGetting Started is a fast-paced introduction. Read the chapter for details.The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and thenexplore the appearance of the rose for other values of A and B.1. Press z to display the MODE screen. Press † † † ~ ~ Í to select Pol graphing mode. Select the defaults (the options on the left) for the other mode settings.2. Press o to display the polar Y= editor. Press 8 ˜ 2.5 " ¤ Í to define r1.3. Press q 6 to select 6:ZStandard and graph the equation in the standard viewing window. The graph shows only five petals of the rose, and the rose does not appear to be symmetrical. This is because the standard window sets qmax=2p and defines the window, rather than the pixels, as square.4. Press p to display the window variables. Press † 4 y B to increase the value of qmax to 4p.5. Press q 5 to select 5:ZSquare and plot the graph.6. Repeat steps 2 through 5 with new values for the variables A and B in the polar equation r1=Asin(Bq). Observe how the new values affect the graph. Chapter 5: Polar Graphing 96
Defining and Displaying Polar GraphsTI-84 Plus Graphing Mode SimilaritiesThe steps for defining a polar graph are similar to the steps for defining a function graph. Chapter5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects ofpolar graphing that differ from function graphing.Setting Polar Graphing ModeTo display the mode screen, press z. To graph polar equations, you must select Pol graphingmode before you enter values for the window variables and before you enter polar equations.Displaying the Polar Y= EditorAfter selecting Pol graphing mode, press o to display the polar Y= editor.In this editor, you can enter and display up to six polar equations, r1 through r6. Each is defined interms of the independent variable q.Selecting Graph StylesThe icons to the left of r1 through r6 represent the graph style of each polar equation. The defaultin Pol graphing mode is ç (line), which connects plotted points. Line, è (thick), ë (path), ì (animate),and í (dot) styles are available for polar graphing.Defining and Editing Polar EquationsTo define or edit a polar equation, follow the steps in Chapter 3 for defining a function or editing afunction. The independent variable in a polar equation is q. In Pol graphing mode, you can enterthe polar variable q in either of two ways.• Press ".• Press ƒ [q].Selecting and Deselecting Polar EquationsThe TI-84 Plus graphs only the selected polar equations. In the Y= editor, a polar equation isselected when the = sign is highlighted. You may select any or all of the equations. Chapter 5: Polar Graphing 97
To change the selection status, move the cursor onto the = sign, and then press Í.Setting Window VariablesTo display the window variable values, press p. These variables define the viewing window.The values below are defaults for Pol graphing in Radian angle mode.qmin=0 Smallest q value to evaluateqmax=6.2831853... Largest q value to evaluate (2p)qstep=.1308996... Increment between q values q window variables.Setting the Graph FormatTo display the current graph format settings, press y .. Chapter 3 describes the formatsettings in detail. The other graphing modes share these format settings.Displaying a GraphWhen you press s, the TI-84 Plus plots the selected polar equations. It evaluates R for eachvalue of q (from qmin to qmax in intervals of qstep) and then plots each point. The windowvariables define the viewing window.As the graph is plotted, X, Y, R, and q are updated.Smart Graph applies to polar graphs.Window Variables and Y.VARS MenusYou can perform these actions from the home screen or a program.• Access functions by using the name of the equation as a variable. These function names are available on the YVARS shortcut menu (t a). Chapter 5: Polar Graphing 98
• Store polar equations.• Select or deselect polar equations.• Store values directly to window variables.Exploring Polar GraphsFree-Moving CursorThe free-moving cursor in PolTo activate TRACE, press r. When TRACE is active, you can move the trace cursor along thegraph of the equation one qstep at a time. When you begin a trace, the trace cursor is on the firstselected function at qmin. If ExprOn format is selected, then the equation is displayed.In RectGC format, TRACE updates the values of X, Y, and q; if CoordOn format is selected, X, Y,and q are displayed. In PolarGC format, TRACE updates X, Y, R, and q; if CoordOn format isselected, R and q are displayed.To move five plotted points at a time on a function, press y | or y ~. If you move the tracecursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screencontinue to change appropriately.Quick Zoom is available in Pol graphing mode; panning is not.Moving the Trace Cursor to Any Valid Theta ValueTo move the trace cursor to any valid q value on the current function, enter the number. When youenter the first digit, a q= prompt and the number you entered are displayed in the bottom-left cornerof the screen. You can enter an expression at the q= prompt. The value must be valid for thecurrent viewing window. When you complete the entry, press Í to move the cursor. Chapter 5: Polar Graphing 99
ZOOMZOOM operations in Pol graphing work the same as in Func graphing. Only the X (Xmin, Xmax, andXscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.The q window variables (qmin, qmax, and qstep) are not affected, except when you selectZStandard. The VARS ZOOM secondary menu ZT/Zq items 4:Zqmin, 5:Zqmax, and 6:Zqstep arezoom memory variables for Pol graphing.CALCCALC operations in Pol graphing work the same as in Func graphing. The CALCULATE menuitems available in Pol graphing are 1:value, 2:dy/dx, and 3:dr/dq. Chapter 5: Polar Graphing 100
Chapter 6:Sequence GraphingGetting Started: Forest and TreesNote: Getting Started is a fast-paced introduction. Read the chapter for details.A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will beharvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forestsize stabilize? If so, in how many years and with how many trees?1. Press z. Press † † † ~ ~ ~ Í to select Seq graphing mode.2. Press y . and select Time axes format and ExprOn format if necessary.3. Press o. If the graph-style icon is not ç (dot), press | |, press Í until ç is displayed, and then press ~ ~.4. Press ~ 3 to select iPart( (integer part) because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain. Press Ë 8 y [u] £ " ¹ 1 ¤ to define the number of trees after each harvest. Press à 1000 ¤ to define the new trees. Press † 4000 to define the number of trees at the beginning of the program. Note: Be sure to press y [u], not t [U]. [u] is the second function of the ¬ key.5. Press p 0 to set nMin=0. Press † 50 to set nMax=50. nMin and nMax evaluate forest size over 50 years. Set the other window variables. PlotStart=1 Xmin=0 Ymin=0 PlotStep=1 Xmax=50 Ymax=6000 Xscl=10 Yscl=1000 Chapter 6: Sequence Graphing 101
6. Press r. Tracing begins at nMin (the start of the forestry plan). Press ~ to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for n (number of years), X (X=n, because n is plotted on the x-axis), and Y (tree count) are displayed at the bottom. When will the forest stabilize? With how many trees?Defining and Displaying Sequence GraphsTI-84 Plus Graphing Mode SimilaritiesThe steps for defining a sequence graph are similar to the steps for defining a function graph.Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 detailsaspects of sequence graphing that differ from function graphing.Setting Sequence Graphing ModeTo display the mode screen, press z. To graph sequence functions, you must select Seqgraphing mode before you enter window variables and before you enter sequence functions.Sequence graphs automatically plot in Simul mode, regardless of the current plotting-order modesetting.TI-84 Plus Sequence Functions u, v, and wThe TI-84 Plus has three sequence functions that you can enter from the keyboard: u, v, and w.They are second functions of the ¬, −, and ® keys. Press y [u] to enter u, for example.You can define sequence functions in terms of:• The independent variable n• The previous term in the sequence function, such as u(nN1)• The term that precedes the previous term in the sequence function, such as u(nN2)• The previous term or the term that precedes the previous term in another sequence function, such as u(nN1) or u(nN2) referenced in the sequence v(n).Note: Statements in this chapter about u(n) are also true for v(n) and w(n); statements about u(nN1)are also true for v(nN1) and w(nN1); statements about u(nN2) are also true for v(nN2) and w(nN2).Displaying the Sequence Y= EditorAfter selecting Seq mode, press o to display the sequence Y= editor. Chapter 6: Sequence Graphing 102
In this editor, you can display and enter sequences for u(n), v(n), and w(n). Also, you can edit thevalue for nMin, which is the sequence window variable that defines the minimum n value toevaluate.The sequence Y= editor displays the nMin value because of its relevance to u(nMin), v(nMin), andw(nMin), which are the initial values for the sequence equations u(n), v(n), and w(n), respectively.nMin in the Y= editor is the same as nMin in the window editor. If you enter a new value for nMin inone editor, the new value for nMin is updated in both editors.Note: Use u(nMin), v(nMin), or w(nMin) only with a recursive sequence, which requires an initialvalue.Selecting Graph StylesThe icons to the left of u(n), v(n), and w(n) represent the graph style of each sequence (Chapter 3).The default in Seq mode is í (dot), which shows discrete values. Dot, ç (line), and è (thick) stylesare available for sequence graphing. Graph styles are ignored in Web format.Selecting and Deselecting Sequence FunctionsThe TI-84 Plus graphs only the selected sequence functions. In the Y= editor, a sequence functionis selected when the = signs of both u(n)= and u(nMin)= are highlighted.To change the selection status of a sequence function, move the cursor onto the = sign of thefunction name, and then press Í. The status is changed for both the sequence function u(n)and its initial value u(nMin).Defining and Editing a Sequence FunctionTo define or edit a sequence function, follow the steps in Chapter 3 for defining a function. Theindependent variable in a sequence is n.In Seq graphing mode, you can enter the sequence variable in either of two ways.• Press ".• Press y N [N].You can enter the function name from the keyboard (y [u], y [v], y [w]).• To enter the function name u, press y [u] (above ¬).• To enter the function name v, press y [v] (above −). Chapter 6: Sequence Graphing 103
• To enter the function name w, press y [w] (above ®).Generally, sequences are either nonrecursive or recursive. Sequences are evaluated only atconsecutive integer values. n is always a series of consecutive integers, starting at zero or anypositive integer.Nonrecursive SequencesIn a nonrecursive sequence, the nth term is a function of the independent variable n. Each term isindependent of all other terms.For example, in the nonrecursive sequence below, you can calculate u(5) directly, without firstcalculating u(1) or any previous term.The sequence equation above returns the sequence 2, 4, 6, 8, 10, … for n = 1, 2, 3, 4, 5, … .Note: You may leave blank the initial value u(nMin) when calculating nonrecursive sequences.Recursive SequencesIn a recursive sequence, the nth term in the sequence is defined in relation to the previous term orthe term that precedes the previous term, represented by u(nN1) and u(nN2). A recursive sequencemay also be defined in relation to n, as in u(n)=u(nN1)+n.For example, in the sequence below you cannot calculate u(5) without first calculating u(1), u(2),u(3), and u(4).Using an initial value u(nMin) = 1, the sequence above returns 1, 2, 4, 8, 16, ... .Note: On the TI-84 Plus, you must type each character of the terms. For example, to enter u(nN1),press y [u] £ " ¹ À ¤.Recursive sequences require an initial value or values, since they reference undefined terms.• If each term in the sequence is defined in relation to the previous term, as in u(nN1), you must specify an initial value for the first term. Chapter 6: Sequence Graphing 104
• If each term in the sequence is defined in relation to the term that precedes the previous term, as in u(nN2), you must specify initial values for the first two terms. Enter the initial values as a list enclosed in brackets ({ }){ } with commas separating the values.The value of the first term is 0 and the value of the second term is 1 for the sequence u(n).Setting Window VariablesTo display the window variables, press p. These variables define the viewing window. Thevalues below are defaults for Seq graphing in both Radian and Degree angle modes.nMin=1 Smallest n value to evaluatenMax=10 Largest n value to evaluatePlotStart=1 First term number to be plottedPlotStep=1 Incremental n value (for graphing onlynMin must be an integer | 0. nMax, PlotStart, and PlotStep must be integers | 1.nMin is the smallest n value to evaluate. nMin also is displayed in the sequence Y= editor. nMax isthe largest n value to evaluate. Sequences are evaluated at u(nMin), u(nMin+1), u(nMin+2), ... ,u(nMax).PlotStart is the first term to be plotted. PlotStart=1 begins plotting on the first term in the sequence.If you want plotting to begin with the fifth term in a sequence, for example, set PlotStart=5. The firstfour terms are evaluated but are not plotted on the graph. Chapter 6: Sequence Graphing 105
PlotStep is the incremental n value for graphing only. PlotStep does not affect sequence evaluation;it only designates which points are plotted on the graph. If you specify PlotStep=2, the sequence isevaluated at each consecutive integer, but it is plotted on the graph only at every other integer.Selecting Axes CombinationsSetting the Graph FormatTo display the current graph format settings, press y .. Chapter 3 describes the formatsettings in detail. The other graphing modes share these format settings. The axes setting on thetop line of the screen is available only in Seq mode.Time Web uv vw uw Type of sequence plot (axes)RectGC Polar GC Rectangular or polar outputCoordOn CoordOff Cursor coordinate display on/offGridOff GridOn Grid display off or onAxesOn AxesOff Axes display on or offLableOff LabelOn Axes label display off or onExprOn ExprOff Expression display on or offSetting Axes FormatFor sequence graphing, you can select from five axes formats. The table below shows the valuesthat are plotted on the x-axis and y-axis for each axes setting. Axes Setting x-axis y-axis Time n u(n), v(n), w(n) Web u(nN1), v(nN1), w(nN1) u(n), v(n), w(n) uv u(n) v(n) vw v(n) w(n) uw u(n) w(n)Displaying a Sequence GraphTo plot the selected sequence functions, press s. As a graph is plotted, the TI-84 Plusupdates X, Y, and n.Smart Graph applies to sequence graphs (Chapter 3). Chapter 6: Sequence Graphing 106
Exploring Sequence GraphsFree-Moving CursorThe free-moving cursor in SeqThe axes format setting affects TRACE.When Time, uv, vw, or uw axes format is selected, TRACE moves the cursor along the sequenceone PlotStep increment at a time. To move five plotted points at once, press y ~ or y |.• When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by PlotStart, even if it is outside the viewing window.• Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, pressÍÍ. The trace cursor returns to nMin.In Web format, the trail of the cursor helps identify points with attracting and repelling behavior inthe sequence. When you begin a trace, the cursor is on the x-axis at the initial value of the firstselected function.Note: To move the cursor to a specified n during a trace, enter a value for n, and press Í. Forexample, to quickly return the cursor to the beginning of the sequence, paste nMin to the n= promptand press Í.Moving the Trace Cursor to Any Valid n ValueTo move the trace cursor to any valid n value on the current function, enter the number. When youenter the first digit, an n= prompt and the number you entered are displayed in the bottom-leftcorner of the screen. You can enter an expression at the n= prompt. The value must be valid for thecurrent viewing window. When you have completed the entry, press Í to move the cursor.ZOOMZOOM operations in Seq graphing work the same as in Func graphing. Only the X (Xmin, Xmax,and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. Chapter 6: Sequence Graphing 107
PlotStart, PlotStep, nMin, and nMax are only affected when you select ZStandard. The VARS Zoomsecondary menu ZU items 1 through 7 are the ZOOM MEMORY variables for Seq graphing.CALCThe only CALC operation available in Seq graphing is value.• When Time axes format is selected, value displays Y (the u(n) value) for a specified n value.• When Web axes format is selected, value draws the web and displays Y (the u(n) value) for a specified n value.• When uv, vw, or uw axes format is selected, value displays X and Y according to the axes format setting. For example, for uv axes format, X represents u(n) and Y represents v(n).Evaluating u, v, and wTo enter the sequence names u, v, or w, press y [u], y [v], or y [w]. You can evaluate thesenames in any of three ways.• Calculate the nth value in a sequence.• Calculate a list of values in a sequence.• Generate a sequence with u(nstart,nstop[,nstep]). nstep is optional; default is 1.Graphing Web PlotsGraphing a Web PlotTo select Web axes format, press y . ~ Í. A web plot graphs u(n) versus u(nN1),which you can use to study long-term behavior (convergence, divergence, or oscillation) of arecursive sequence. You can see how the sequence may change behavior as its initial valuechanges.Valid Functions for Web PlotsWhen Web axes format is selected, a sequence will not graph properly or will generate an error.• It must be recursive with only one recursion level (u(nN1) but not u(nN2)).• It cannot reference n directly.• It cannot reference any defined sequence except itself. Chapter 6: Sequence Graphing 108
Displaying the Graph ScreenIn Web format, press s to display the graph screen. The TI-84 Plus:• Draws a y=x reference line in AxesOn format.• Plots the selected sequences with u(nN1) as the independent variable.Note: A potential convergence point occurs whenever a sequence intersects the y=x referenceline. However, the sequence may or may not actually converge at that point, depending on thesequence's initial value.Drawing the WebTo activate the trace cursor, press r. The screen displays the sequence and the current n, X,and Y values (X represents u(nN1) and Y represents u(n)). Press ~ repeatedly to draw the webstep by step, starting at nMin. In Web format, the trace cursor follows this course.1. It starts on the x-axis at the initial value u(nMin) (when PlotStart=1).2. It moves vertically (up or down) to the sequence.3. It moves horizontally to the y=x reference line.4. It repeats this vertical and horizontal movement as you continue to press ~.Using Web Plots to Illustrate ConvergenceExample: Convergence1. Press o in Seq mode to display the sequence Y= editor. Make sure the graph style is set to í (dot), and then define nMin, u(n) and u(nMin) as shown below u(n) = -.8u(n-1) + 3.6.2. Press y . Í to set Time axes format.3. Press p and set the variables as shown below. nMin=1 Xmin=0 Ymin=L10 nMax=25 Xmax=25 Ymax=10 PlotStart=1 Xscl=1 Yscl=1 PlotStep=14. Press s to graph the sequence. Chapter 6: Sequence Graphing 109
5. Press y . and select the Web axes setting.6. Press p and change the variables below. Xmin=L10 Xmax=107. Press s to graph the sequence.8. Press r, and then press ~ to draw the web. The displayed cursor coordinates n, X (u(nN1)), and Y (u(n)) change accordingly. When you press ~, a new n value is displayed, and the trace cursor is on the sequence. When you press ~ again, the n value remains the same, and the cursor moves to the y=x reference line. This pattern repeats as you trace the web.Graphing Phase PlotsGraphing with uv, vw, and uwThe phase-plot axes settings uv, vw, and uw show relationships between two sequences. To selecta phase-plot axes setting, press y ., press ~ until the cursor is on uv, vw, or uw, and thenpress Í. Axes Setting x-axis y-axis uv u(n) v(n) vw v(n) w(n) uw u(n) w(n)Example: Predator-Prey ModelUse the predator-prey model to determine the regional populations of a predator and its prey thatwould maintain population equilibrium for the two species.This example uses the model to determine the equilibrium populations of foxes and rabbits, withinitial populations of 200 rabbits (u(nMin)) and 50 foxes (v(nMin)). Chapter 6: Sequence Graphing 110
5. Press r ~ to individually trace the number of rabbits (u(n)) and foxes (v(n)) over time (n). Note: Press a number, and then press Í to jump to a specific n value (month) while in TRACE.6. Press y . ~ ~ Í to select uv axes format.7. Press p and change these variables as shown below. Xmin=84 Ymin=25 Xmax=237 Ymax=75 Xscl=50 Yscl=108. Press r. Trace both the number of rabbits (X) and the number of foxes (Y) through 400 generations. Note: When you press r, the equation for u is displayed in the top-left corner. Press } or † to see the equation for v.Comparing TI-84 Plus and TI-82 Sequence VariablesSequences and Window VariablesRefer to the table if you are familiar with the TI-82. It shows TI-84 Plus sequences and sequencewindow variables, as well as their TI-82 counterparts.TI-84 Plus TI-82In the Y= editor: u(n) Un u(nMin) UnStart (window variable) v(n) Vn v(nMin) VnStart (window variable) w(n) not available w(nMin) not availableIn the window editor: nMin nStart Chapter 6: Sequence Graphing 112
Chapter 7:TablesGetting Started: Roots of a FunctionGetting Started is a fast-paced introduction. Read the chapter for details.Evaluate the function Y = X3 N 2X at each integer between L10 and 10. How many sign changesoccur, and at what X values?1. Press z † † † Í to set Func graphing mode.2. Press o. Press " 3 to select 3. Then press ¹ 2 " to enter the function Y1=X3N2X.3. Press y - to display the TABLE SETUP screen. Press Ì 10 Í to set TblStart=L10. Press 1 Í to set @Tbl=1. Press Í to select Indpnt: Auto (automatically generated independent values). Press † Í to select Depend: Auto (automatically generated dependent values).4. Press y 0 to display the table screen. Note: The message on the entry line, "Press + for @Tbl" is a reminder that you can change @Tbl from this table view. The entry line is cleared when you press any key.5. Press † until you see the sign changes in the value of Y1. How many sign changes occur, and at what X values? In this case, you can also see the roots of the function by finding when Y1=0. You can explore changes in X by pressing à to display the @TTbl prompt, entering a new value, and searching for your answer. Chapter 7: Tables 114
Setting Up the TableTABLE SETUP ScreenTo display the TABLE SETUP screen, press y -.TblStart, @TblTblStart (table start) defines the initial value for the independent variable. TblStart applies onlywhen the independent variable is generated automatically (when Indpnt: Auto is selected).@Tbl (table step) defines the increment for the independent variable.Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: AskSelections Table CharacteristicsIndpnt: Auto Values are displayed automatically in both the independent-Depend: Auto variable column and in all dependent-variable columns.Indpnt: Ask The table is empty. When you enter a value for the independentDepend: Auto variable, all corresponding dependent-variable values are calculated and displayed automatically.Indpnt: Auto Values are displayed automatically for the independent variable.Depend: Ask To generate a value for a dependent variable, move the cursor to that cell and press Í.Indpnt: Ask The table is empty; enter values for the independent variable. ToDepend: Ask generate a value for a dependent variable, move the cursor to that cell and press Í.Setting Up the Table from the Home Screen or a ProgramTo store a value to TblStart, @Tbl, or Tbl[nput from the home screen or a program, select thevariable name from the VARS TABLE secondary menu. TblZnput is a list of independent-variablevalues in the current table.When you press y - in the program editor, you can select IndpntAuto, IndpntAsk,DependAuto, and DependAsk. Chapter 7: Tables 115
Defining the Dependent VariablesDefining Dependent Variables from the Y= EditorIn the Y= editor, enter the functions that define the dependent variables. Only functions that areselected in the Y= editor are displayed in the table. The current graphing mode is used. Inparametric mode, you must define both components of each parametric equation (Chapter 4).Editing Dependent Variables from the Table EditorTo edit a selected Y= function from the table editor, follow these steps.1. Press y 0 to display the table, then press ~ or | to move the cursor to a dependent- variable column.2. Press } until the cursor is on the function name at the top of the column. The function is displayed on the bottom line.3. Press Í. The cursor moves to the bottom line. Edit the function.4. Press Í or †. The new values are calculated. The table and the Y= function are updated automatically. Note: You also can use this feature to view the function that defines a dependent variable without having to leave the table. Chapter 7: Tables 116
Displaying the TableThe TableTo display the table, press y 0.Note: The table abbreviates the values, if necessary. Current cellIndependent-variable Dependent-variablevalues in the first values in the secondcolumn and third columns Current cell's full value @Tbl" is on the entry line. ThisNote: When the table first displays, the message "Press + formessage reminds you that you can press à to change @Tbl at any time. When you press any key,the message disappears.Independent and Dependent VariablesThe current graphing mode determines which independent and dependent variables are displayedin the table (Chapter 1). In the table above, for example, the independent variable X and thedependent variables Y1 and Y2 are displayed because Func graphing mode is set. Independent VariableGraphing Mode Dependent VariableFunc (function) X Y1 through Y9, and Y0Par (parametric) T X1T/Y1T through X6T/Y6TPol (polar) q r1 through r6Seq (sequence) n u(n), v(n), and w(n)Clearing the Table from the Home Screen or a ProgramFrom the home screen, select the ClrTable instruction from the CATALOG. To clear the table, pressÍ.From a program, select 9:ClrTable from the PRGM I/O menu or from the CATALOG. The table iscleared upon execution. If IndpntAsk is selected, all independent and dependent variable valueson the table are cleared. If DependAsk is selected, all dependent variable values on the table arecleared. Chapter 7: Tables 117
Scrolling Independent-Variable ValuesIf Indpnt: Auto is selected, you can press } and † in the independent-variable column to displaymore values. As you scroll the column, the corresponding dependent-variable values also aredisplayed. All dependent-variable values may not be displayed if Depend: Ask is selected.Note: You can scroll back from the value entered for TblStart. As you scroll, TblStart is updatedautomatically to the value shown on the top line of the table. In the example above, TblStart=0 and@Tbl=1 generates and displays values of X=0, …, 6; but you can press } to scroll back and displaythe table for X=M1, …, 5.Changing Table Settings from the Table ViewYou can change table settings from the table view by highlighting a value in the table, pressing Ã,and entering a new @ value.1. Press o and then press 1 t ^ 1 2 ~ " to enter the function Y1=1/2x.2. Press y 0.3. Press † † † to move the cursor to highlight 3, and then press Ã.4. Press 1 t ^ 1 2 to change the table settings to view changes in X in increments of 1/2. Chapter 7: Tables 118
5. Press Í.Displaying Other Dependent VariablesIf you have defined more than two dependent variables, the first two selected Y= functions aredisplayed initially. Press ~ or | to display dependent variables defined by other selected Y=functions. The independent variable always remains in the left column, except during a trace withparametric graphing mode and G-T split-screen mode set.Note: To simultaneously display two dependent variables on the table that are not defined asconsecutive Y= functions, go to the Y= editor and deselect the Y= functions between the two youwant to display. For example, to simultaneously display Y4 and Y7 on the table, go to the Y= editorand deselect Y5 and Y6. Chapter 7: Tables 119
6. Press Í. The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph.Consider repeating this activity with the mode set tothe number of decimal places desired. The first screenshows four decimal places. The second screen showsthe decimal setting at Float.Using the DRAW MenuDRAW MenuTo display the DRAW menu, press y <. The TI-84 Plus's interpretation of these instructionsdepends on whether you accessed the menu from the home screen or the program editor ordirectly from a graph.DRAW POINTS STO1: ClrDraw Clears all drawn elements.2: Line( Draws a line segment between 2 points.3: Horizontal Draws a horizontal line.4: Vertical Draws a vertical line.5: Tangent( Draws a line segment tangent to a function.6: DrawF Draws a function.7: Shade( Shades an area between two functions.8: DrawInv Draws the inverse of a function.9: Circle( Draws a circle.0: Text( Draws text on a graph screen.A: Pen Activates the free-form drawing tool.Before Drawing on a GraphThe DRAW instructions draw on top of graphs. Therefore, before you use the DRAW instructions,consider whether you want to perform one or more of the following actions.• Change the mode settings on the mode screen.• Change the format settings on the format screen. You can press y . or use the shortcut on the mode screen to go to the format graph screen. Chapter 8: Draw Instructions 121
• Enter or edit functions in the Y= editor.• Select or deselect functions in the Y= editor.• Change the window variable values.• Turn stat plots on or off.• Clear existing drawings with ClrDraw.Note: If you draw on a graph and then perform any of the actions listed above, the graph isreplotted without the drawings when you display the graph again. Before you clear drawings, youcan store them with StorePic.Drawing on a GraphYou can use any DRAW menu instructions except DrawInv to draw on Func, Par, Pol, and Seqgraphs. DrawInv is valid only in Func graphing. The coordinates for all DRAW instructions are thedisplay's x-coordinate and y-coordinate values.You can use most DRAW menu and DRAW POINTS menu instructions to draw directly on a graph,using the cursor to identify the coordinates. You also can execute these instructions from the homescreen or from within a program. If a graph is not displayed when you select a DRAW menuinstruction, the home screen is displayed.Clearing DrawingsClearing Drawings When a Graph Is DisplayedAll points, lines, and shading drawn on a graph with DRAW instructions are temporary.To clear drawings from the currently displayed graph, select 1:ClrDraw from the DRAW menu. Thecurrent graph is replotted and displayed with no drawn elements.Clearing Drawings from the Home Screen or a ProgramTo clear drawings on a graph from the home screen or a program, begin on a blank line on thehome screen or in the program editor. Select 1:ClrDraw from the DRAW menu. The instruction iscopied to the cursor location. Press Í.When ClrDraw is executed, it clears all drawings from the current graph and displays the messageDone. When you display the graph again, all drawn points, lines, circles, and shaded areas will begone.Note: Before you clear drawings, you can store them with StorePic. Chapter 8: Draw Instructions 122
Drawing Line SegmentsDrawing a Line Segment Directly on a GraphTo draw a line segment when a graph is displayed, follow these steps.1. Select 2:Line( from the DRAW menu.2. Place the cursor on the point where you want the line segment to begin, and then press Í.3. Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press Í.To continue drawing line segments, repeat steps 2 and 3. To cancel Line(, press '.Drawing a Line Segment from the Home Screen or a ProgramLine( also draws a line segment between the coordinates (X1,Y1) and (X2,Y2). The values may beentered as expressions.Line(X1,Y1,X2,Y2)To erase a line segment, enter Line(X1,Y1,X2,Y2,0) Chapter 8: Draw Instructions 123
Drawing Horizontal and Vertical LinesDrawing a Line Directly on a GraphTo draw a horizontal or vertical line when a graph is displayed, follow these steps.1. Select 3:Horizontal or 4:Vertical from the DRAW menu. A line is displayed that moves as you move the cursor.2. Place the cursor on the y-coordinate (for horizontal lines) or x-coordinate (for vertical lines) through which you want the drawn line to pass.3. Press Í to draw the line on the graph.To continue drawing lines, repeat steps 2 and 3.To cancel Horizontal or Vertical, press '.Drawing a Line from the Home Screen or a ProgramHorizontal (horizontal line) draws a horizontal line at Y=y. y, which can be an expression but not alist.Horizontal yVertical (vertical line) draws a vertical line at X=x. x, which can be an expression but not a list.Vertical xTo instruct the TI-84 Plus to draw more than one horizontal or vertical line, separate eachinstruction with a colon ( : ).MathPrint™ Classic Chapter 8: Draw Instructions 124
Drawing Tangent LinesDrawing a Tangent Line Directly on a GraphTo draw a tangent line when a graph is displayed, follow these steps.1. Select 5:Tangent( from the DRAW menu.2. Press † and } to move the cursor to the function for which you want to draw the tangent line. The current graph's Y= function is displayed in the top-left corner, if ExprOn is selected.3. Press ~ and | or enter a number to select the point on the function at which you want to draw the tangent line.4. Press Í. In Func mode, the X value at which the tangent line was drawn is displayed on the bottom of the screen, along with the equation of the tangent line. In all other modes, the dy/dx value is displayed.5. Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for X and the equation for Y.Drawing a Tangent Line from the Home Screen or a ProgramTangent( (tangent line) draws a line tangent to expression in terms of X, such as Y1 or X2, at pointX=value. X can be an expression. expression is interpreted as being in Func mode. Chapter 8: Draw Instructions 125
Tangent(expression,value)Drawing Functions and InversesDrawing a FunctionDrawF (draw function) draws expression as a function in terms of X on the current graph. When youselect 6:DrawF from the DRAW menu, the TI-84 Plus returns to the home screen or the programeditor. DrawF is not interactive.DrawF expressionNote: You cannot use a list in expression to draw a family of curves.Drawing an Inverse of a FunctionDrawInv (draw inverse) draws the inverse of expression by plotting X values on the y-axis and Yvalues on the x-axis. When you select 8:DrawInv from the DRAW menu, the TI-84 Plus returns tothe home screen or the program editor. DrawInv is not interactive. DrawInv works in Func modeonly.DrawInv expressionNote: You cannot use a list of expressions with DrawInv. Chapter 8: Draw Instructions 126
Shading Areas on a GraphShading a GraphTo shade an area on a graph, select 7:Shade( from the DRAW menu. The instruction is pasted tothe home screen or to the program editor.Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres])MathPrint™ ClassicShade( draws lowerfunc and upperfunc in terms of X on the current graph and shades the area that isspecifically above lowerfunc and below upperfunc. Only the areas where lowerfunc < upperfunc areshaded.Xleft and Xright, if included, specify left and right boundaries for the shading. Xleft and Xright must benumbers between Xmin and Xmax, which are the defaults.pattern specifies one of four shading patterns.pattern=1 vertical (default)pattern=2 horizontalpattern=3 negative—slope 45¡pattern=4 positive—slope 45¡patres specifies one of eight shading resolutions.patres=1 shades every pixel (default)patres=2 shades every second pixelpatres=3 shades every third pixelpatres=4 shades every fourth pixelpatres=5 shades every fifth pixelpatres=6 shades every sixth pixelpatres=7 shades every seventh pixelpatres=8 shades every eighth pixelDrawing CirclesDrawing a Circle Directly on a GraphTo draw a circle directly on a displayed graph using the cursor, follow these steps.1. Select 9:Circle( from the DRAW menu. Chapter 8: Draw Instructions 127
2. Place the cursor at the center of the circle you want to draw. Press Í.3. Move the cursor to a point on the circumference. Press Í to draw the circle on the graph.Note: This circle is displayed as circular, regardless of the window variable values, because youdrew it directly on the display. When you use the Circle( instruction from the home screen or aprogram, the current window variables may distort the shape.To continue drawing circles, repeat steps 2 and 3. To cancel Circle(, press '.Drawing a Circle from the Home Screen or a ProgramCircle( draws a circle with center (X,Y) and radius. These values can be expressions.Circle(X,Y,radius)Note: When you use Circle( on the home screen or from a program, the current window valuesmay distort the drawn circle. Use ZSquare (Chapter 3) before drawing the circle to adjust thewindow variables and make the circle circular.Placing Text on a GraphPlacing Text Directly on a GraphTo place text on a graph when the graph is displayed, follow these steps.1. Select 0:Text( from the DRAW menu.2. Place the cursor where you want the text to begin.3. Enter the characters. Press ƒ or y 7 to enter letters and q. You may enter TI-84 Plus functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph.To cancel Text(, press '. Chapter 8: Draw Instructions 128
Placing Text on a Graph from the Home Screen or a ProgramText( places on the current graph the characters comprising value, which can include TI-84 Plusfunctions and instructions. The top-left corner of the first character is at pixel (row,column), where rowis an integer between 0 and 57 and column is an integer between 0 and 94. Both row and column canbe expressions.Text(row,column,value,value…)value can be text enclosed in quotation marks ( " ), or it can be an expression. The TI-84 Plus willevaluate an expression and display the result with up to 10 characters.ClassicSplit ScreenOn a Horiz split screen, the maximum value for row is 25. On a G-T split screen, the maximumvalue for row is 45, and the maximum value for column is 46.Using Pen to Draw on a GraphUsing Pen to Draw on a GraphPen draws directly on a graph only. You cannot execute Pen from the home screen or a program.You can capture the image you created using TI-Connect™ software and save it to your computerfor homework or teaching material or store it as a picture file on your TI-84 Plus (see Storing GraphPictures below).To draw on a displayed graph, follow these steps.1. Select A:Pen from the DRAW menu.2. Place the cursor on the point where you want to begin drawing. Press Í to turn on the pen.3. Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time.4. Press Í to turn off the pen. Chapter 8: Draw Instructions 129
For example, Pen was used to create the arrow pointing to the local minimum of the selectedfunction. Note: To continue drawing on the graph, move the cursor to a new position where you want to begin drawing again, and then repeat steps 2, 3, and 4. To cancel Pen, press '.Drawing Points on a GraphDRAW POINTS MenuTo display the DRAW POINTS menu, press y < ~. The TI-84 Plus's interpretation of theseinstructions depends on whether you accessed this menu from the home screen or the programeditor or directly from a graph.DRAW POINTS STO1: Pt-On( Turns on a point.2: Pt-Off( Turns off a point.3: Pt-Change( Toggles a point on or off.4: Pxl-On( Turns on a pixel.5: Pxl-Off( Turns off a pixel.6: Pxl-Change( Toggles a pixel on or off.7: pxl-Test( Returns 1 if pixel on, 0 if pixel off.Drawing Points Directly on a Graph with Pt-On(To draw a point on a graph, follow these steps.1. Select 1:Pt-On( from the DRAW POINTS menu.2. Move the cursor to the position where you want to draw the point.3. Press Í to draw the point.To continue drawing points, repeat steps 2 and 3. To cancel Pt-On(, press '. Chapter 8: Draw Instructions 130
Erasing Points with Pt-Off(To erase (turn off) a drawn point on a graph, follow these steps.1. Select 2:Pt-Off( (point off) from the DRAW POINTS menu.2. Move the cursor to the point you want to erase.3. Press Í to erase the point.To continue erasing points, repeat steps 2 and 3. To cancel Pt-Off(, press '.Changing Points with Pt-Change(To change (toggle on or off) a point on a graph, follow these steps.1. Select 3:Pt-Change( (point change) from the DRAW POINTS menu.2. Move the cursor to the point you want to change.3. Press Í to change the point's on/off status.To continue changing points, repeat steps 2 and 3. To cancel Pt-Change(, press '.Drawing Points from the Home Screen or a ProgramPt-On( (point on) turns on the point at (X=x,Y=y). Pt-Off( turns the point off. Pt-Change( toggles thepoint on or off. mark is optional; it determines the point's appearance; specify 1, 2, or 3, where: 1 = ¦ (dot; default) 2 = › (box) 3 = + (cross)Pt-On(x,y[,mark])Pt-Off(x,y[,mark])Pt-Change(x,y)Note: If you specified mark to turn on a point with Pt-On(, you must specify mark when you turn offthe point with Pt-Off(. Pt-Change( does not have the mark option.Drawing PixelsTI-84 Plus PixelsA pixel is a square dot on the TI-84 Plus display. The Pxl- (pixel) instructions let you turn on, turnoff, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from Chapter 8: Draw Instructions 131
the DRAW POINTS menu, the TI-84 Plus returns to the home screen or the program editor. Thepixel instructions are not interactive.Turning On and Off Pixels with Pxl-On( and Pxl-Off(Pxl-On( (pixel on) turns on the pixel at (row,column), where row is an integer between 0 and 62 andcolumn is an integer between 0 and 94.Pxl-Off( turns the pixel off. Pxl-Change( toggles the pixel on and off.Pxl-On(row,column)Pxl-Off(row,column)Pxl-Change(row,column)Using pxl-Test(pxl-Test( (pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is turned off onthe current graph. row must be an integer between 0 and 62. column must be an integer between 0and 94.pxl-Test(row,column)Split ScreenOn a Horiz split screen, the maximum value for row is 30 for Pxl-On(, Pxl-Off(, Pxl-Change(, andpxl-Test(.On a G-T split screen, the maximum value for row is 50 and the maximum value for column is 46 forPxl-On(, Pxl-Off(, Pxl-Change(, and pxl-Test(. Chapter 8: Draw Instructions 132
Storing Graph Pictures (Pic)DRAW STO MenuTo display the DRAW STO menu, press y < |. When you select an instruction from theDRAW STO menu, the TI-84 Plus returns to the home screen or the program editor. The pictureand graph database instructions are not interactive.DRAW POINTS STO1: StorePic Stores the current picture.2: RecallPic Recalls a saved picture.3: StoreGDB Stores the current graph database.4: RecallGDB Recalls a saved graph database.Storing a Graph PictureYou can store up to 10 graph pictures, each of which is an image of the current graph display, inpicture variables Pic1 through Pic9, or Pic0. Later, you can superimpose the stored picture onto adisplayed graph from the home screen or a program.A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does notinclude axes labels, lower and upper bound indicators, prompts, or cursor coordinates. Any partsof the display hidden by these items are stored with the picture.To store a graph picture, follow these steps.1. Select 1:StorePic from the DRAW STO menu. StorePic is pasted to the current cursor location.2. Enter the number (from 1 to 9, or 0) of the picture variable to which you want to store the picture. For example, if you enter 3, the TI-84 Plus will store the picture to Pic3. Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to StorePic.3. Press Í to display the current graph and store the picture. Chapter 8: Draw Instructions 133
Recalling Graph Pictures (Pic)Recalling a Graph PictureTo recall a graph picture, follow these steps.1. Select 2:RecallPic from the DRAW STO menu. RecallPic is pasted to the current cursor location.2. Enter the number (from 1 to 9, or 0) of the picture variable from which you want to recall a picture. For example, if you enter 3, the TI-84 Plus will recall the picture stored to Pic3. Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to RecallPic.3. Press Í to display the current graph with the picture superimposed on it. Note: Pictures are drawings. You cannot trace a curve that is part of a picture.Deleting a Graph PictureTo delete graph pictures from memory, use the MEMORY MANAGEMENT/DELETE secondary menu(Chapter 18).Storing Graph Databases (GDB)What Is a Graph Database?A graph database (GDB) contains the set of elements that defines a particular graph. You canrecreate the graph from these elements. You can store up to 10 GDBs in variables GDB1 throughGDB9, or GDB0 and recall them to recreate graphs.A GDB stores five elements of a graph.• Graphing mode• Window variables• Format settings• All functions in the Y= editor and the selection status of each• Graph style for each Y= functionGDBs do not contain drawn items or stat plot definitions.Storing a Graph DatabaseTo store a graph database, follow these steps. Chapter 8: Draw Instructions 134
1. Select 3:StoreGDB from the DRAW STO menu. StoreGDB is pasted to the current cursor location.2. Enter the number (from 1 to 9, or 0) of the GDB variable to which you want to store the graph database. For example, if you enter 7, the TI-84 Plus will store the GDB to GDB7. Note: You also can select a variable from the GDB secondary menu ( 3). The variable is pasted next to StoreGDB.3. Press Í to store the current database to the specified GDB variable.Recalling Graph Databases (GDB)Recalling a Graph DatabaseCAUTION: When you recall a GDB, it replaces all existing Y= functions. Consider storing thecurrent Y= functions to another database before recalling a stored GDB.To recall a graph database, follow these steps.1. Select 4:RecallGDB from the DRAW STO menu. RecallGDB is pasted to the current cursor location.2. Enter the number (from 1 to 9, or 0) of the GDB variable from which you want to recall a GDB. For example, if you enter 7, the TI-84 Plus will recall the GDB stored to GDB7. Note: You also can select a variable from the GDB secondary menu ( 3). The variable is pasted next to RecallGDB.3. Press Í to replace the current GDB with the recalled GDB. The new graph is not plotted. The TI-84 Plus changes the graphing mode automatically, if necessary.Deleting a Graph DatabaseTo delete a GDB from memory, use the MEMORY MANAGEMENT/DELETE secondary menu(Chapter 18). Chapter 8: Draw Instructions 135
Chapter 9:Split ScreenGetting Started: Exploring the Unit CircleGetting Started is a fast-paced introduction. Read the chapter for details.Use G-T (graph-table) split-screen mode to explore the unit circle and its relationship to thenumeric values for the commonly used trigonometric angles of 0¡ 30¡, 45¡, 60¡, 90¡, and so on.1. Press z to display the mode screen. Press † † ~ Í to select Degree mode. Press † ~ Í to select Par (parametric) graphing mode. Press † † † † ~ ~ Í to select G-T (graph- table) split-screen mode.2. Press † † † † ~ Í to display the format screen. Press † † † † † ~ Í to select ExprOff.3. Press o to display the Y= editor for Par graphing mode. Press ™ " ¤ Í to store cos(T) to X1T. Press ÷ ˜ " ¤ Í to store sin(T) to Y1T.4. Press p to display the window editor. Enter these values for the window variables. Tmin=0 Xmin=L2.3 Ymin=L2.5 Tmax=360 Xmax=2.3 Ymax=2.5 Tstep=15 Xscl=1 Yscl=15. Press r. On the left, the unit circle is graphed parametrically in Degree mode and the trace cursor is activated. When T=0 (from the graph trace coordinates), you can see from the table on the right that the value of X1T (cos(T)) is 1 and Y1T (sin(T)) is 0. Press ~ to move the cursor to the next 15¡ angle increment. As you trace around the circle in steps of 15¡, an approximation of the standard value for each angle is highlighted in the table.6. Press y - and change Indpnt to Ask. Chapter 9: Split Screen 136
7. Press y 0 to make the table portion of the split screen active.Using Split ScreenSetting a Split-Screen ModeTo set a split-screen mode, press z, and then move the cursor to Horiz or G-T and press Í.• Select Horiz (horizontal) to display the graph screen and another screen split horizontally.• Select G-T (graph-table) to display the graph screen and table screen split vertically. $ $The split screen is activated when you press any key that applies to either half of the split screen.If stat plots are turned on, the plots are shown along with the x-y plots in graphs. Press y 0to make the table portion of the split screen active and to display the list data. Press † or } tohighlight a value you want to edit, and then enter a new value directly in the table to overwrite theprevious value. Press ~ repeatedly to display each column of data (both table and list data). Chapter 9: Split Screen 137
Split-screen display with both x-y plots and stat plotsSome screens are never displayed as split screens. For example, if you press z in Horiz or G-Tmode, the mode screen is displayed as a full screen. If you then press a key that displays eitherhalf of a split screen, such as r, the split screen returns.When you press a key or key combination in either Horiz or G-T mode, the cursor is placed in thehalf of the display to which that key applies. For example, if you press r, the cursor is placedin the half where the graph is displayed. If you press y 0, the cursor is placed in the halfwhere the table is displayed.The TI-84 Plus will remain in split-screen mode until you change back to Full screen mode.Horiz (Horizontal) Split ScreenHoriz ModeIn Horiz (horizontal) split-screen mode, a horizontal line splits the screen into top and bottomhalves.The top half displays the graph.The bottom half displays any of these screens.• Home screen (four lines)• Y= editor (four lines)• Stat list editor (two rows)• Window editor (three settings)• Table editor (two rows)Moving from Half to Half in Horiz ModeTo use the top half of the split screen: Chapter 9: Split Screen 138
• Press s or r.• Select a ZOOM or CALC operation.To use the bottom half of the split screen:• Press any key or key combination that displays the home screen.• Press o (Y= editor).• Press … Í (stat list editor).• Press p (window editor).• Press y 0 (table editor).Full Screens in Horiz ModeAll other screens are displayed as full screens in Horiz split-screen mode.To return to the Horiz split screen from a full screen when in Horiz mode, press any key or keycombination that displays the graph, home screen, Y= editor, stat list editor, window editor, or tableeditor.G-T (Graph-Table) Split ScreenG-T ModeIn G-T (graph-table) split-screen mode, a vertical line splits the screen into left and right halves.The left half displays all active graphs and plots.The right half displays either table data corresponding to the graph at the left or list datacorresponding to the plot at the left.Moving from Half to Half in G-T ModeTo use the left half of the split screen:• Press s or r.• Select a ZOOM or CALC operation.To use the right half of the split screen, press y 0. If the values on the right are list data,these values can be edited similarly to using the Stat List Editor. Chapter 9: Split Screen 139
Using TRACE in G-T ModeAs you press | or ~ to move the trace cursor along a graph in the split screen's left half in G-Tmode, the table on the right half automatically scrolls to match the current cursor values. If morethan one graph or plot is active, you can press } or † to select a different graph or plot.Note: When you trace in Par graphing mode, both components of an equation (XnT and YnT) aredisplayed in the two columns of the table. As you trace, the current value of the independentvariable T is displayed on the graph.Full Screens in G-T ModeAll screens other than the graph and the table are displayed as full screens in G-T split-screenmode.To return to the G-T split screen from a full screen when in G-T mode, press any key or keycombination that displays the graph or the table.TI-84 Plus Pixels in Horiz and G-T ModesTI-84 Plus Pixels in Horiz and G-T ModesNote: Each set of numbers in parentheses above represents the row and column of a corner pixel,which is turned on.DRAW POINTS Menu Pixel InstructionsFor Pxl-On(, Pxl-Off(, Pxl-Change(, and pxl-Test(:• In Horiz mode, row must be {30; column must be {94.• In G-T mode, row must be {50; column must be {46.Pxl-On(row,column) Chapter 9: Split Screen 140
DRAW Menu Text( InstructionFor the Text( instruction:• In Horiz mode, row must be {25; column must be {94.• In G-T mode, row must be {45; column must be {46.Text(row,column,"text")PRGM I/O Menu Output( InstructionFor the Output( instruction:• In Horiz mode, row must be {4; column must be {16.• In G-T mode, row must be {8; column must be {16.Output(row,column,"text")Note: The Output( instruction can only be used within a program.Setting a Split-Screen Mode from the Home Screen or a ProgramTo set Horiz or G-T from a program, follow these steps.1. Press z while the cursor is on a blank line in the program editor.2. Select Horiz or G-T.The instruction is pasted to the cursor location. The mode is set when the instruction isencountered during program execution. It remains in effect after execution.Note: You also can paste Horiz or G-T to the home screen or program editor from the CATALOG(Chapter 15). Chapter 9: Split Screen 141
Chapter 10:MatricesGetting Started: Using the MTRX Shortcut MenuGetting Started is a fast-paced introduction. Read the chapter for details.You can use the MTRX shortcut menu (t `) to enter a quick matrix calculation on the homescreen or in the Y= editor.Note: To input a fraction in a matrix, delete the pre-populated zero first.Example: Add the following matrices: and store the result to matrix C.1. Press t ` to display the quick matrix editor. The default size of the matrix is two rows by two columns.2. Press † † to highlight OK and then press Í.3. Press 2 ~ k 3 ~ 5 ~ 8 ~ to create the first matrix.4. Press à t ` † † Í 4 ~ 3 ~ 2 ~ 1 ~ Í to create the second matrix and perform the calculation.5. Press v y Q and select 3:[C]. Chapter 10: Matrices 142
6. Press Í to store the matrix to [C].In the matrix editor (y Q), you can see thatmatrix [C] has dimension 2x2.You can press ~ ~ to display the EDIT screen andthen select [C] to edit it.Getting Started: Systems of Linear EquationsGetting Started is a fast-paced introduction. Read the chapter for details.Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-84 Plus, you can solve asystem of linear equations by entering the coefficients as elements in a matrix, and then using rref(to obtain the reduced row-echelon form.1. Press y . Press ~ ~ to display the MATRX EDIT menu. Press 1 to select 1: [A].2. Press 2 Í 4 Í to define a 2×4 matrix. The rectangular cursor indicates the current element. Ellipses (...) indicate additional columns beyond the screen.3. Press 1 Í to enter the first element. The rectangular cursor moves to the second column of the first row. Chapter 10: Matrices 143
4. Press 2 Í 3 Í 3 Í to complete the first row for X + 2Y + 3Z = 3.5. Press 2 Í 3 Í 4 Í 3 Í to enter the second row for 2X + 3Y + 4Z = 3.6. Press y 5 to return to the home screen. If necessary, press ' to clear the home screen. Press y ~ to display the MATRX MATH menu. Press } to wrap to the end of the menu. Select B:rref( to copy rref( to the home screen.7. Press y 1 to select 1: [A] from the MATRX NAMES menu. Press ¤ Í. The reduced row-echelon form of the matrix is displayed and stored in Ans. 1X N 1Z = L3 therefore X = L3 + Z 1Y + 2Z = 3 therefore Y = 3 N 2ZDefining a MatrixWhat Is a Matrix?A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix editor.You can also define a matrix using the MTRX shortcut menu (t `).The TI-84 Plus has 10matrix variables, [A] through [J]. You can define a matrix directly in an expression. A matrix,depending on available memory, may have up to 99 rows or columns. You can store only realnumbers in TI-84 Plus matrices. Fractions are stored as real numbers and can be used inmatrices.Selecting a MatrixBefore you can define or display a matrix in the editor, you first must select the matrix name. To doso, follow these steps.1. Press y | to display the MATRX EDIT menu. The dimensions of any previously defined matrices are displayed.2. Select the matrix you want to define. The MATRX EDIT screen is displayed. Chapter 10: Matrices 144
Accepting or Changing Matrix DimensionsThe dimensions of the matrix (row × column) are displayed on the top line. The dimensions of a newmatrix are 1 × 1. You must accept or change the dimensions each time you edit a matrix. When youselect a matrix to define, the cursor highlights the row dimension.• To accept the row dimension, press Í.• To change the row dimension, enter the number of rows (up to 99), and then press Í.The cursor moves to the column dimension, which you must accept or change the same way youaccepted or changed the row dimension. When you press Í, the rectangular cursor moves tothe first matrix element.Viewing and Editing Matrix ElementsDisplaying Matrix ElementsAfter you have set the dimensions of the matrix, you can view the matrix and enter values for thematrix elements. In a new matrix, all values are zero.Select the matrix from the MATRX EDIT menu and enter or accept the dimensions. The centerportion of the matrix editor displays up to seven rows and three columns of a matrix, showing thevalues of the elements in abbreviated form if necessary. The full value of the current element,which is indicated by the rectangular cursor, is displayed on the bottom line.This is an 8 × 4 matrix. Ellipses in the left or right column indicate additional columns. # or $ in theright column indicate additional rows.Deleting a MatrixTo delete matrices from memory, use the MEMORY MANAGEMENT/DELETE secondary menu(Chapter 18).Viewing a MatrixThe matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursorkeys to move quickly from one matrix element to the next. The full value of the highlighted elementis displayed on the edit line. Chapter 10: Matrices 145
Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions.Using Viewing-Context KeysKey Function| or ~ Moves the cursor within the current row† or } Moves the cursor within the current column; on the top row, } moves the cursor to the column dimension; on the column dimension, } moves the cursor to the row dimensionÍ Switches to editing context; activates the edit cursor on the bottom line' Switches to editing context; clears the value on the bottom lineAny entry character Switches to editing context; clears the value on the bottom line; copies the character to the bottom liney6 Nothing{ NothingEditing a Matrix ElementIn editing context, an edit cursor is active on the bottom line. To edit a matrix element value, followthese steps.1. Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions.2. Press |, }, ~, and † to move the cursor to the matrix element you want to change.3. Switch to editing context by pressing Í, ', or an entry key.4. Change the value of the matrix element using the editing-context keys described below. You may enter an expression, which is evaluated when you leave editing context. Note: You can press ' Í to restore the value at the cursor if you make a mistake.5. Press Í, }, or † to move to another element. Chapter 10: Matrices 146
Using Editing-Context KeysKey Function| or ~ Moves the edit cursor within the value† or } Stores the value displayed on the edit line to the matrix element; switches to viewing context and moves the cursor within the columnÍ Stores the value displayed on the edit line to the matrix element; switches to viewing context and moves the cursor to the next row element' Clears the value on the bottom lineAny entry character Copies the character to the location of the edit cursor on the bottom liney6 Activates the insert cursor{ Deletes the character under the edit cursor on the bottom lineUsing Matrices with ExpressionsTo use a matrix in an expression, you can do any of the following.• Copy the name from the MATRX NAMES menu.• Recall the contents of the matrix into the expression with y K (Chapter 1).• Enter the matrix directly (see below).Entering a Matrix in an ExpressionYou can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly inan expression.To enter a matrix in an expression, follow these steps.1. Press y [ [ ] to indicate the beginning of the matrix.2. Press y [ [ ] to indicate the beginning of a row.3. Enter a value, which can be an expression, for each element in the row. Separate the values with commas.4. Press y [ ] ] to indicate the end of a row.5. Repeat steps 2 through 4 to enter all of the rows.6. Press y [ ] ] to indicate the end of the matrix. The resulting matrix is displayed in the form: [[element1,1,...,element1,n],...,[elementm,1,...,elementm,n]] Any expressions are evaluated when the entry is executed. Chapter 10: Matrices 147
Note: • The commas that you must enter to separate elements are not displayed on output. • Closing brackets are required when you enter a matrix directly on the home screen or in an expression. • When you define a matrix using the matrix editor, it is automatically stored. However, when you enter a matrix directly on the home screen or in an expression, it is not automatically stored, but you can store it.In MathPrint™ mode, you could also use the MTRX shortcut menu to enter this kind of matrix:1. Press t ` † ~ ~ Í † Í to define the matrix dimension.2. Press 1 ~ 2 ~ 2 ~ 4 ~ 5 ~ 6 ~ to define the matrix.3. Press Í to perform the calculation.Displaying and Copying MatricesDisplaying a MatrixTo display the contents of a matrix on the home screen, select the matrix from the MATRX NAMESmenu, and then press Í.In MathPrint™ mode:• An arrow at the left or right indicates additional columns.• An arrow at the top or bottom indicates additional rows.In Classic mode:• Ellipses in the left or right column indicate additional columns. Chapter 10: Matrices 148
• # or $ in the right column indicate additional rows.In either mode, press ~, |, †, and } to scroll the matrix. You can scroll the matrix after youpress Í to calculate the matrix. If you cannot scroll the matrix, press } Í Í to repeatthe calculation.MathPrint™ ClassicNote:• You cannot copy a matrix output from the history.• Matrix calculations are not saved when you change from MathPrint™ mode to Classic mode or vice-versa.Copying One Matrix to AnotherTo copy a matrix, follow these steps.1. Press y > to display the MATRX NAMES menu.2. Select the name of the matrix you want to copy.3. Press ¿.4. Press y > again and select the name of the new matrix to which you want to copy the existing matrix.5. Press Í to copy the matrix to the new matrix name.Accessing a Matrix ElementOn the home screen or from within a program, you can store a value to, or recall a value from, amatrix element. The element must be within the currently defined matrix dimensions. Select matrixfrom the MATRX NAMES menu.[matrix](row,column) Chapter 10: Matrices 149
Using Math Functions with MatricesUsing Math Functions with MatricesYou can use many of the math functions on the TI-84 Plus keypad, the MATH menu, the MATH NUMmenu, and the MATH TEST menu with matrices. However, the dimensions must be appropriate.Each of the functions below creates a new matrix; the original matrix remains the same.Addition, Subtraction, MultiplicationTo add or subtract matrices, the dimensions must be the same. The answer is a matrix in whichthe elements are the sum or difference of the individual corresponding elements.matrixA+matrixBmatrixANmatrixBTo multiply two matrices together, the column dimension of matrixA must match the row dimensionof matrixB.matrixA…matrixBMultiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrixis multiplied by value.matrix…valuevalue…matrix Chapter 10: Matrices 150
NegationNegating a matrix returns a matrix in which the sign of every element is changed.Lmatrixabs(abs( (absolute value, MATH NUM menu) returns a matrix containing the absolute value of eachelement of matrix.abs(matrix)round(round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals ( 9). If#decimals is omitted, the elements are rounded to 10 digits.round(matrix[,#decimals])InverseUse the L1 function (œ) or › L1 to invert a matrix. matrix must be square. The determinant cannotequal zero. Chapter 10: Matrices 151
1matrixLPowersTo raise a matrix to a power, matrix must be square. You can use 2 (¡), 3 (MATH menu), or ^power(›) for integer power between 0 and 255.matrix2matrix3matrix^power MathPrint™ ClassicRelational OperationsTo compare two matrices using the relational operations = and ƒ (TEST menu), they must have thesame dimensions. = and ƒ compare matrixA and matrixB on an element-by-element basis. The otherrelational operations are not valid with matrices.matrixA=matrixB returns 1 if every comparison is true; it returns 0 if any comparison is false.matrixAƒmatrixB returns 1 if at least one comparison is false; it returns 0 if no comparison is false. Chapter 10: Matrices 152
iPart(, fPart(, int(iPart( (integer part), fPart( (fractional part), and int( (greatest integer) are on the MATH NUM menu.iPart( returns a matrix containing the integer part of each element of matrix.fPart( returns a matrix containing the fractional part of each element of matrix.int( returns a matrix containing the greatest integer of each element of matrix.iPart(matrix)fPart(matrix)int(matrix)Using the MATRX MATH OperationsMATRX MATH MenuTo display the MATRX MATH menu, press y ~.NAMES MATH EDIT1: det( Calculates the determinant.2: T Transposes the matrix.3: dim( Returns the matrix dimensions.4: Fill( Fills all elements with a constant.5: identity( Returns the identity matrix.6: randM( Returns a random matrix.7: augment( Appends two matrices.8: Matr4list( Stores a matrix to a list. Chapter 10: Matrices 153
NAMES MATH EDIT9: List4matr( Stores a list to a matrix.0: cumSum( Returns the cumulative sums of a matrix.A: ref( Returns the row-echelon form of a matrix.B: rref( Returns the reduced row-echelon form.C: rowSwap( Swaps two rows of a matrix.D: row+( Adds two rows; stores in the second row.E: …row( Multiplies the row by a number.F: …row+( Multiplies the row, adds to the second row.det(det( (determinant) returns the determinant (a real number) of a square matrix.det(matrix)TransposeT (transpose) returns a matrix in which each element (row, column) is swapped with thecorresponding element (column, row) of matrix.matrixTAccessing Matrix Dimensions with dim(dim( (dimension) returns a list containing the dimensions ({rows columns}) of matrix.dim(matrix) Chapter 10: Matrices 154
Note: dim(matrix)"Ln:Ln(1) returns the number of rows. dim(matrix)"Ln:Ln(2) returns the number ofcolumns.Creating a Matrix with dim(Use dim( with ¿ to create a new matrixname of dimensions rows × columns with 0 as each element.{rows,columns}"dim(matrixname)Redimensioning a Matrix with dim(Use dim( with ¿ to redimension an existing matrixname to dimensions rows × columns. Theelements in the old matrixname that are within the new dimensions are not changed. Additionalcreated elements are zeros. Matrix elements that are outside the new dimensions are deleted.{rows,columns}"dim(matrixname)Fill(Fill( stores value to every element in matrixname.Fill(value,matrixname)identity(identity( returns the identity matrix of dimension rows × dimension columns.identity(dimension) Chapter 10: Matrices 155
Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list with a specificcolumn from matrix, you must enter column# after matrix.Matr4list(matrix,column#,listname)List4matr(List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list. Ifdimensions of all lists are not equal, List4matr( fills each extra matrixname row with 0. Complex lists arenot valid.List4matr(listA,...,list n,matrixname)cumSum(cumSum( returns cumulative sums of the elements in matrix, starting with the first element. Eachelement is the cumulative sum of the column from top to bottom.cumSum(matrix)Row OperationsMATRX MATH menu items A through F are row operations. You can use a row operation in anexpression. Row operations do not change matrix in memory. You can enter all row numbers andvalues as expressions. You can select the matrix from the MATRX NAMES menu. Chapter 10: Matrices 157
ref(, rref(ref( (row-echelon form) returns the row-echelon form of a real matrix. The number of columns mustbe greater than or equal to the number of rows.ref(matrix)rref( (reduced row-echelon form) returns the reduced row-echelon form of a real matrix. The numberof columns must be greater than or equal to the number of rows.rref(matrix)rowSwap(rowSwap( returns a matrix. It swaps rowA and rowB of matrix.rowSwap(matrix,rowA,rowB)row+(row+( (row addition) returns a matrix. It adds rowA and rowB of matrix and stores the results in rowB.row+(matrix,rowA,rowB) Chapter 10: Matrices 158
…row(…row( (row multiplication) returns a matrix. It multiplies row of matrix by value and stores the results inrow.…row(value,matrix,row)…row+(…row+( (row multiplication and addition) returns a matrix. It multiplies rowA of matrix by value, adds itto rowB, and stores the results in rowB.…row+(value,matrix,rowA,rowB) Chapter 10: Matrices 159
Chapter 11:ListsGetting Started: Generating a SequenceGetting Started is a fast-paced introduction. Read the chapter for details.Calculate the first eight terms of the sequence 1/A2. Store the results to a user-created list. Thendisplay the results in fraction form. Begin this example on a blank line on the home screen.1. Press y 9 ~ to display the LIST OPS menu.2. Press 5 to select 5:seq(, which pastes seq( to the current cursor location.3. Press t ^ Í 1 ~ ƒ [A] ¡ ~ ¢ ƒ [A] ¢ 1 ¢ 8 ¢ 1 ¤ to enter the sequence.4. Press ¿, and then press y 7 to turn on alpha-lock. Press [S] [E] [Q], and then press ƒ to turn off alpha-lock. Press 1 to complete the list name. Note: Since the seq( command creates a list, you can name give the list a name up to five characters long.5. Press Í to generate the list and store it in SEQ1. The list is displayed on the home screen. An ellipsis (...) indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.6. Press y 9 to display the LIST NAMES menu. Press 7 to select 7:SEQ1 to paste ÙSEQ1 to the current cursor location. (If SEQ1 is not item 7 on your LIST NAMES menu, move the cursor to SEQ1 before you press Í.) Chapter 11: Lists 160
7. Press to display the MATH menu. Press 2 to select 2:4Dec, which pastes 4Dec to the current cursor location.8. Press Í to show the sequence in decimal form. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.Naming ListsUsing TI-84 Plus List Names L1 through L6The TI-84 Plus has six list names in memory: L1, L2, L3, L4, L5, and L6. The list names L1 throughL6 are the second functions of À through ¸. To paste one of these names to a valid screen, pressy, and then press the appropriate key. L1 through L6 are stored in stat list editor columns 1through 6 when you reset memory.Creating a List Name on the Home ScreenTo create a list name on the home screen, follow these steps.1. Press y E, enter one or more list elements, and then press y F. Separate list elements with commas. List elements can be real numbers, complex numbers, or expressions.2. Press ¿.3. Press ƒ [letter from A to Z or q] to enter the first letter of the name.4. Enter zero to four letters, q, or numbers to complete the name.5. Press Í. The list is displayed on the next line. The list name and its elements are stored in memory. The list name becomes an item on the LIST NAMES menu. Note: If you want to view a user-created list in the stat list editor, you must retrieve the list in the stat list editor (Chapter 12).You also can create a list name in these four places.• At the Name= prompt in the stat list editor• At an Xlist:, Ylist:, or Data List: prompt in the stat plot editor Chapter 11: Lists 161
• At a List:, List1:, List2:, Freq:, Freq1:, Freq2:, XList:, or YList: prompt in the inferential stat editors• On the home screen using SetUpEditorYou can create as many list names as your TI-84 Plus memory has space to store.Storing and Displaying ListsStoring Elements to a ListYou can store list elements in either of two ways.• Use brackets and ¿ on the home screen.• Use the stat list editor (Chapter 12).The maximum dimension of a list is 999 elements.Note: When you store a complex number to a list, the entire list is converted to a list of complexnumbers. To convert the list to a list of real numbers, display the home screen, and then enterreal(listname)!listname.Displaying a List on the Home ScreenTo display the elements of a list on the home screen, enter the name of the list (preceded by Ù, ifnecessary), and then press Í. An ellipsis indicates that the list continues beyond the viewingwindow. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.Copying One List to AnotherTo copy a list, store it to another list.Accessing a List ElementYou can store a value to or recall a value from a specific list element. You can store to any elementwithin the current list dimension or one element beyond. Chapter 11: Lists 162
listname(element)Deleting a List from MemoryTo delete lists from memory, including L1 through L6, use the MEMORY MANAGEMENT/DELETEsecondary menu (Chapter 18). Resetting memory restores L1 through L6. Removing a list from thestat list editor does not delete it from memory.Using Lists in GraphingTo graph a family of curves, you can use lists (Chapter 3) or the Transformation Graphing App.Entering List NamesUsing the LIST NAMES MenuTo display the LIST NAMES menu, press y 9. Each item is a user-created list name except forL1 through L6. LIST NAMES menu items are sorted automatically in alphanumerical order. Only thefirst 10 items are labeled, using 1 through 9, then 0. To jump to the first list name that begins with aparticular alpha character or q, press ƒ [letter from A to Z or q].Note: From the top of a menu, press } to move to the bottom. From the bottom, press † to moveto the top.When you select a list name from the LIST NAMES menu, the list name is pasted to the currentcursor location.• The list name symbol Ù precedes a list name when the name is pasted where non-list name data also is valid, such as the home screen.• The Ù symbol does not precede a list name when the name is pasted where a list name is the only valid input, such as the stat list editor's Name= prompt or the stat plot editor's XList: and YList: prompts. Chapter 11: Lists 163
Entering a User-Created List Name DirectlyTo enter an existing list name directly, follow these steps.1. Press y 9 ~ to display the LIST OPS menu.2. Select B:Ù, which pastes Ù to the current cursor location. Ù is not always necessary. Note: You also can paste Ù to the current cursor location from the CATALOG.3. Enter the characters that comprise the list name.Attaching Formulas to List NamesAttaching a Formula to a List NameYou can attach a formula to a list name so that each list element is a result of the formula. Whenexecuted, the attached formula must resolve to a list.When anything in the attached formula changes, the list to which the formula is attached isupdated automatically.• When you edit an element of a list that is referenced in the formula, the corresponding element in the list to which the formula is attached is updated.• When you edit the formula itself, all elements in the list to which the formula is attached are updated.For example, the first screen below shows that elements are stored to L3, and the formula L3+10 isattached to the list name ÙADD10. The quotation marks designate the formula to be attached toÙADD10. Each element of ÙADD10 is the sum of an element in L3 and 10.The next screen shows another list, L4. The elements of L4 are the sum of the same formula that isattached to L3. However, quotation marks are not entered, so the formula is not attached to L4.On the next line, L6!L3(1):L3 changes the first element in L3 to L6, and then redisplays L3. Chapter 11: Lists 164
The last screen shows that editing L3 updated ÙADD10, but did not change L4. This is because theformula L3+10 is attached to ÙADD10, but it is not attached to L4.Note: To view a formula that is attached to a list name, use the stat list editor (Chapter 12).Attaching a Formula to a List on the Home Screen or in a ProgramTo attach a formula to a list name from a blank line on the home screen or from a program, followthese steps.1. Press ƒ [ã], enter the formula (which must resolve to a list), and press ƒ [ã] again. Note: When you include more than one list name in a formula, each list must have the same dimension.2. Press ¿.3. Enter the name of the list to which you want to attach the formula. • Press y, and then enter a TI-84 Plus list name L1 through L6. • Press y 9 and select a user.created list name from the LIST NAMES menu. • Enter a user.created list name directly using Ù.4. Press Í.Note: The stat list editor displays a formula-lock symbol next to each list name that has an attachedformula. Chapter 12 describes how to use the stat list editor to attach formulas to lists, editattached formulas, and detach formulas from lists.Detaching a Formula from a ListYou can detach (clear) an attached formula from a list in several ways.For example:• Enter ã ã !listname on the home screen.• Edit any element of a list to which a formula is attached.• Use the stat list editor (Chapter 12). Chapter 11: Lists 165
• Use ClrList or ClrAllList to detach a formula from a list (Chapter 18).Using Lists in ExpressionsUsing Lists in an ExpressionYou can use lists in an expression in any of three ways. When you press Í, any expression isevaluated for each list element, and a list is displayed.• Use L1–L6 or any user-created list name in an expression.• Enter the list elements directly.• Use y K to recall the contents of the list into an expression at the cursor location (Chapter 1).Note: You must paste user-created list names to the Rcl prompt by selecting them from theLIST NAMES menu. You cannot enter them directly using Ù.Using Lists with Math FunctionsYou can use a list to input several values for some math functions. See Appendix A specify forinformation about where a list is valid. The function is evaluated for each list element, and a list isdisplayed.• When you use a list with a function, the function must be valid for every element in the list. In graphing, an invalid element, such as L1 in ‡({1,0,L1}), is ignored. This returns an error. This graphs X…‡(1) and X…‡(0), but skips X…‡(L1).• When you use two lists with a two-argument function, the dimension of each list must be the same. The function is evaluated for corresponding elements. Chapter 11: Lists 166
• When you use a list and a value with a two-argument function, the value is used with each element in the list.LIST OPS MenuLIST OPS MenuTo display the LIST OPS menu, press y 9 ~.NAMES OPS MATH1: SortA( Sorts lists in ascending order.2: SortD( Sorts lists in descending order.3: dim( Sets the list dimension.4: Fill( Fills all elements with a constant.5: seq( Creates a sequence.6: cumSum( Returns a list of cumulative sums.7: @List( Returns difference of successive elements.8: Select( Selects specific data points.9: augment( Concatenates two lists.0: List4matr( Stores a list to a matrix.A: Matr4list( Stores a matrix to a list.B: Ù Designates the list-name data type.With one list, SortA( and SortD( sort the elements of listname and update the list in memory.SortA(listname) SortD(listname) Chapter 11: Lists 167
With two or more lists, SortA( and SortD( sort keylistname, and then sort each dependlist by placing itselements in the same order as the corresponding elements in keylistname. All lists must have thesame dimension.SortA(keylistname,dependlist1[,dependlist2,...,dependlist n])SortD(keylistname,dependlist1[,dependlist2,...,dependlist n])Note:• In the example, 5 is the first element in L4, and 1 is the first element in L5. After SortA(L4,L5), 5 becomes the second element of L4, and likewise, 1 becomes the second element of L5.• SortA( and SortD( are the same as SortA( and SortD( on the STAT EDIT menu (Chapter 12).• You cannot sort a locked list.Using dim( to Find List Dimensionsdim( (dimension) returns the length (number of elements) of list.dim(list)Using dim( to Create a ListYou can use dim( with ¿ to create a new listname with dimension length from 1 to 999. Theelements are zeros.length!dim(listname)Using dim( to Redimension a ListYou can use dim with ¿ to redimension an existing listname to dimension length from 1 to 999.• The elements in the old listname that are within the new dimension are not changed.• Extra list elements are filled by 0.• Elements in the old list that are outside the new dimension are deleted. Chapter 11: Lists 168
length!dim(listname)Fill(Fill( replaces each element in listname with value.Fill(value,listname)Note: dim( and Fill( are the same as dim( and Fill( on the MATRX MATH menu (Chapter 10).seq(seq( (sequence) returns a list in which each element is the result of the evaluation of expression withregard to variable for the values ranging from begin to end at steps of increment. variable need not bedefined in memory. increment can be negative; the default value for increment is 1. seq( is not validwithin expression. Complex lists are not valid.seq(expression,variable,begin,end[,increment])cumSum(cumSum( (cumulative sum) returns the cumulative sums of the elements in list, starting with thefirst element. list elements can be real or complex numbers.cumSum(list)@List(@List( returns a list containing the differences between consecutive elements in list. @List subtractsthe first element in list from the second element, subtracts the second element from the third, and Chapter 11: Lists 169
so on. The list of differences is always one element shorter than the original list. list elements canbe a real or complex numbers.@List(list)Select(Select( selects one or more specific data points from a scatter plot or xyLine plot (only), and thenstores the selected data points to two new lists, xlistname and ylistname. For example, you can useSelect( to select and then analyze a portion of plotted CBL 2™/CBL™ or CBR™ data.Select(xlistname,ylistname)Note: Before you use Select(, you must have selected (turned on) a scatter plot or xyLine plot.Also, the plot must be displayed in the current viewing window.Before Using Select(Before using Select(, follow these steps.1. Create two list names and enter the data.2. Turn on a stat plot, select " (scatter plot) or Ó (xyLine), and enter the two list names for Xlist: and Ylist: (Chapter 12).3. Use ZoomStat to plot the data (Chapter 3). MathPrint™ ClassicUsing Select( to Select Data Points from a PlotTo select data points from a scatter plot or xyLine plot, follow these steps.1. Press y 9 ~ 8 to select 8:Select( from the LIST OPS menu. Select( is pasted to the home screen. Chapter 11: Lists 170
2. Enter xlistname, press ¢, enter ylistname, and then press ¤ to designate list names into which you want the selected data to be stored.3. Press Í. The graph screen is displayed with Left Bound? in the bottom-left corner.4. Press } or † (if more than one stat plot is selected) to move the cursor onto the stat plot from which you want to select data points.5. Press | and ~ to move the cursor to the stat plot data point that you want as the left bound.6. Press Í. A 4 indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottom-left corner. Chapter 11: Lists 171
7. Press | or ~ to move the cursor to the stat plot point that you want for the right bound, and then press Í. The x-values and y-values of the selected points are stored in xlistname and ylistname. A new stat plot of xlistname and ylistname replaces the stat plot from which you selected data points. The list names are updated in the stat plot editor.Note: The two new lists (xlistname and ylistname) will include the points you select as left bound andright bound. Also, left-bound x-value { right-bound x-value must be true.augment(augment( concatenates the elements of listA and listB. The list elements can be real or complexnumbers.augment(listA,listB)List4matr(List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list.If the dimensions of all lists are not equal, then List4matr( fills each extra matrixname row with 0.Complex lists are not valid. Chapter 11: Lists 172
List4matr(list1,list2, ... ,list n,matrixname)Matr4list(Matr4list( (matrix stored to lists) fills each listname with elements from each column in matrix. If thenumber of listname arguments exceeds the number of columns in matrix, then Matr4list( ignoresextra listname arguments. Likewise, if the number of columns in matrix exceeds the number oflistname arguments, then Matr4list( ignores extra matrix columns.Matr4list(matrix,listname1,listname2, . . . ,listname n)Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list with aspecific column from matrix, you must enter a column# after matrix.Matr4list(matrix,column#,listname)Ù preceding one to five characters identifies those characters as a user-created listname. listnamemay comprise letters, q, and numbers, but it must begin with a letter from A to Z or q.ÙlistnameGenerally, Ù must precede a user-created list name when you enter a user-created list namewhere other input is valid, for example, on the home screen. Without the Ù, the TI-84 Plus maymisinterpret a user-created list name as implied multiplication of two or more characters.Ù need not precede a user-created list name where a list name is the only valid input, for example,at the Name= prompt in the stat list editor or the Xlist: and Ylist: prompts in the stat plot editor. Ifyou enter Ù where it is not necessary, the TI-84 Plus will ignore the entry. Chapter 11: Lists 173
LIST MATH MenuLIST MATH MenuTo display the LIST MATH menu, press y 9 |.NAMES OPS MATH1: min( Returns minimum element of a list.2: max( Returns maximum element of a list.3: mean( Returns mean of a list.4: median( Returns median of a list.5: sum( Returns sum of elements in a list.6: prod( Returns product of elements in list.7: stdDev( Returns standard deviation of a list.8: variance( Returns the variance of a list.min(, max(min( (minimum) and max( (maximum) return the smallest or largest element of listA. If two lists arecompared, it returns a list of the smaller or larger of each pair of elements in listA and listB. For acomplex list, the element with smallest or largest magnitude (modulus) is returned.min(listA[,listB])max(listA[,listB])MathPrint™ ClassicNote: min( and max( are the same as min( and max( on the MATH NUM menu.mean(, median(mean( returns the mean value of list. median( returns the median value of list. The default value forfreqlist is 1. Each freqlist element counts the number of consecutive occurrences of thecorresponding element in list. Complex lists are not valid. Chapter 11: Lists 174
mean(list[,freqlist])median(list[,freqlist])MathPrint™ Classicsum(, prod(sum( (summation) returns the sum of the elements in list. start and end are optional; they specify arange of elements. list elements can be real or complex numbers.prod( returns the product of all elements of list. start and end elements are optional; they specify arange of list elements. list elements can be real or complex numbers.sum(list[,start,end]) prod(list[,start,end])Sums and Products of Numeric SequencesYou can combine sum( or prod( with seq( to obtain:upper upperG expression(x) expression(x)x=lower x=lowerTo evaluate G 2 (N–1) from N=1 to 4:stdDev(, variance(stdDev( returns the standard deviation of the elements in list. The default value for freqlist is 1. Eachfreqlist element counts the number of consecutive occurrences of the corresponding element in list.Complex lists are not valid. Chapter 11: Lists 175
stdDev(list[,freqlist])MathPrint™ Classicvariance( returns the variance of the elements in list. The default value for freqlist is 1. Each freqlistelement counts the number of consecutive occurrences of the corresponding element in list.Complex lists are not valid.variance(list[,freqlist])MathPrint™ Classic Chapter 11: Lists 176
4. Press 6 Ë 5 Í to store the first pendulum string length (6.5 cm) in L1. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 string length values in the table.5. Press ~ to move the rectangular cursor to the first row in L2. Press Ë 51 Í to store the first time measurement (.51 sec) in L2. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 time values in the table.6. Press o to display the Y= editor. If necessary, press ' to clear the function Y1. As necessary, press }, Í, and ~ to turn off Plot1, Plot2, and Plot3 from the top line of the Y= editor (Chapter 3). As necessary, press †, |, and Í to deselect functions.7. Press y , 1 to select 1:Plot1 from the STAT PLOTS menu. The stat plot editor is displayed for plot 1.8. Press Í to select On, which turns on plot 1. Press † Í to select " (scatter plot). Press † y d to specify Xlist:L1 for plot 1. Press † y e to specify Ylist:L2 for plot 1. Press † ~ Í to select + as the Mark for each data point on the scatter plot.9. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and plot 1 is displayed. This is a scatter plot of the time-versus-length data.Since the scatter plot of time-versus-length data appears to be approximately linear, fit a line to thedata.10. Press … ~ 4 to select 4:LinReg(ax+b) (linear regression model) from the STAT CALC menu. LinReg(ax+b) is pasted to the home screen. Chapter 12: Statistics 178
11 LinReg(ax+b). Note: You can also use the YVARS (t a)shortcut menu to select Y1.12. Press Í to execute LinReg(ax+b). The linear regression for the data in L1 and L2 is calculated. Values for a and b are displayed on the home screen. The linear regression equation is stored in Y1. Residuals are calculated and stored automatically in the list name RESID, which becomes an item on the LIST NAMES menu. Note: - You can control the number of decimal places displayed by changing the decimal mode setting. - The statistics reported are not stored in the history on the home screen.13. Press s. The regression line and the scatter plot are displayed.The regression line appears to fit the central portion of the scatter plot well. However, a residualplot may provide more information about this fit.14. Press … 1 to select 1:Edit. The stat list editor is displayed. Press ~ and } to move the cursor onto L3. Press y 6. An unnamed column is displayed in column 3; L3, L4, L5, and L6 shift right one column. The Name= prompt is displayed in the entry line, and alpha-lock is on.15. Press y 9 to display the LIST NAMES menu. If necessary, press † to move the cursor onto the list name RESID.16. Press Í to select RESID and paste it to the stat list editor's Name= prompt. Chapter 12: Statistics 179
17. Press Í. RESID is stored in column 3 of the stat list editor. Press † repeatedly to examine the residuals.Notice that the first three residuals are negative. They correspond to the shortest pendulum stringlengths in L1. The next five residuals are positive, and three of the last four are negative. The lattercorrespond to the longer string lengths in L1. Plotting the residuals will show this pattern moreclearly.18. Press y , 2 to select 2:Plot2 from the STAT PLOTS menu. The stat plot editor is displayed for plot 2.19. Press Í to select On, which turns on plot 2. Press † Í to select " (scatter plot). Press † y d to specify Xlist:L1 for plot 2. Press † ãRä ãEä ãSä ãIä ãDä (alpha-lock is on) to specify Ylist:RESID for plot 2. Press † Í to select › as the mark for each data point on the scatter plot.20. Press o to display the Y= editor. Press | to move the cursor onto the = sign, and then press Í to deselect Y1. Press } Í to turn off plot 1.21. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.Notice the pattern of the residuals: a group of negative residuals, then a group of positiveresiduals, and then another group of negative residuals.The residual pattern indicates a curvature associated with this data set for which the linear modeldid not account. The residual plot emphasizes a downward curvature, so a model that curves Chapter 12: Statistics 180
down with the data would be more accurate. Perhaps a function such as square root would fit. Trya power regression to fit a function of the form y = a … xb.22. Press o to display the Y= editor. Press ' to clear the linear regression equation from Y1. Press } Í to turn on plot 1. Press ~ Í to turn off plot 2.23. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and the original scatter plot of time- versus-length data (plot 1) is displayed.24. Press … ~ ƒ ãAä to select A:PwrReg from the STAT CALC menu. PwrReg is pasted to the home screen PwrReg. Note: You can also use the YVARS (t a)shortcut menu to select Y1.25. Press Í to calculate the power regression. Values for a and b are displayed on the home screen. The power regression equation is stored in Y1. Residuals are calculated and stored automatically in the list name RESID.26. Press s. The regression line and the scatter plot are displayed.The new function y=.192x.522 appears to fit the data well. To get more information, examine aresidual plot.27. Press o to display the Y= editor. Press | Í to deselect Y1. Press } Í to turn off plot 1. Press ~ Í to turn on plot 2. Note: Step 19 defined plot 2 to plot residuals (RESID) versus string length (L1). Chapter 12: Statistics 181
28. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.The new residual plot shows that the residuals are random in sign, with the residuals increasing inmagnitude as the string length increases.To see the magnitudes of the residuals, continue with these steps.29. Press r. Press ~ and | to trace the data. Observe the values for Y at each point. With this model, the largest positive residual is about 0.041 and the smallest negative residual is about L0.027. All other residuals are less than 0.02 in magnitude.Now that you have a good model for the relationship between length and period, you can use themodel to predict the period for a given string length. To predict the periods for a pendulum withstring lengths of 20 cm and 50 cm, continue with these steps.30. Press ~ 1 to display the VARS Y-VARS FUNCTION secondary menu, and then press 1 to select 1:Y1. Y1 is pasted to the home screen. Note: You can also use the YVARS (t a)shortcut menu to select Y1.31. Press £ 20 ¤ to enter a string length of 20 cm. Press Í to calculate the predicted time of about 0.92 seconds. Based on the residual analysis, we would expect the prediction of about 0.92 seconds to be within about 0.02 seconds of the actual value. Chapter 12: Statistics 182
32. Press y [ to recall the Last Entry. Press | | | 5 to change the string length to 50 cm.33. Press Í to calculate the predicted time of about 1.48 seconds. Since a string length of 50 cm exceeds the lengths in the data set, and since residuals appear to be increasing as string length increases, we would expect more error with this estimate. Note: You also can make predictions using the table with the TABLE SETUP settings Indpnt:Ask and Depend:Auto (Chapter 7).Setting Up Statistical AnalysesUsing Lists to Store DataData for statistical analyses is stored in lists, which you can create and edit using the stat listeditor. The TI-84 Plus has six list variables in memory, L1 through L6, to which you can store datafor statistical calculations. Also, you can store data to list names that you create (Chapter 11).Setting Up a Statistical AnalysisTo set up a statistical analysis, follow these steps. Read the chapter for details.1. Enter the statistical data into one or more lists.2. Plot the data.3. Calculate the statistical variables or fit a model to the data.4. Graph the regression equation for the plotted data.5. Graph the residuals list for the given regression model.Displaying the Stat List EditorThe stat list editor is a table where you can store, edit, and view up to 20 lists that are in memory.Also, you can create list names from the stat list editor.To display the stat list editor, press …, and then select 1:Edit from the STAT EDIT menu. Chapter 12: Statistics 183
The top line displays list names. L1 through L6 are stored in columns 1 through 6 after a memoryreset. The number of the current column is displayed in the top-right corner.The bottom line is the entry line. All data entry occurs on this line. The characteristics of this linechange according to the current context.The center area displays up to seven elements of up to three lists; it abbreviates values whennecessary. The entry line displays the full value of the current element.Using the Stat List EditorEntering a List Name in the Stat List EditorTo enter a list name in the stat list editor, follow these steps.1. Display the Name= prompt in the entry line in either of two ways. • Move the cursor onto the list name in the column where you want to insert a list, and then press y 6. An unnamed column is displayed and the remaining lists shift right one column. • Press } until the cursor is on the top line, and then press ~ until you reach the unnamed column. Note: If list names are stored to all 20 columns, you must remove a list name to make room for an unnamed column. The Name= prompt is displayed and alpha-lock is on.2. Enter a valid list name in any of four ways. • Select a name from the LIST NAMES menu (Chapter 11). • Enter L1, L2, L3, L4, L5, or L6 from the keyboard. • Enter an existing user-created list name directly from the keyboard. • Enter a new user-created list name.3. Press Í or † to store the list name and its elements, if any, in the current column of the stat list editor. Chapter 12: Statistics 184
To begin entering, scrolling, or editing list elements, press †. The rectangular cursor is displayed. Note: If the list name you entered in step 2 already was stored in another stat list editor column, then the list and its elements, if any, move to the current column from the previous column. Remaining list names shift accordingly.Creating a Name in the Stat List EditorTo create a name in the stat list editor, follow these steps.1. Display the Name= prompt.2. Press [letter from A to Z or q] to enter the first letter of the name. The first character cannot be a number.3. Enter zero to four letters, q, or numbers to complete the new user-created list name. List names can be one to five characters long.4. Press Í or † to store the list name in the current column of the stat list editor. The list name becomes an item on the LIST NAMES menu (Chapter 11).Removing a List from the Stat List EditorTo remove a list from the stat list editor, move the cursor onto the list name and then press {. Thelist is not deleted from memory; it is only removed from the stat list editor.Notes:• To delete a list name from memory, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18).• If you archive a list, it will be removed from the stat list editor.Removing All Lists and Restoring L1 through L6You can remove all user-created lists from the stat list editor and restore list names L1 through L6to columns 1 through 6 in either of two ways.• Use SetUpEditor with no arguments.• Reset all memory (Chapter 18). Chapter 12: Statistics 185
Clearing All Elements from a ListYou can clear all elements from a list in any of five ways.• Use ClrList to clear specified lists.• In the stat list editor, press } to move the cursor onto a list name, and then press ' Í.• In the stat list editor, move the cursor onto each element, and then press { one by one.• On the home screen or in the program editor, enter 0!dim(listname) to set the dimension of listname to 0 (Chapter 11).• Use ClrAllLists to clear all lists in memory (Chapter 18).Editing a List ElementTo edit a list element, follow these steps.1. Move the cursor onto the element you want to edit.2. Press Í to move the cursor to the entry line. Note: If you want to replace the current value, you can enter a new value without first pressing Í. When you enter the first character, the current value is cleared automatically.3. Edit the element in the entry line. • Press one or more keys to enter the new value. When you enter the first character, the current value is cleared automatically. You can use the shortcut menus to enter values. When you use n/d to enter a fraction, it is not displayed as a stacked fraction in the list. Instead, the fraction has a thick bar separating the numerator and denominator. Thick-bar fraction on the list editor entry line: Thin-bar fraction on the home screen (regular division): Note: Order of operations applies to fractions. For example, evaluates to because the order of operations dictates that division is performed before addition. To evaluate , enter with parentheses around the numerator. • Press ~ to move the cursor to the character before which you want to insert, press y 6, and then enter one or more characters. • Press ~ to move the cursor to a character you want to delete, and then press { to delete the character. To cancel any editing and restore the original element at the rectangular cursor, press ' Í. Chapter 12: Statistics 186
Note: You can enter expressions and variables for elements.4. Press Í, }, or † to update the list. If you entered an expression, it is evaluated. If you entered only a variable, the stored value is displayed as a list element. When you edit a list element in the stat list editor, the list is updated in memory immediately.Attaching Formulas to List NamesAttaching a Formula to a List Name in Stat List EditorYou can attach a formula to a list name in the stat list editor, and then display and edit thecalculated list elements. When executed, the attached formula must resolve to a list. Chapter 11describes in detail the concept of attaching formulas to list names.To attach a formula to a list name that is stored in the stat list editor, follow these steps.1. Press … Í to display the stat list editor.2. Press } to move the cursor to the top line.3. Press | or ~, if necessary, to move the cursor onto the list name to which you want to attach the formula. Note: If a formula in quotation marks is displayed on the entry line, then a formula is already attached to the list name. To edit the formula, press Í, and then edit the formula.4. Press ƒ ããä, enter the formula, and press ƒ ããä. Note: If you do not use quotation marks, the TI-84 Plus calculates and displays the same initial list of answers, but does not attach the formula for future calculations. Note: Any user-created list name referenced in a formula must be preceded by an Ù symbol (Chapter 11). Chapter 12: Statistics 187
5. Press Í. The TI-84 Plus calculates each list element and stores it to the list name to which the formula is attached. A lock symbol is displayed in the stat list editor, next to the list name to which the formula is attached. lock symbolUsing the Stat List Editor When Formula-Generated Lists Are DisplayedWhen you edit an element of a list referenced in an attached formula, the TI-84 Plus updates thecorresponding element in the list to which the formula is attached (Chapter 11).When a list with a formula attached is displayed in the stat list editor and you edit or enter elementsof another displayed list, then the TI-84 Plus takes slightly longer to accept each edit or entry thanwhen no lists with formulas attached are in view.Note: To speed editing time, scroll horizontally until no lists with formulas are displayed, orrearrange the stat list editor so that no lists with formulas are displayed.Handling Errors Resulting from Attached FormulasOn the home screen, you can attach to a list a formula that references another list with dimension0 (Chapter 11). However, you cannot display the formula-generated list in the stat list editor or onthe home screen until you enter at least one element to the list that the formula references.All elements of a list referenced by an attached formula must be valid for the attached formula. Forexample, if Real number mode is set and the attached formula is log(L1), then each element of L1must be greater than 0, since the logarithm of a negative number returns a complex result.When you use the shortcut menus, all values must be valid for use in the templates. For example,if you use the n/d template, both the numerator and demoninator must be integers.Notes:• If an error menu is returned when you attempt to display a formula-generated list in the stat list editor, you can select 2:Goto, write down the formula that is attached to the list, and then press ' Í to detach (clear) the formula. You then can use the stat list editor to find the Chapter 12: Statistics 188
source of the error. After making the appropriate changes, you can reattach the formula to a list.• If you do not want to clear the formula, you can select 1:Quit, display the referenced list on the home screen, and find and edit the source of the error. To edit an element of a list on the home screen, store the new value to listname(element#) (Chapter 11).Detaching Formulas from List NamesDetaching a Formula from a List NameYou can detach (clear) a formula from a list name in several ways.For example:• In the stat list editor, move the cursor onto the name of the list to which a formula is attached. Press Í ' Í. All list elements remain, but the formula is detached and the lock symbol disappears.• In the stat list editor, move the cursor onto an element of the list to which a formula is attached. Press Í, edit the element, and then press Í. The element changes, the formula is detached, and the lock symbol disappears. All other list elements remain.• Use ClrList. All elements of one or more specified lists are cleared, each formula is detached, and each lock symbol disappears. All list names remain.• Use ClrAllLists (Chapter 18). All elements of all lists in memory are cleared, all formulas are detached from all list names, and all lock symbols disappear. All list names remain.Editing an Element of a Formula-Generated ListAs described above, one way to detach a formula from a list name is to edit an element of the listto which the formula is attached. The TI-84 Plus protects against inadvertently detaching theformula from the list name by editing an element of the formula-generated list.Because of the protection feature, you must press Í before you can edit an element of aformula-generated list.The protection feature does not allow you to delete an element of a list to which a formula isattached. To delete an element of a list to which a formula is attached, you must first detach theformula in any of the ways described above.Switching Stat List Editor ContextsStat List Editor ContextsThe stat list editor has four contexts.• View-elements context• View-names context Chapter 12: Statistics 189
• Edit-elements context• Enter-name contextThe stat list editor is first displayed in view-elements context. To switch through the four contexts,select 1:Edit from the STAT EDIT menu and follow these steps.1. Press } to move the cursor onto a list name and switch to view-names context. Press ~ and | to view list names stored in other stat list editor columns.2. Press Í to switch to edit-elements context. You may edit any element in a list. All elements of the current list are displayed in braces ( { } ) in the entry line. Press ~ and | to view more list elements.3. Press Í again to switch to view-elements context. Press ~, |, †, and } to view other list elements. The current element's full value is displayed in the entry line.4. Press Í again to switch back to edit-elements context. You may edit the current element in the entry line.5. Press } until the cursor is on a list name, then press y 6 to switch to enter-name context.6. Press ' to switch to view-names context.7. Press † to switch back to view-elements context. Chapter 12: Statistics 190
Stat List Editor ContextsView-Elements ContextIn view-elements context, the entry line displays the list name, the current element's place in thatlist, and the full value of the current element, up to 12 characters at a time. An ellipsis (...) indicatesthat the element continues beyond 12 characters.To page down the list six elements, press ƒ †. To page up six elements, press ƒ }. Todelete a list element, press {. Remaining elements shift up one row. To insert a new element,press y 6. 0 is the default value for a new element.Edit-Elements ContextIn edit-elements context, the data displayed in the entry line depends on the previous context.• When you switch to edit-elements context from view-elements context, the full value of the current element is displayed. You can edit the value of this element, and then press † and } to edit other list elements.• When you switch to edit-elements context from view-names context, the full values of all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press ~ and | to edit any element in the list.Note: In edit-elements context, you can attach a formula to a list name only if you switched to itfrom view-names context. Chapter 12: Statistics 191
View-Names ContextIn view-names context, the entry line displays the list name and the list elements.To remove a list from the stat list editor, press {. Remaining lists shift to the left one column. Thelist is not deleted from memory.To insert a name in the current column, press y 6. Remaining columns shift to the right onecolumn.Enter-Name ContextIn enter-name context, the Name= prompt is displayed in the entry line, and alpha-lock is on.At the Name= prompt, you can create a new list name, paste a list name from L1 to L6 from thekeyboard, or paste an existing list name from the LIST NAMES menu (Chapter 11). The Ù symbol isnot required at the Name= prompt.To leave enter-name context without entering a list name, press '. The stat list editorswitches to view-names context.STAT EDIT MenuSTAT EDIT MenuTo display the STAT EDIT menu, press ….EDIT CALC TESTS1: Edit... Displays the stat list editor.2: SortA( Sorts a list in ascending order.3: SortD( Sorts a list in descending order.4: ClrList Deletes all elements of a list.5: SetUpEditor Stores specified lists in the stat list editor. Chapter 12: Statistics 192
SortA( and SortD( each can sort in either of two ways.• With one listname, SortA( and SortD( sort the elements in listname and update the list in memory.• With two or more lists, SortA( and SortD( sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname. This lets you sort two-variable data on X and keep the data pairs together. All lists must have the same dimension.The sorted lists are updated in memory.SortA(listname)SortD(listname)SortA(keylistname,dependlist1[,dependlist2,...,dependlist n])SortD(keylistname,dependlist1[,dependlist2,...,dependlist n])Note: SortA( and SortD( are the same as SortA( and SortD( on the LIST OPS menu.ClrListClrList clears (deletes) from memory the elements of one or more listnames. ClrList also detachesany formula attached to a listname.ClrList listname1,listname2,...,listname nNote: To clear from memory all elements of all list names, use ClrAllLists (Chapter 18).SetUpEditorWith SetUpEditor you can set up the stat list editor to display one or more listnames in the order thatyou specify. You can specify zero to 20 listnames.Additionally, if you want to use listnames which happen to be archived, the SetUp Editor willautomatically unarchive the listnames and place them in the stat list editor at the same time.SetUpEditor [listname1,listname2,...,listname n] Chapter 12: Statistics 193
SetUpEditor with one to 20 listnames removes all list names from the stat list editor and then storeslistnames in the stat list editor columns in the specified order, beginning in column 1.MathPrint™ClassicIf you enter a listname that is not stored in memory already, then listname is created and stored inmemory; it becomes an item on the LIST NAMES menu.Restoring L1 through L6 to the Stat List EditorSetUpEditor with no listnames removes all list names from the stat list editor and restores list namesL1 through L6 in the stat list editor columns 1 through 6.Regression Model FeaturesRegression Model FeaturesSTAT CALC menu items 3 through C are regression models. The automatic residual list andautomatic regression equation features apply to all regression models. Diagnostics display modeapplies to some regression models.Automatic Residual ListWhen you execute a regression model, the automatic residual list feature computes and stores theresiduals to the list name RESID. RESID becomes an item on the LIST NAMES menu (Chapter 11). Chapter 12: Statistics 194
The TI-84 Plus uses the formula below to compute RESID list elements. The next sectiondescribes the variable RegEQ.RESID = Ylistname N RegEQ(Xlistname)Automatic Regression EquationEach regression model has an optional argument, regequ, for which you can specify a Y= variablesuch as Y1. Upon execution, the regression equation is stored automatically to the specified Y=variable and the Y= function is selected.MathPrint™ MathPrint™Classic ClassicRegardless of whether you specify a Y= variable for regequ, the regression equation always isstored to the TI-84 Plus variable RegEQ, which is item 1 on the VARS Statistics EQ secondarymenu.Note: For the regression equation, you can use the fixed-decimal mode setting to control thenumber of digits stored after the decimal point (Chapter 1). However, limiting the number of digitsto a small number could affect the accuracy of the fit.Diagnostics Display ModeWhen you execute some regression models, the TI-84 Plus computes and stores diagnosticsvalues for r (correlation coefficient) and r2 (coefficient of determination) or for R2 (coefficient ofdetermination). You can control whether these values are displayed by turning StatDiagnostics onor off on the mode screen.r and r2 are computed and stored for these regression models.LinReg(ax+b) LnReg PwrRegLinReg(a+bx) ExpReg Chapter 12: Statistics 195
R2 is computed and stored for these regression models.QuadReg CubicReg QuartRegThe r and r2 that are computed for LnReg, ExpReg, and PwrReg are based on the linearlytransformed data. For example, for ExpReg (y=ab^x), r and r2 are computed on ln y=ln a+x(ln b).By default, these values are not displayed with the results of a regression model when youexecute it. However, you can set the diagnostics display mode by executing the DiagnosticOn orDiagnosticOff instruction. Each instruction is in the CATALOG (Chapter 15).• To turn diagnostics on or off from the mode screen, select On or Off for StatDiagnostics. The default is Off.• To set DiagnosticOn or DiagnosticOff from the home screen, press y N, and then select the instruction for the mode you want. The instruction is pasted to the home screen. Press Í to set the mode.When DiagnosticOn is set, diagnostics are displayed with the results when you execute aregression model.MathPrint™ClassicWhen DiagnosticOff is set, diagnostics are not displayed with the results when you execute aregression model.MathPrint™Classic Chapter 12: Statistics 196
STAT CALC MenuSTAT CALC MenuTo display the STAT CALC menu, press … ~.EDIT CALC TESTS1: 1-Var Stats Calculates 1-variable statistics.2: 2-Var Stats Calculates 2-variable statistics.3: Med-Med Calculates a median-median line.4: LinReg(ax+b) Fits a linear model to data.5: QuadReg Fits a quadratic model to data.6: CubicReg Fits a cubic model to data.7: QuartReg Fits a quartic model to data.8: LinReg(a+bx) Fits a linear model to data.9: LnReg Fits a logarithmic model to data.0: ExpReg Fits an exponential model to data.A: PwrReg Fits a power model to data.B: Logistic Fits a logistic model to data.C: SinReg Fits a sinusoidal model to data.D: Manual Linear Fit Fits a linear equation interactively to a scatter plot.For each STAT CALC menu item, if neither Xlistname nor Ylistname is specified, then the default listnames are L1 and L2. If you do not specify freqlist, then the default is 1 occurrence of each listelement.Frequency of Occurrence for Data PointsFor most STAT CALC menu items, you can specify a list of data occurrences, or frequencies(freqlist).Each element in freqlist indicates how many times the corresponding data point or data pair occursin the data set you are analyzing.For example, if L1={15,12,9,14} and ÙFREQ={1,4,1,3}, then the TI-84 Plus interprets the instruction1-Var Stats L1, ÙFREQ to mean that 15 occurs once, 12 occurs four times, 9 occurs once, and 14occurs three times.Each element in freqlist must be ' 0, and at least one element must be > 0.Noninteger freqlist elements are valid. This is useful when entering frequencies expressed aspercentages or parts that add up to 1. However, if freqlist contains noninteger frequencies, Sx andSy are undefined; values are not displayed for Sx and Sy in the statistical results. Chapter 12: Statistics 197
1-Var Stats1-Var Stats (one-variable statistics) analyzes data with one measured variable. Each element infreqlist is the frequency of occurrence for each corresponding data point in Xlistname. freqlistelements must be real numbers > 0.1-Var Stats [Xlistname,freqlist]2-Var Stats2-Var Stats (two-variable statistics) analyzes paired data. Xlistname is the independent variable.Ylistname is the dependent variable. Each element in freqlist is the frequency of occurrence for eachdata pair (Xlistname,Ylistname).2-Var Stats [Xlistname,Ylistname,freqlist]Med-Med (ax+b)Med-Med (median-median) fits the model equation y=ax+b to the data using the median-medianline (resistant line) technique, calculating the summary points x1, y1, x2, y2, x3, and y3. Med-Meddisplays values for a (slope) and b (y-intercept).Med-Med [Xlistname,Ylistname,freqlist,regequ]LinReg (ax+b)LinReg(ax+b) (linear regression) fits the model equation y=ax+b to the data using a least-squares fit.It displays values for a (slope) and b (y-intercept); when DiagnosticOn is set, it also displays valuesfor r2 and r.LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ]QuadReg (ax2+bx+c)QuadReg (quadratic regression) fits the second-degree polynomial y=ax2+bx+c to the data. Itdisplays values for a, b, and c; when DiagnosticOn is set, it also displays a value for R2. For threedata points, the equation is a polynomial fit; for four or more, it is a polynomial regression. At leastthree data points are required.QuadReg [Xlistname,Ylistname,freqlist,regequ] Chapter 12: Statistics 198
CubicReg—(ax 3+bx 2+cx+d)CubicReg (cubic regression) fits the third-degree polynomial y=ax 3+bx 2+cx+d to the data. Itdisplays values for a, b, c, and d; when DiagnosticOn is set, it also displays a value for R2. For fourpoints, the equation is a polynomial fit; for five or more, it is a polynomial regression. At least fourpoints are required.CubicReg [Xlistname,Ylistname,freqlist,regequ]QuartReg—(ax 4+bx 3+cx 2+ dx+e)QuartReg (quartic regression) fits the fourth-degree polynomial y=ax 4+bx 3+cx 2+dx+e to the data. Itdisplays values for a, b, c, d, and e; when DiagnosticOn is set, it also displays a value for R2. Forfive points, the equation is a polynomial fit; for six or more, it is a polynomial regression. At leastfive points are required.QuartReg [Xlistname,Ylistname,freqlist,regequ]LinReg—(a+bx)LinReg(a+bx) (linear regression) fits the model equation y=a+bx to the data using a least-squares fit.It displays values for a (y-intercept) and b (slope); when DiagnosticOn is set, it also displays valuesfor r2 and r.LinReg(a+bx) [Xlistname,Ylistname,freqlist,regequ]LnReg—(a+b ln(x))LnReg (logarithmic regression) fits the model equation y=a+b ln(x) to the data using a least-squares fit and transformed values ln(x) and y. It displays values for a and b; when DiagnosticOn isset, it also displays values for r2 and r.LnReg [Xlistname,Ylistname,freqlist,regequ]ExpReg—(ab x)ExpReg (exponential regression) fits the model equation y=abx to the data using a least-squares fitand transformed values x and ln(y). It displays values for a and b; when DiagnosticOn is set, it alsodisplays values for r2 and r.ExpReg [Xlistname,Ylistname,freqlist,regequ] Chapter 12: Statistics 199
PwrReg—(axb)PwrReg (power regression) fits the model equation y=axb to the data using a least-squares fit andtransformed values ln(x) and ln(y). It displays values for a and b; when DiagnosticOn is set, it alsodisplays values for r2 and r.PwrReg [Xlistname,Ylistname,freqlist,regequ]Logistic—c/(1+a…e-bx)Logistic fits the model equation y=c/(1+a…eLbx) to the data using an iterative least-squares fit. Itdisplays values for a, b, and c.Logistic [Xlistname,Ylistname,freqlist,regequ]SinReg—a sin(bx+c)+dSinReg (sinusoidal regression) fits the model equation y=a sin(bx+c)+d to the data using aniterative least-squares fit. It displays values for a, b, c, and d. At least four data points are required.At least two data points per cycle are required in order to avoid aliased frequency estimates.SinReg [iterations,Xlistname,Ylistname,period,regequ]iterations is the maximum number of times the algorithm will iterate to find a solution. The value foriterations can be an integer ' 1 and 16; if not specified, the default is 3. The algorithm may find asolution before iterations is reached. Typically, larger values for iterations result in longer executiontimes and better accuracy for SinReg, and vice versa.A period guess is optional. If you do not specify period, the difference between time values inXlistname must be equal and the time values must be ordered in ascending sequential order. If youspecify period, the algorithm may find a solution more quickly, or it may find a solution when it wouldnot have found one if you had omitted a value for period. If you specify period, the differencesbetween time values in Xlistname can be unequal.Note: The output of SinReg is always in radians, regardless of the Radian/Degree mode setting. Chapter 12: Statistics 200
SinReg Example: Daylight Hours in Alaska for One YearCompute the regression model for the number of hours of daylight in Alaska during one year.MathPrint™Classic 1 periodWith noisy data, you will achieve better convergence results when you specify an accurateestimate for period. You can obtain a period guess in either of two ways.• Plot the data and trace to determine the x-distance between the beginning and end of one complete period, or cycle. The illustration above and to the right graphically depicts a complete period, or cycle.• Plot the data and trace to determine the x-distance between the beginning and end of N complete periods, or cycles. Then divide the total distance by N.After your first attempt to use SinReg and the default value for iterations to fit the data, you may findthe fit to be approximately correct, but not optimal. For an optimal fit, executeSinReg 16,Xlistname,Ylistname,2p/b where b is the value obtained from the previous SinReg execution.Manual Linear FitManual Linear Fit allows you to visually fit a linear function to a scatter plot. Manual Linear Fit is anoption in the … / menu. Chapter 12: Statistics 201
After entering List data and viewing the StatPlot, select the Manual-Fit function.1. Press … to display the Stat menu. Press ~ to select CALC. Press † several times to scroll down to select D:Manual-Fit. Press Í. This displays a free-floating cursor at the center of the display screen2. Press the cursor navigation keys (} † | ~ ) to move the cursor to the desired location. Press Í to select the first point.3. Press the cursor navigation keys (} † | ~ ) to move the cursor to the second location. Press Í. This displays a line containing the two points selected.The linear function is displayed. The Manual-Fit Line equation displays in the form of Y=mX+b.The current value of the first parameter (m) is highlighted in the symbolic expression.Modify parameter valuesPress the cursor navigation keys ( | ~ ) to move from the first parameter (m) or (b) the secondparameter. You can press Í and type a new parameter value. Press Í to display the newparameter value. When you edit the value of the selected parameter, the edit can include insert,delete, type over, or mathematical expression.The screen dynamically displays the revised parameter value. Press Í to complete themodification of the selected parameter, save the value, and refresh the displayed graph. Thesystem displays the revised parameter value in the symbolic expression Y=mX+B, and refreshesthe graph with the updated Manual-Fit Line.Select y 5 to finish the Manual Fit function. The calculator stores the current mX+bexpression into Y1 and makes that function active for graphing. You can also select Manual-Fitwhile on the Home screen. You can then enter a different Y-Var such as Y4 and then press Í.This takes you to the Graph screen and then pastes the Manual-Fit equation in the specified Y-Var.In this example, Y4.Statistical VariablesThe statistical variables are calculated and stored as indicated below. To access these variablesfor use in expressions, press , and select 5:Statistics. Then select the VARS menu shown in Chapter 12: Statistics 202
Statistical Analysis in a ProgramEntering Stat DataYou can enter statistical data, calculate statistical results, and fit models to data from a program.You can enter statistical data into lists directly within the program (Chapter 11).Statistical CalculationsTo perform a statistical calculation from a program, follow these steps.1. On a blank line in the program editor, select the type of calculation from the STAT CALC menu.2. Enter the names of the lists to use in the calculation. Separate the list names with a comma.3. Enter a comma and then the name of a Y= variable, if you want to store the regression equation to a Y= variable.Statistical PlottingSteps for Plotting Statistical Data in ListsYou can plot statistical data that is stored in lists. The six types of plots available are scatter plot,xyLine, histogram, modified box plot, regular box plot, and normal probability plot. You can defineup to three plots.To plot statistical data in lists, follow these steps.1. Store the stat data in one or more lists.2. Select or deselect Y= functions as appropriate.3. Define the stat plot.4. Turn on the plots you want to display.5. Define the viewing window.6. Display and explore the graph. Chapter 12: Statistics 204
ScatterScatter (")plots plot the data points from Xlist and Ylist as coordinate pairs, showing each point asa box ( › ), cross ( + ), or dot ( ¦ ). Xlist and Ylist must be the same length. You can use the samelist for Xlist and Ylist.xyLinexyLine (Ó)is a scatter plot in which the data points are plotted and connected in order ofappearance in Xlist and Ylist. You may want to use SortA( or SortD( to sort the lists before you plotthem.HistogramHistogram (Ò) plots one-variable data. The Xscl window variable value determines the width ofeach bar, beginning at Xmin. ZoomStat adjusts Xmin, Xmax, Ymin, and Ymax to include all values,and also adjusts Xscl. The inequality (Xmax N Xmin) à Xscl 47 must be true. A value that occurs onthe edge of a bar is counted in the bar to the right.ModBoxplotModBoxplot (Õ) (modified box plot) plots one-variable data, like the regular box plot, exceptpoints that are 1.5 … Interquartile Range beyond the quartiles. (The Interquartile Range is definedas the difference between the third quartile Q3 and the first quartile Q1.) These points are plottedindividually beyond the whisker, using the Mark (› or + or ¦) you select. You can trace these points,which are called outliers. Chapter 12: Statistics 205
The prompt for outlier points is x=, except when the outlier is the maximum point (maxX) or theminimum point (minX). When outliers exist, the end of each whisker will display x=. When nooutliers exist, minX and maxX are the prompts for the end of each whisker. Q1, Med (median), andQ3 define the boxBoxplotBoxplot (Ö)(regular box plot) plots one-variable data. The whiskers on the plot extend from theminimum data point in the set (minX) to the first quartile (Q1) and from the third quartile (Q3) to themaximum point (maxX). The box is defined by Q1, Med (median), and Q3NormProbPlotNormProbPlot (Ô) (normal probability plot) plots each observation X in Data List versus thecorresponding quantile z of the standard normal distribution. If the plotted points lie close to astraight line, then the plot indicates that the data are normal.Enter a valid list name in the Data List field. Select X or Y for the Data Axis setting.• If you select X, the TI-84 Plus plots the data on the x-axis and the z-values on the y-axis. Chapter 12: Statistics 206
Data Data Plot Type XList YList Mark Freq List Axis Ô NormProbPlot œ œ _ œ _ _5. Enter list names or select options for the plot type. • Xlist (list name containing independent data) • Ylist (list name containing dependent data) • Mark (› or + or ¦) • Freq (frequency list for Xlist elements; default is 1) • Data List (list name for NormProbPlot) • Data Axis (axis on which to plot Data List)Displaying Other Stat Plot EditorsEach stat plot has a unique stat plot editor. The name of the current stat plot (Plot1, Plot2, or Plot3)is highlighted in the top line of the stat plot editor. To display the stat plot editor for a different plot,press } and ~ to move the cursor onto the name in the top line, and then press Í. The statplot editor for the selected plot is displayed, and the selected name remains highlighted.Turning On and Turning Off Stat PlotsPlotsOn and PlotsOff allow you to turn on or turn off stat plots from the home screen or a program.With no plot number, PlotsOn turns on all plots and PlotsOff turns off all plots. With one or moreplot numbers (1, 2, and 3), PlotsOn turns on specified plots, and PlotsOff turns off specified plots.PlotsOff [1,2,3]PlotsOn [1,2,3]Note: You also can turn on and turn off stat plots in the top line of the Y= editor (Chapter 3). Chapter 12: Statistics 208
Defining the Viewing WindowStat plots are displayed on the current graph. To define the viewing window, press p andenter values for the window variables. ZoomStat redefines the viewing window to display allstatistical data points.Tracing a Stat PlotWhen you trace a scatter plot or xyLine, tracing begins at the first element in the lists.When you trace a histogram, the cursor moves from the top center of one column to the top centerof the next, starting at the first column.When you trace a box plot, tracing begins at Med (the median). Press | to trace to Q1 and minX.Press ~ to trace to Q3 and maxX.When you press } or † to move to another plot or to another Y= function, tracing moves to thecurrent or beginning point on that plot (not the nearest pixel).The ExprOn/ExprOff format setting applies to stat plots (Chapter 3). When ExprOn is selected, theplot number and plotted data lists are displayed in the top-left corner.Statistical Plotting in a ProgramDefining a Stat Plot in a ProgramTo display a stat plot from a program, define the plot, and then display the graph.To define a stat plot from a program, begin on a blank line in the program editor and enter data intoone or more lists; then, follow these steps.1. Press y , to display the STAT PLOTS menu.2. Select the plot to define, which pastes Plot1(, Plot2(, or Plot3( to the cursor location.3. Press y , ~ to display the STAT TYPE menu. Chapter 12: Statistics 209
4. Select the type of plot, which pastes the name of the plot type to the cursor location.5. Press ¢. Enter the list names, separated by commas.6. Press ¢ y , | to display the STAT PLOT MARK menu. (This step is not necessary if you selected 3:Histogram or 5:Boxplot in step 4.) Select the type of mark (› or + or ¦) for each data point. The selected mark symbol is pasted to the cursor location.7. Press ¤ Í to complete the command line.Displaying a Stat Plot from a ProgramTo display a plot from a program, use the DispGraph instruction (Chapter 16) or any of the ZOOMinstructions (Chapter 3). Chapter 12: Statistics 210
Chapter 13:Inferential Statistics and DistributionsGetting Started: Mean Height of a PopulationGetting Started is a fast-paced introduction. Read the chapter for details.Suppose you want to estimate the mean height of a population of women given the randomsample below. Because heights among a biological population tend to be normally distributed, a tdistribution confidence interval can be used when estimating the mean. The 10 height valuesbelow are the first 10 of 90 values, randomly generated from a normally distributed population withan assumed mean of 165.1 centimeters and a standard deviation of 6.35 centimeters(randNorm(165.1,6.35,90) with a seed of 789).Height (in centimeters) of Each of 10 Women169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04 167.15 159.531. Press … Í to display the stat list editor. Press } to move the cursor onto L1, and then press y 6 to insert a new list. The Name= prompt is displayed on the bottom line. The Ø cursor indicates that alpha-lock is on. The existing list name columns shift to the right. Note: Your stat editor may not look like the one pictured here, depending on the lists you have already stored.2. Enter [H] [G] [H] [T] at the Name= prompt, and then press Í to create the list to store the women's height data. Press † to move the cursor into the first row of the list. HGHT(1)= is displayed on the bottom line. Press Í.3. Press 169 Ë 43 to enter the first height value. As you enter it, it is displayed on the bottom line. Press Í. The value is displayed in the first row, and the rectangular cursor moves to the next row. Enter the other nine height values the same way. Chapter 13: Inferential Statistics and Distributions 211
4. Press … | to display the STAT TESTS menu, and then press † until 8:TInterval is highlighted.5. Press Í to select 8:TInterval. The inferential stat editor for TInterval is displayed. If Data is not selected for Inpt:, press | Í to select Data. Press † y 9 and press † until HGHT is highlighted and then press Í. Press † † Ë 99 to enter a 99 percent confidence level at the C-Level: prompt.6. Press † to move the cursor onto Calculate, and then press Í. The confidence interval is calculated, and the TInterval results are displayed on the home screen.Interpreting the resultsThe first line, (159.74,173.94), shows that the 99 percent confidence interval for the populationmean is between about 159.74 centimeters and 173.94 centimeters. This is about a 14.2centimeters spread.The .99 confidence level indicates that in a very large number of samples, we expect 99 percent ofthe intervals calculated to contain the population mean. The actual mean of the populationsampled is 165.1 centimeters, which is in the calculated interval.The second line gives the mean height of the sample v used to compute this interval. The third linegives the sample standard deviation Sx. The bottom line gives the sample size n.To obtain a more precise bound on the population mean m of women's heights, increase thesample size to 90. Use a sample mean v of 163.8 and sample standard deviation Sx of 7.1calculated from the larger random sample. This time, use the Stats (summary statistics) inputoption.1. Press … | 8 to display the inferential stat editor for TInterval. Press ~ Í to select Inpt:Stats. The editor changes so that you can enter summary statistics as input. Chapter 13: Inferential Statistics and Distributions 212
2. Press † 163 Ë 8 Í to store 163.8 to v. Press 7 Ë 1 Í to store 7.1 to Sx. Press 90 Í to store 90 to n.3. Press † to move the cursor onto Calculate, and then press Í to calculate the new 99 percent confidence interval. The results are displayed on the home screen.If the height distribution among a population of women is normally distributed with a mean m of165.1 centimeters and a standard deviation s of 6.35 centimeters, what height is exceeded by only5 percent of the women (the 95th percentile)?4. Press ' to clear the home screen. Press y = to display the DISTR (distributions) menu.5. Press 3 to paste invNorm( to the home screen. Press Ë 95 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤ Í. .95 is the area, 165.1 is m, and 6.35 is s.The result is displayed on the home screen; it shows that five percent of the women are taller than175.5 centimeters.Now graph and shade the top 5 percent of the population.6. Press p and set the window variables to these values. Xmin=145 Ymin=L.02 Xres=1 Xmax=185 Ymax=.08 Xscl=5 Yscl=07. Press y = ~ to display the DISTR DRAW menu. Chapter 13: Inferential Statistics and Distributions 213
8. Press Í to paste ShadeNorm( to the home screen. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. Ans (175.5448205 from step 11) is the lower bound. 1â99 is the upper bound. The normal curve is defined by a mean m of 165.1 and a standard deviation s of 6.35.9. Press Í to plot and shade the normal curve. Area is the area above the 95th percentile. low is the lower bound. up is the upper bound.Inferential Stat EditorsDisplaying the Inferential Stat EditorsWhen you select a hypothesis test or confidence interval instruction from the home screen, theappropriate inferential statistics editor is displayed. The editors vary according to each test orinterval's input requirements. Below is the inferential stat editor for T-Test.Note: When you select the ANOVA( instruction, it is pasted to the home screen. ANOVA( does nothave an editor screen.Using an Inferential Stat EditorTo use an inferential stat editor, follow these steps.1. Select a hypothesis test or confidence interval from the STAT TESTS menu. The appropriate editor is displayed.2. Select Data or Stats input, if the selection is available. The appropriate editor is displayed.3. Enter real numbers, list names, or expressions for each argument in the editor.4. Select the alternative hypothesis (ƒÄ, <, or >) against which to test, if the selection is available.5. Select No or Yes for the Pooled option, if the selection is available.6. Select Calculate or Draw (when Draw is available) to execute the instruction. • When you select Calculate, the results are displayed on the home screen. Chapter 13: Inferential Statistics and Distributions 214
• When you select Draw, the results are displayed in a graph.This chapter describes the selections in the above steps for each hypothesis test and confidenceinterval instruction.Select Data or Select anStats input alternative hypothesisEnter valuesfor arguments Select Calculate or Draw outputSelecting Data or StatsMost inferential stat editors prompt you to select one of two types of input. (1-PropZInt and2-PropZTest, 1-PropZInt and 2-PropZInt, c2-Test, c2GOF-Test, LinRegTInt, and LinRegTTest do not.)• Select Data to enter the data lists as input.• Select Stats to enter summary statistics, such as v, Sx, and n, as input.To select Data or Stats, move the cursor to either Data or Stats, and then press Í.Entering the Values for ArgumentsInferential stat editors require a value for every argument. If you do not know what a particularargument symbol represents, see the Inferential Statistics Input Descriptions tables.When you enter values in any inferential stat editor, the TI-84 Plus stores them in memory so thatyou can run many tests or intervals without having to reenter every value.Selecting an Alternative Hypothesis (ă < >)Most of the inferential stat editors for the hypothesis tests prompt you to select one of threealternative hypotheses.• The first is a ƒ alternative hypothesis, such as mƒm0 for the Z-Test.• The second is a < alternative hypothesis, such as m1<m2 for the 2-SampTTest.• The third is a > alternative hypothesis, such as p1>p2 for the 2-PropZTest.To select an alternative hypothesis, move the cursor to the appropriate alternative, and then pressÍ.Selecting the Pooled OptionPooled (2-SampTTest and 2-SampTInt only) specifies whether the variances are to be pooled for thecalculation. Chapter 13: Inferential Statistics and Distributions 215
• Select No if you do not want the variances pooled. Population variances can be unequal.• Select Yes if you want the variances pooled. Population variances are assumed to be equal.To select the Pooled option, move the cursor to Yes, and then press Í.Selecting Calculate or Draw for a Hypothesis TestAfter you have entered all arguments in an inferential stat editor for a hypothesis test, you mustselect whether you want to see the calculated results on the home screen (Calculate) or on thegraph screen (Draw).• Calculate calculates the test results and displays the outputs on the home screen.• Draw draws a graph of the test results and displays the test statistic and p-value with the graph. The window variables are adjusted automatically to fit the graph.To select Calculate or Draw, move the cursor to either Calculate or Draw, and then press Í. Theinstruction is immediately executed.Selecting Calculate for a Confidence IntervalAfter you have entered all arguments in an inferential stat editor for a confidence interval, selectCalculate to display the results. The Draw option is not available.When you press Í, Calculate calculates the confidence interval results and displays theoutputs on the home screen.Bypassing the Inferential Stat EditorsTo paste a hypothesis test or confidence interval instruction to the home screen without displayingthe corresponding inferential stat editor, select the instruction you want from the CATALOG menu.Appendix A describes the input syntax for each hypothesis test and confidence interval instruction.Note: You can paste a hypothesis test or confidence interval instruction to a command line in aprogram. From within the program editor, select the instruction from either the CATALOG(Chapter 15) or the STAT TESTS menu.STAT TESTS MenuSTAT TESTS MenuTo display the STAT TESTS menu, press … |. When you select an inferential statisticsinstruction, the appropriate inferential stat editor is displayed. Chapter 13: Inferential Statistics and Distributions 216
Most STAT TESTS instructions store some output variables to memory. For a list of these variables,see the Test and Interval Output Variables table.EDIT CALC TESTS1: Z-Test... Test for 1 m, known s2: T-Test... Test for 1 m, unknown s3: 2-SampZTest... Test comparing 2 m's, known s's4: 2-SampTTest... Test comparing 2 m's, unknown s's5: 1-PropZTest... Test for 1 proportion6: 2-PropZTest... Test comparing 2 proportions7: ZInterval... Confidence interval for 1 m, known s8: TInterval... Confidence interval for 1 m, unknown s9: 2-SampZInt... Confidence interval for difference of 2 m's, known s's0: 2-SampTInt... Confidence interval for difference of 2 m's, unknown s'sA: 1-PropZInt... Confidence interval for 1 proportionB: 2-PropZInt... Confidence interval for difference of 2 proportionsC: c2-Test... Chi-square test for 2-way tablesD: c2-GOF Test... Chi-square Goodness of Fit testE: 2-SampÛTest... Test comparing 2 s'sF: LinRegTTest... t test for regression slope and rG: LinRegTInt... Confidence interval for linear regression slope coefficient bH: ANOVA( One-way analysis of varianceNote: When a new test or interval is computed, all previous output variables are invalidated.Inferential Stat Editors for the STAT TESTS InstructionsIn this chapter, the description of each STAT TESTS instruction shows the unique inferential stateditor for that instruction with example arguments.• Descriptions of instructions that offer the Data/Stats input choice show both types of input screens.• Descriptions of instructions that do not offer the Data/Stats input choice show only one input screen.The description then shows the unique output screen for that instruction with the example results.• Descriptions of instructions that offer the Calculate/Draw output choice show both types of screens: calculated and graphic results.• Descriptions of instructions that offer only the Calculate output choice show the calculated results on the home screen. Chapter 13: Inferential Statistics and Distributions 217
1-PropZInt1-PropZInt (one-proportion z confidence interval; item A) computes a confidence interval for anunknown proportion of successes. It takes as input the count of successes in the sample x and thecount of observations in the sample n. The computed confidence interval depends on the user-specified confidence level. Input: Calculated results:2-PropZInt2-PropZInt (two-proportion z confidence interval; item B) computes a confidence interval for thedifference between the proportion of successes in two populations (p1Np2). It takes as input thecount of successes in each sample (x1 and x2) and the count of observations in each sample(n1 and n2). The computed confidence interval depends on the user-specified confidence level. Input: Calculated results: Chapter 13: Inferential Statistics and Distributions 226
c2-Testc2-Test (chi-square test; item C) computes a chi-square test for association on the two-way table ofcounts in the specified Observed matrix. The null hypothesis H 0 for a two-way table is: noassociation exists between row variables and column variables. The alternative hypothesis is: thevariables are related.Before computing a c2-Test, enter the observed counts in a matrix. Enter that matrix variable nameat the Observed: prompt in the c2.Test editor; default=[A]. At the Expected: prompt, enter the matrixvariable name to which you want the computed expected counts to be stored; default=[B]. Matrix Note: Press y ú ~ ~ 1 to editor: select 1:[A] from the MATRX EDIT menu. Input: Note: Press y ú †] Í to display matrix [B]. Calculated results: Drawn results:c2GOF-Testc2GOF-Test (Chi Square Goodness of Fit; item D) performs a test to confirm that sample data isfrom a population that conforms to a specified distribution. For example, c2 GOF can confirm thatthe sample data came from a normal distribution. Chapter 13: Inferential Statistics and Distributions 227
automatically stored to the specified Y= equation. In the example below, the regression equation isstored to Y1, which is then selected (turned on).In the example:L3={38, 56, 59, 64, 74}L4={41, 63, 70, 72, 84} Input: Calculated results:When LinRegTTest is executed, the list of residuals is created and stored to the list name RESIDautomatically. RESID is placed on the LIST NAMES menu.Note: For the regression equation, you can use the fix-decimal mode setting to control the numberof digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a smallnumber could affect the accuracy of the fit.LinRegTIntLinRegTInt computes a linear regression T confidence interval for the slope coefficient b. If theconfidence interval contains 0, this is insufficient evidence to indicate that the data exhibits a linearrelationship. Chapter 13: Inferential Statistics and Distributions 230
In the example:list 1={4, 5, 6, 7, 8}list 2={1, 2, 3, 3.5, 4.5} LinRegTInt input Note: Press … ~ ~ to screen: select TESTS. Press † several times to select G:LinRegTint... Press Í. Press † several times to select Calculate. Press Í. Calculated results:Xlist, Ylist is the list of independent and dependent variables. The list containing the Freq(frequency) values for the data is stored in List. The default is 1. All elements must be realnumbers. Each element in the Freq list is the frequency of occurence for each corresponding datapoint in the input list specified in the List fields. RegEQ (optional) is the designated Yn variable forstoring the regression equation. StoreRegEqn (optional) is the designated variable for storing theregression equation. The C level is the Confidence level probability with default = .95.ANOVA(ANOVA( (one-way analysis of variance; item H) computes a one-way analysis of variance forcomparing the means of two to 20 populations. The ANOVA procedure for comparing these meansinvolves analysis of the variation in the sample data. The null hypothesis H0: m1=m2=...=mk istested against the alternative Ha: not all m1...mk are equal.ANOVA(list1,list2[,...,list20]) Chapter 13: Inferential Statistics and Distributions 231
In the example:L1={7 4 6 6 5}L2={6 5 5 8 7}L3={4 7 6 7 6} Input: Calculated results:Note: SS is sum of squares and MS is mean square.Inferential Statistics Input DescriptionsThe tables in this section describe the inferential statistics inputs discussed in this chapter. Youenter values for these inputs in the inferential stat editors. The tables present the inputs in thesame order that they appear in this chapter.Input Descriptionm0 Hypothesized value of the population mean that you are testing.s The known population standard deviation; must be a real number > 0.List The name of the list containing the data you are testing.Freq The name of the list containing the frequency values for the data in List. Default=1. All elements must be integers | 0.Calculate/Draw Determines the type of output to generate for tests and intervals. Calculate displays the output on the home screen. In tests, Draw draws a graph of the results.v, Sx, n Summary statistics (mean, standard deviation, and sample size) for the one-sample tests and intervals. Chapter 13: Inferential Statistics and Distributions 232
Input Descriptions1 The known population standard deviation from the first population for the two-sample tests and intervals. Must be a real number > 0.s2 The known population standard deviation from the second population for the two-sample tests and intervals. Must be a real number > 0.List1, List2 The names of the lists containing the data you are testing for the two-sample tests and intervals. Defaults are L1 and L2, respectively.Freq1, Freq2 The names of the lists containing the frequencies for the data in List1 and List2 for the two-sample tests and intervals. Defaults=1. All elements must be integers | 0.v1, Sx1, n1, v2, Sx2, n2 Summary statistics (mean, standard deviation, and sample size) for sample one and sample two in the two-sample tests and intervals.Pooled Specifies whether variances are to be pooled for 2-SampTTest and 2-SampTInt. No instructs the TI-84 Plus not to pool the variances. Yes instructs the TI-84 Plus to pool the variances.p0 The expected sample proportion for 1-PropZTest. Must be a real number, such that 0 < p0 < 1.x The count of successes in the sample for the 1-PropZTest and 1-PropZInt. Must be an integer | 0.n The count of observations in the sample for the 1-PropZTest and 1-PropZInt. Must be an integer > 0.x1 The count of successes from sample one for the 2-PropZTest and 2-PropZInt. Must be an integer | 0.x2 The count of successes from sample two for the 2-PropZTest and 2-PropZInt. Must be an integer | 0.n1 The count of observations in sample one for the 2-PropZTest and 2-PropZInt. Must be an integer > 0.n2 The count of observations in sample two for the 2-PropZTest and 2-PropZInt. Must be an integer > 0.C-Level The confidence level for the interval instructions. Must be ' 0 and < 100. If it is ' 1, it is assumed to be given as a percent and is divided by 100. Default=0.95.Observed (Matrix) The matrix name that represents the columns and rows for the observed values of a two-way table of counts for the c2-Test and c2GOF-Test. Observed must contain all integers | 0. Matrix dimensions must be at least 2×2.Expected (Matrix) The matrix name that specifies where the expected values should be stored. Expected is created upon successful completion of the c2-Test and c2GOF-Test.df df (degree of freedom) represents (number of sample categories) - (number of estimated parameters for the selected distribution + 1). Chapter 13: Inferential Statistics and Distributions 233
normalpdf(x[,m,s]) Note: For this example, Xmin = 28 Xmax = 42 Xscl = 1 Ymin = 0 Ymax = .2 Yscl = .1Note: For plotting the normal distribution, you can set window variables Xmin and Xmax so that themean m falls between them, and then select 0:ZoomFit from the ZOOM menu.normalcdf(normalcdf( computes the normal distribution probability between lowerbound and upperbound for thespecified mean m and standard deviation s. The defaults are m=0 and s=1.normalcdf(lowerbound,upperbound[,m,s])invNorm(invNorm( computes the inverse cumulative normal distribution function for a given area under thenormal distribution curve specified by mean m and standard deviation s. It calculates the x valueassociated with an area to the left of the x value. 0 area 1 must be true. The defaults are m=0 ands=1.invNorm(area[,m,s])invT(invT( computes the inverse cumulative Student-t probability function specified by Degree ofFreedom, df for a given Area under the curve. Chapter 13: Inferential Statistics and Distributions 236
Üpdf(x,numerator df,denominator df) Note: For this example, Xmin = 0 Xmax = 5 Ymin = 0 Ymax = 1Fcdf(Ücdf( computes the Ü distribution probability between lowerbound and upperbound for the specifiednumerator df (degrees of freedom) and denominator df. numerator df and denominator df must be integers> 0.Ücdf(lowerbound,upperbound,numerator df,denominator df)binompdfbinompdf( computes a probability at x for the discrete binomial distribution with the specifiednumtrials and probability of success (p) on each trial. x can be an integer or a list of integers. 0p1must be true. numtrials must be an integer > 0. If you do not specify x, a list of probabilities from 0 tonumtrials is returned. The probability density function (pdf) is: fx = p 1 – p n x n–x ,x = 0,1,...,n x where n = numtrialsbinompdf(numtrials,p[,x])binomcdf(binomcdf( computes a cumulative probability at x for the discrete binomial distribution with thespecified numtrials and probability of success (p) on each trial. x can be a real number or a list ofreal numbers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list ofcumulative probabilities is returned. Chapter 13: Inferential Statistics and Distributions 239
binomcdf(numtrials,p[,x])poissonpdf(poissonpdf( computes a probability at x for the discrete Poisson distribution with the specifiedmean m, which must be a real number > 0. x can be an integer or a list of integers. The probabilitydensity function (pdf) is: – x f x = e x! ,x = 0,1,2,...poissonpdf(m,x)poissoncdf(poissoncdf( computes a cumulative probability at x for the discrete Poisson distribution with thespecified mean m, which must be a real number > 0. x can be a real number or a list of realnumbers.poissoncdf(m,x)geometpdf(geometpdf( computes a probability at x, the number of the trial on which the first success occurs,for the discrete geometric distribution with the specified probability of success p. 0p1 must betrue. x can be an integer or a list of integers. The probability density function (pdf) is: x–1 fx = p1 – p ,x = 1,2,...geometpdf(p,x) Chapter 13: Inferential Statistics and Distributions 240
geometcdf(geometcdf( computes a cumulative probability at x, the number of the trial on which the firstsuccess occurs, for the discrete geometric distribution with the specified probability of success p.0p1 must be true. x can be a real number or a list of real numbers.geometcdf(p,x)MathPrint™ ClassicDistribution ShadingDISTR DRAW MenuTo display the DISTR DRAW menu, press y = ~. DISTR DRAW instructions draw varioustypes of density functions, shade the area specified by lowerbound and upperbound, and display thecomputed area value.To clear the drawings, select 1:ClrDraw from the DRAW menu (Chapter 8).Note: Before you execute a DISTR DRAW instruction, you must set the window variables so that thedesired distribution fits the screen.DISTR DRAW1: ShadeNorm( Shades normal distribution.2: Shade_t( Shades Student-t distribution.3: Shadec2( Shades c2 distribution.4: ShadeÜ( Shades Üdistribution.Note: L1â99 and 1â99 specify infinity. If you want to view the area left of upperbound, for example,specify lowerbound=L1â99.ShadeNorm(ShadeNorm( draws the normal density function specified by mean m and standard deviation s andshades the area between lowerbound and upperbound. The defaults are m=0 and s=1. Chapter 13: Inferential Statistics and Distributions 241
Chapter 14:ApplicationsThe Applications MenuThe TI-84 Plus comes with several applications already installed and listed on the APPLICATIONSmenu. These applications include the following:FinanceTopics in Algebra 1Science ToolsCatalog Help 1.1CellSheet™Conic GraphingInequality GraphingTransformation GraphingVernier EasyData™DataMatePolynomial Root Finder and Simultaneous Equation SolverStudyCards™LearningCheck™Except for the Finance application, you can add and remove applications as space permits. TheFinance application is built into the TI-84 Plus code and cannot be deleted.Many other applications in addition to the ones mentioned above, including language localizationapplications, are included on your TI-84 Plus. Press ŒÎ to see the complete list of applicationsthat came with your calculator.You can download additional TI-84 Plus software applications from education.ti.com that allow youto customize your calculator's functionality even further. The calculator reserves 1.54 M of spacewithin ROM memory specifically for applications.Guidebooks for applications are on the Texas Instruments Web site at: education.ti.com/guides.Steps for Running the Finance ApplicationFollow these basic steps when using the Finance application.1. Press Œ Í to select the Finance application. Chapter 14: Applications 244
2. Select from list of functions.Getting Started: Financing a CarGetting Started is a fast-paced introduction. Read the chapter for details.You have found a car you would like to buy. You can afford payments of 250 per month for fouryears. The car costs 9,000. Your bank offers an interest rate of 5%. What will your payments be?Can you afford it?1. Press z † ~ ~ ~ Í to set the fixed-decimal mode setting to 2. (The TI-84 Plus will display all numbers with two decimal places.)2. Press Œ Í to select 1:Finance from the APPLICATIONS menu.3. Press Í to select 1:TVM Solver from the CALC VARS menu. The TVM Solver is displayed.4. Enter the data: N (number of payments)= 48 I% (interest rate)=5 PV (present value)=9000 FV (future value)=0 P/Y (payments per year)=12 C/Y (compounding periods per year)=125. Select PMT:END, which indicates that payments are due at the end of each period.6. Move the cursor to PMT and press ƒ . Can you afford the payment? Chapter 14: Applications 245
Getting Started: Computing Compound InterestAt what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000 in 7 years?Note: Because there are no payments when you solve compound interest problems, PMT must beset to 0 and P/Y must be set to 1.1. Press Œ Í to select 1:Finance from the APPLICATIONS menu.2. Press Í to select 1:TVM Solver from the CALC VARS menu. The TVM Solver is displayed.3. Enter the data: N=7 PV=M1250 PMT=0 FV=2000 P/Y=1 C/Y=124. Move the curstor to æ and press ƒ . YYou need to look for an interest rate of 6.73% to grow 1250 to 2000 in 7 years.Using the TVM SolverUsing the TVM SolverThe TVM Solver displays the time-value-of-money (TVM) variables. Given four variable values,the TVM Solver solves for the fifth variable.The FINANCE VARS menu section describes the five TVM variables (Ú, æ, PV, PMT, and FV) andP/Y and C/Y.PMT: END BEGIN in the TVM Solver corresponds to the FINANCE CALC menu items Pmt_End(payment at the end of each period) and Pmt_Bgn (payment at the beginning of each period).To solve for an unknown TVM variable, follow these steps.1. Press Œ Í Í to display the TVM Solver. The screen below shows the default values with the fixed-decimal mode set to two decimal places. Chapter 14: Applications 246
2. Enter the known values for four TVM variables. Note: Enter cash inflows as positive numbers and cash outflows as negative numbers.3. Enter a value for P/Y, which automatically enters the same value for C/Y; if P/Y ƒ C/Y, enter a unique value for C/Y.4. Select END or BEGIN to specify the payment method.5. Place the cursor on the TVM variable for which you want to solve.6. Press ƒ . The answer is computed, displayed in the TVM Solver, and stored to the appropriate TVM variable. An indicator square in the left column designates the solution variable.Using the Financial FunctionsEntering Cash Inflows and Cash OutflowsWhen using the TI-84 Plus financial functions, you must enter cash inflows (cash received) aspositive numbers and cash outflows (cash paid) as negative numbers. The TI-84 Plus follows thisconvention when computing and displaying answers.FINANCE CALC MenuTo display the FINANCE CALC menu, press ÎŒ Í.CALC VARS1: TVM Solver... Displays the TVM Solver.2: tvm_Pmt Computes the amount of each payment.3: tvm_¾æ Computes the interest rate per year.4: tvm_PV Computes the present value.5: tvm_òÚ Computes the number of payment periods.6: tvm_FV Computes the future value.7: npv( Computes the net present value. Chapter 14: Applications 247
CALC VARS8: irr( Computes the internal rate of return.9: bal( Computes the amortization sched. balance.0: GPrn( Computes the amort. sched. princ. sum.A: GInt( Computes the amort. sched. interest sum.B: 4Nom( Computes the nominal interest rate.C: 4Eff( Computes the effective interest rate.D: dbd( Calculates the days between two dates.E: Pmt_End Selects ordinary annuity (end of period).F: Pmt_Bgn Selects annuity due (beginning of period).Use these functions to set up and perform financial calculations on the home screen.TVM SolverTVM Solver displays the TVM Solver.Calculating Time Value of Money (TVM)Calculating Time Value of MoneyUse time-value-of-money (TVM) functions (menu items 2 through 6) to analyze financialinstruments such as annuities, loans, mortgages, leases, and savings.Each TVM function takes zero to six arguments, which must be real numbers. The values that youspecify as arguments for TVM functions are not stored to the TVM variables.Note: To store a value to a TVM variable, use the TVM Solver or use ¿ and any TVM variable onthe FINANCE VARS menu.If you enter less than six arguments, the TI-84 Plus substitutes a previously stored TVM variablevalue for each unspecified argument.If you enter any arguments with a TVM function, you must place the argument or arguments inparentheses. Chapter 14: Applications 248
tvm_Pmttvm_Pmt computes the amount of each payment.tvm_Pmt[(òÚ,¾æ,PV,FV,P/Y,C/Y)]Note: In the example above, the values are stored to the TVM variables in the TVM Solver. Thepayment (tvm_Pmt) is computed on the home screen using the values in the TVM Solver. Next, theinterest rate is changed to 9.5 to illustrate the effect on the payment amount.tvm_I%tvm_æ computes the annual interest rate.tvm_¾æ [(Ú,PV,PMT,FV,P/Y,C/Y)] ClassicMathPrint™tvm_PVtvm_PV computes the present value.tvm_PV[(Ú,¾æ,PMT,FV,P/Y,C/Y)]MathPrint™ Classictvm_Ntvm_Ú computes the number of payment periods. Chapter 14: Applications 249
tvm_Ú[(æ¾,PV,PMT,FV,P/Y,C/Y)]MathPrint™ Classictvm_FVtvm_FV computes the future value.tvm_FV[(Ú,¾æ,PV,PMT,P/Y,C/Y)]MathPrint™ ClassicCalculating Cash FlowsCalculating a Cash FlowUse the cash flow functions (menu items 7 and 8) to analyze the value of money over equal timeperiods. You can enter unequal cash flows, which can be cash inflows or outflows. The syntaxdescriptions for npv( and irr( use these arguments.• interest rate is the rate by which to discount the cash flows (the cost of money) over one period.• CF0 is the initial cash flow at time 0; it must be a real number.• CFList is a list of cash flow amounts after the initial cash flow CF0.• CFFreq is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they must be positive integers < 10,000.For example, express this uneven cash flow in lists.2000 2000 2000 4000 4000 -3000 Chapter 14: Applications 250
CF0 = 2000CFList = {2000,L3000,4000}CFFreq = {2,1,2}npv(, irr(npv( (net present value) is the sum of the present values for the cash inflows and outflows. Apositive result for npv indicates a profitable investment.npv(interest rate,CF0,CFList[,CFFreq])irr( (internal rate of return) is the interest rate at which the net present value of the cash flows isequal to zero.irr(CF0,CFList[,CFFreq]) 1000 0 5000 3000-2000 -2500Calculating AmortizationCalculating an Amortization ScheduleUse the amortization functions (menu items 9, 0, and A) to calculate balance, sum of principal, andsum of interest for an amortization schedule.bal(bal( computes the balance for an amortization schedule using stored values for æ, PV, and PMT.npmt is the number of the payment at which you want to calculate a balance. It must be a positiveinteger < 10,000. roundvalue specifies the internal precision the calculator uses to calculate thebalance; if you do not specify roundvalue, then the TI-84 Plus uses the current Float/Fix decimal-mode setting. Chapter 14: Applications 251
bal(npmt[,roundvalue])GPrn(, GInt(GPrn( computes the sum of the principal principal; if you do not specify roundvalue, the TI-84 Plus uses thecurrent Float/Fix decimal-mode setting.Note: You must enter values for æ, PV, PMT, and before computing the principal.GPrn(pmt1,pmt2[,roundvalue])GInt( computes the sum of the interest interest; if you do not specify roundvalue, the TI-84 Plus uses thecurrent Float/Fix decimal-mode setting.GInt(pmt1,pmt2[,roundvalue])Amortization Example: Calculating an Outstanding Loan BalanceYou want to buy a home with a 30-year mortgage at 8 percent APR. Monthly payments are 800.Calculate the outstanding loan balance after each payment and display the results in a graph andin the table.1. Press z. Press † ~ ~ ~ Í to set the fixed-decimal mode setting to 2. Press † † ~ Í to select Par graphing mode.2. Press Î Œ Í Í to display the TVM Solver. Chapter 14: Applications 252
3. Press 360 to enter number of payments. Press † 8 to enter the interest rate. Press † † Ì 800 to enter the payment amount. Press † 0 to enter the future value of the mortgage. Press † 12 to enter the payments per year, which also sets the compounding periods per year to 12. Press † † Í to select PMT:END.4. Move the cursor to the PV prompt and then press ƒ to solve for the present value.5. Press o to display the parametric Y= editor. Turn off all stat plots. Press " to define X1T as T. Press † Œ Í 9 " ¤ to define Y1T as bal(T).6. Press p to display the window variables. Enter the values below. Tmin=0 Xmin=0 Ymin=0 Tmax=360 Xmax=360 Ymax=125000 Tstep=12 Xscl=50 Yscl=100007. Press r to draw the graph and activate the trace cursor. Press ~ and | to explore the graph of the outstanding balance over time. Press a number and then press Í to view the balance at a specific time T.8. Press y - and enter the values below. TblStart=0 @Tbl=129. Press y 0 to display the table of outstanding balances (Y1T).10. Press z and select G-T split-screen mode, so that the graph and table are displayed simultaneously. Press r to display X1T (time) and Y1T (balance) in the table. Chapter 14: Applications 253
Calculating Interest ConversionCalculating an Interest ConversionUse the interest conversion functions (menu items B and C) to convert interest rates from anannual effective rate to a nominal rate (4Nom( ) or from a nominal rate to an annual effective rate(4Eff( ).4Nom(4Nom( computes the nominal interest rate. effective rate and compounding periods must be realnumbers. compounding periods must be >0.4Nom(effective rate,compounding periods)4Eff(4Eff( computes the effective interest rate. nominal rate and compounding periods must be real numbers.compounding periods must be >0.4Eff(nominal rate,compounding periods)Finding Days between Dates/Defining Payment Methoddbd(Use the date function dbd( (menu item D) to calculate the number of days between two dates usingthe actual-day-count method. date1 and date2 can be numbers or lists of numbers within the rangeof the dates on the standard calendar.Note: Dates must be between the years 1950 through 2049.dbd(date1,date2)You can enter date1 and date2 in either of two formats.• MM.DDYY (United States)• DDMM.YY (Europe) Chapter 14: Applications 254
The decimal placement differentiates the date formats.MathPrint™ ClassicDefining the Payment MethodPmt_End and Pmt_Bgn (menu items E and F) specify a transaction as an ordinary annuity or anannuity due. When you execute either command, the TVM Solver is updated.Pmt_EndPmt_End (payment end) specifies an ordinary annuity, where payments occur at the end of eachpayment period. Most loans are in this category. Pmt_End is the default.Pmt_EndOn the TVM Solver's PMT:END BEGIN line, select END to set PMT to ordinary annuity.Pmt_BgnPmt_Bgn (payment beginning) specifies an annuity due, where payments occur at the beginning ofeach payment period. Most leases are in this category.Pmt_BgnOn the TVM Solver's PMT:END BEGIN line, select BEGIN to set PMT to annuity due.Using the TVM VariablesFINANCE VARS MenuTo display the FINANCE VARS menu, press Œ Í ~. You can use TVM variables in TVMfunctions and store values to them on the home screen.CALC VARS1: Ú Total number of payment periods2: æ Annual interest rate3: PV Present value4: PMT Payment amount5: FV Future value6: P/Y Number of payment periods per year Chapter 14: Applications 255
CALC VARS7: C/Y Number of compounding periods/yearN, I%, PV, PMT, FVÚ, æ, PV, PMT, and FV are the five TVM variables. They represent the elements of commonfinancial transactions, as described in the table above. æ is an annual interest rate that isconverted to a per-period rate based on the values of P/Y and C/Y.P/Y and C/YP/Y is the number of payment periods per year in a financial transaction.C/Y is the number of compounding periods per year in the same transaction.When you store a value to P/Y, the value for C/Y automatically changes to the same value. To storea unique value to C/Y, you must store the value to C/Y after you have stored a value to P/Y.The EasyData™ ApplicationThe Vernier EasyData™ application by Vernier Software & Technology allows you to view andanalyze real-world data when the TI-84 Plus is connected to data collection devices such as TexasInstruments CBR 2é, CBL 2é, Vernier LabProê, Vernier USB sensors, Vernier Go!éMotion, orVernier Motion Detector Unit. The TI-84 Plus comes with the EasyData™ App already installed.Note: The application will only work with Vernier auto-ID sensors when using CBL 2é andVernier LabProê.The EasyData™ App will autolaunch on your TI-84 Plus if you plug in a USB sensor such as theCBR 2é or Vernier USB Temperature sensor.Steps for Running the EasyData™ AppFollow these basic steps when using the EasyData™ App. Chapter 14: Applications 256
Starting the EasyData™ App1. Attach your data collection device to your TI-84 Plus. Make sure the cables are firmly connected.2. If the EasyData™ App has not auto-launched, press Œ and the } or † to select the EasyData™ App.3. Press Í. The EasyData™ information screen is displayed for about three seconds followed by the main screen.Quitting the EasyData™ App1. To quit the EasyData™ App, select Quit (press s). The Ready to quit? screen is displayed, which indicates that the collected data has been transferred to lists L1 through L4 on the TI-84 Plus.2. Press OK (press s) to quit.EasyData™ SettingsChanging EasyData™ settingsThe EasyData™ App displays the most commonly used settings before data collection begins.To change a predefined setting:1. From the main screen in the EasyData™ App, choose Setup and select 2: Time Graph. The current settings are displayed on the calculator. Note: If using a motion detector, settings for 3: Distance Match and 4: Ball Bounce in the Setup menu are preset and cannot be changed.2. Select Next (press q) to move to the setting you want to change. Press ' to clear a setting.3. Repeat to cycle through the available options. When the option is correct, select Next to move to the next option.4. To change a setting, enter 1 or 2 digits, and then select Next (press q).5. When all the settings are correct, select OK (press s) to return to the main menu.6. Select Start (press q) to begin collecting data.Restoring the EasyData™ App to the default settingsThe default settings are appropriate for a wide variety of sampling situations. If you are unsure ofthe best settings, begin with the default settings, and then adjust the settings for your specificactivity.To restore the default settings in the EasyData™ App while a data collection device is connectedto the TI-84 Plus, choose File and select 1:New. Chapter 14: Applications 257
Starting and Stopping Data CollectionStarting Data CollectionTo start sampling, select Start (press q). Sampling will automatically stop when the number ofsamples set in the Time Graph Settings menu is reached. The TI-84 Plus will then display a graphof the sampled data.Stopping Data CollectionTo stop sampling before it automatically stops, select Stop (press and hold q) at any timeduring the sampling process. When sampling stops, a graph of the sampled data is displayed.Saving Collected DataCollected data is automatically transferred to the TI-84 Plus and stored in lists L1 through L4 whendata collection is complete. When you exit the EasyData™ App, a prompt reminds you of the listsin which time, distance, velocity, and acceleration are stored.This manual describes basic operation for the EasyData2™ application. For more informationabout the EasyData2™ App, visit Chapter 14: Applications 258
Chapter 15:CATALOG, Strings, Hyperbolic FunctionsBrowsing the TI-84 Plus CATALOGWhat Is the CATALOG?The CATALOG is an alphabetical list of all functions and instructions on the TI-84 Plus. You alsocan access each CATALOG item from a menu or the keyboard, except:• The six string functions• The six hyperbolic functions• The solve( instruction without the equation solver editor (Chapter 2)• The inferential stat functions without the inferential stat editors (Chapter 13)Note: The only CATALOG programming commands you can execute from the home screen areGetCalc(, Get(, and Send(.Selecting an Item from the CATALOGTo select a CATALOG item, follow these steps.1. Press y N to display the CATALOG. The 4 in the first column is the selection cursor.2. Press † or } to scroll the CATALOG until the selection cursor points to the item you want. • To jump to the first item beginning with a particular letter, press that letter; alpha-lock is on. • Items that begin with a number are in alphabetical order according to the first letter after the number. For example, 2-PropZTest( is among the items that begin with the letter P. • Functions that appear as symbols, such as +, L1, <, and ‡(, follow the last item that begins with Z. To jump to the first symbol, !, press [q].3. Press Í to paste the item to the current screen. Chapter 15: CATALOG, Strings, Hyperbolic Functions 259
Note:• From the top of the CATALOG menu, press } to move to the bottom. From the bottom, press † to move to the top.• When your TI-84 Plus is in MathPrint™ mode, many functions will paste the MathPrint™ template on the home screen. For example, abs( pastes the absolute value template on the home screen instead of abs(. MathPrint™ ClassicEntering and Using StringsWhat Is a String?A string is a sequence of characters that you enclose within quotation marks. On the TI-84 Plus, astring has two primary applications.• It defines text to be displayed in a program.• It accepts input from the keyboard in a program.Characters are the units that you combine to form a string.• Each number, letter, and space counts as one character.• Each instruction or function name, such as sin( or cos(, counts as one character; the TI-84 Plus interprets each instruction or function name as one character.Entering a StringTo enter a string on a blank line on the home screen or in a program, follow these steps.1. Press ƒ [ã] to indicate the beginning of the string.2. Enter the characters that comprise the string. • Use any combination of numbers, letters, function names, or instruction names to create the string. • To enter a blank space, press ƒ O. • To enter several alpha characters in a row, press y 7 to activate alpha-lock.3. Press ƒ [ã] to indicate the end of the string. ãstringã4. Press Í. On the home screen, the string is displayed on the next line without quotations. An ellipsis (...) indicates that the string continues beyond the screen. To scroll to see the entire string, press ~ and |. Chapter 15: CATALOG, Strings, Hyperbolic Functions 260
Note: A string must be enclosed in quotation marks. The quotation marks do not count as stringcharacters.Storing Strings to String VariablesString VariablesThe TI-84 Plus has 10 variables to which you can store strings. You can use string variables withstring functions and instructions.To display the VARS STRING menu, follow these steps.1. Press to display the VARS menu. Move the cursor to 7:String.2. Press Í to display the STRING secondary menu.Storing a String to a String VariableTo store a string to a string variable, follow these steps.1. Press ƒ [ã], enter the string, and press ƒ [ã].2. Press ¿.3. Press 7 to display the VARS STRING menu.4. Select the string variable (from Str1 to Str9, or Str0) to which you want to store the string. Chapter 15: CATALOG, Strings, Hyperbolic Functions 261
The string variable is pasted to the current cursor location, next to the store symbol (!).5. Press Í to store the string to the string variable. On the home screen, the stored string is displayed on the next line without quotation marks.Displaying the Contents of a String VariableTo display the contents of a string variable on the home screen, select the string variable from theVARS STRING menu, and then press Í. The string is displayed.String Functions and Instructions in the CATALOGDisplaying String Functions and Instructions in the CATALOGString functions and instructions are available only from the CATALOG. The table below lists thestring functions and instructions in the order in which they appear among the other CATALOGmenu items. The ellipses in the table indicate the presence of additional CATALOG items.CATALOG ... Equ4String( Converts an equation to a string. ... expr( Converts a string to an expression. ... inString( Returns a character's place number. ... length( Returns a string's character length. ... String4Equ( Converts a string to an equation. sub( Returns a string subset as a string. ... Chapter 15: CATALOG, Strings, Hyperbolic Functions 262
ConcatenationTo concatenate two or more strings, follow these steps.1. Enter string1, which can be a string or string name.2. Press Ã.3. Enter string2, which can be a string or string name. If necessary, press à and enter string3, and so on. string1+string2+string3...4. Press Í to display the strings as a single string.Selecting a String Function from the CATALOGTo select a string function or instruction and paste it to the current screen, follow the steps forselecting an item from the CATALOG.Equ4String(Equ4String( converts an equation to a string. The equation must be store in a VARS Y-VARSvariable. Yn contains the equation. Strn (from Str1 to Str9, or Str0) is the string variable to which youwant the equation to be stored.Equ4String(Yn,Strn)expr(expr( converts the character string contained in string to an expression and executes it. string can bea string or a string variable. Chapter 15: CATALOG, Strings, Hyperbolic Functions 263
expr(string)inString(inString( returns the character position in string of the first character of substring. string can be a stringor a string variable. start is an optional character position at which to start the search; the defaultis 1.inString(string,substring[,start])Note: If string does not contain substring, or start is greater than the length of string, inString( returns 0.length(length( returns the number of characters in string. string can be a string or string variable.Note: An instruction or function name, such as sin( or cos(, counts as one character.length(string)String4Equ(String4Equ( converts string into an equation and stores the equation to Yn. string can be a string orstring variable. String4Equ( is the inverse of Equ4String(.String4Equ(string,Yn) Chapter 15: CATALOG, Strings, Hyperbolic Functions 264
sub(sub( returns a string that is a subset of an existing string. string can be a string or a string variable.begin is the position number of the first character of the subset. length is the number of characters inthe subset.sub(string,begin,length)Entering a Function to Graph during Program ExecutionIn a program, you can enter a function to graph during program execution using these commands.Note: When you execute this program, enter a function to store to Y3 at the ENTRY= prompt. Chapter 15: CATALOG, Strings, Hyperbolic Functions 265
Hyperbolic Functions in the CATALOGHyperbolic FunctionsThe hyperbolic functions are available only from the CATALOG. The table below lists thehyperbolic functions in the order in which they appear among the other CATALOG menu items. Theellipses in the table indicate the presence of additional CATALOG items.CATALOG ... cosh( Hyperbolic cosine cosh-1( Hyperbolic arccosine ... sinh( Hyperbolic sine sinh-1( Hyperbolic arcsine ... tanh( Hyperbolic tangent tanh-1( Hyperbolic arctangent ...sinh(, cosh(, tanh(sinh(, cosh(, and tanh( are the hyperbolic functions. Each is valid for real numbers, expressions,and lists.sinh(value)cosh(value)tanh(value)sinh-1(, cosh-1(, tanh-1(sinh-1( is the hyperbolic arcsine function. cosh-1( is the hyperbolic arccosine function. tanh-1( is thehyperbolic arctangent function. Each is valid for real numbers, expressions, and lists. Chapter 15: CATALOG, Strings, Hyperbolic Functions 266
Chapter 16:ProgrammingGetting Started: Volume of a CylinderGetting Started is a fast-paced introduction. Read the chapter for details.A program is a set of commands that the TI-84 Plus executes sequentially, as if you had enteredthem from the keyboard. Create a program that prompts for the radius R and the height H of acylinder and then computes its volume.1. Press ~ ~ to display the PRGM NEW menu.2. Press Í to select 1:Create New. The Name= prompt is displayed, and alpha-lock is on. Press C Y L I N D E R, and then press Í to name the program CYLINDER. You are now in the program editor. The colon ( : ) in the first column of the second line indicates the beginning of a command line.3. Press ~ 2 to select 2:Prompt from the PRGM I/O menu. Prompt is copied to the command line. Press ƒ R ¢ ƒ H to enter the variable names for radius and height. Press Í.4. Press y B ƒ R ¡ ƒ H ¿ ƒ V Í to enter the expression pR 2H and store it to the variable V.5. Press ~ 3 to select 3:Disp from the PRGM I/O menu. Disp is pasted to the command line. Press y 7 [ã] V O L U M E O I S [ã] ƒ ¢ ƒ V Í to set up the program to display the text VOLUME IS on one line and the calculated value of V on the next.6. Press y 5 to display the home screen. Chapter 16: Programming 268
7. Press to display the PRGM EXEC menu. The items on this menu are the names of stored programs.8. Press Í to paste prgmCYLINDER to the current cursor location. (If CYLINDER is not item 1 on your PRGM EXEC menu, move the cursor to CYLINDER before you press Í.)9. Press Í to execute the program. Enter 1.5 for the radius, and then press Í. Enter 3 for the height, and then press Í. The text VOLUME IS, the value of V, and Done are displayed. Repeat steps 7 through 9 and enter different values for R and H.Creating and Deleting ProgramsWhat Is a Program?A program is a set of one or more command lines. Each line contains one or more instructions.When you execute a program, the TI-84 Plus performs each instruction on each command line inthe same order in which you entered them. The number and size of programs that the TI-84 Pluscan store is limited only by available memory.What Is New with Operating System 2.53MP?• Programs created with OS 2.43 and earlier should run correctly but may give unexpected results when you run them using OS 2.53MP. You should test programs created with earlier OS versions to make sure you get the desired results.• Programs can run in Classic or MathPrint™ mode.• Shortcut menus are available wherever the MATH menu can be accessed.• MathPrint™ templates are not available for programs. All input and output is in Classic format.• You can use fractions in programs, but you should test the program to make sure that you get the desired results.• The spacing of the display may be slightly different in MathPrint™ mode than in Classic mode. If you prefer the spacing in Classic mode, set the mode using a command in your program. Screen shots for the examples in this chapter were taken in Classic mode. Chapter 16: Programming 269
Creating a New ProgramTo create a new program, follow these steps.1. Press | to display the PRGM NEW menu.2. Press Í to select 1:Create New. The Name= prompt is displayed, and alpha-lock is on.3. Press a letter from A to Z or q to enter the first character of the new program name. Note: A program name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q.4. Enter zero to seven letters, numbers, or q to complete the new program name.5. Press Í. The program editor is displayed.6. Enter one or more program commands.7. Press y 5 to leave the program editor and return to the home screen.Managing Memory and Deleting a ProgramTo check whether adequate memory is available for a program you want to enter:1. Press y L to display the MEMORY menu.2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu (Chapter 18).3. Select 7:Prgm to display the PRGM editor.The TI-84 Plus expresses memory quantities in bytes.You can increase available memory in one of two ways. You can delete one or more programs oryou can archive some programs.To increase available memory by deleting a specific program:1. Press y L and then select 2:Mem Mgmt/Del from the MEMORY menu.2. Select 7:Prgm to display the PRGM editor (Chapter 18). Chapter 16: Programming 270
3. Press } and † to move the selection cursor (4) next to the program you want to delete, and then press {. The program is deleted from memory. Note: You will receive a message asking you to confirm this delete action. Select 2:yes to continue. To leave the PRGM editor screen without deleting anything, press y 5, which displays the home screen.To increase available memory by archiving a program:4. Press y L and then select 2:Mem Mgmt/Del from the MEMORY menu.5. Select 2:Mem Mgmt/Del to display the MEM MGMT/DEL menu.6. Select 7:Prgm... to display the PRGM menu.7. Press Í to archive the program. An asterisk will appear to the left of the program to indicate it is an archived program. To unarchive a program in this screen, put the cursor next to the archived program and press Í. The asterisk will disappear. Note: Archive programs cannot be edited or executed. In order to edit or execute an archived program, you must first unarchive it.Entering Command Lines and Executing ProgramsEntering a Program Command LineYou can enter on a command line any instruction or expression that you could execute from thehome screen. In the program editor, each new command line begins with a colon. To enter morethan one instruction or expression on a single command line, separate each with a colon.Note: A command line can be longer than the screen is wide.While in the program editor, you can display and select from menus. You can return to the programeditor from a menu in either of two ways.• Select a menu item, which pastes the item to the current command line. — or —• Press '.When you complete a command line, press Í. The cursor moves to the next command line. Chapter 16: Programming 271
Programs can access variables, lists, matrices, and strings saved in memory. If a program stores anew value to a variable, list, matrix, or string, the program changes the value in memory duringexecution.You can call another program as a subroutine.Executing a ProgramTo execute a program, begin on a blank line on the home screen and follow these steps.1. Press to display the PRGM EXEC menu.2. Select a program name from the PRGM EXEC menu. prgmname is pasted to the home screen (for example, prgmCYLINDER).3. Press Í to execute the program. While the program is executing, the busy indicator is on.Last Answer (Ans) is updated during program execution. Last Entry is not updated as eachcommand is executed (Chapter 1).The TI-84 Plus checks for errors during program execution. It does not check for errors as youenter a program.Breaking a ProgramTo stop program execution, press É. The ERR:BREAK menu is displayed.• To return to the home screen, select 1:Quit.• To go where the interruption occurred, select 2:Goto.Editing ProgramsEditing a ProgramTo edit a stored program, follow these steps.1. Press ~ to display the PRGM EDIT menu.2. Select a program name from the PRGM EDIT menu. Up to the first seven lines of the program are displayed. Note: The program editor does not display a $ to indicate that a program continues beyond the screen.3. Edit the program command lines. • Move the cursor to the appropriate location, and then delete, overwrite, or insert. • Press ' to clear all program commands on the command line (the leading colon remains), and then enter a new program command. Chapter 16: Programming 272
Note: To move the cursor to the beginning of a command line, press y |; to move to the end,press y ~. To scroll the cursor down seven command lines, press ƒ †. To scroll the cursorup seven command lines, press ƒ }.Inserting and Deleting Command LinesTo insert a new command line anywhere in the program, place the cursor where you want the newline, press y 6, and then press Í. A colon indicates a new line.To delete a command line, place the cursor on the line, press ' to clear all instructions andexpressions on the line, and then press { to delete the command line, including the colon.Copying and Renaming ProgramsCopying and Renaming a ProgramTo copy all command lines from one program into a new program, follow steps 1 through 5 forCreating a New Program, and then follow these steps.1. Press y K. Rcl is displayed on the bottom line of the program editor in the new program (Chapter 1).2. Press | to display the PRGM EXEC menu.3. Select a name from the menu. prgmname is pasted to the bottom line of the program editor.4. Press Í. All command lines from the selected program are copied into the new program.Copying programs has at least two convenient applications.• You can create a template for groups of instructions that you use frequently.• You can rename a program by copying its contents into a new program.Note: You also can copy all the command lines from one existing program to another existingprogram using RCL.Scrolling the PRGM EXEC and PRGM EDIT MenusThe TI-84 Plus sorts PRGM EXEC and PRGM EDIT menu items automatically into alphanumericalorder. Each menu only labels the first 10 items using 1 through 9, then 0.To jump to the first program name that begins with a particular alpha character or q, press ƒ[letter from A to Z or q].Note: From the top of either the PRGM EXEC or PRGM EDIT menu, press } to move to the bottom.From the bottom, press † to move to the top. To scroll the cursor down the menu seven items,press ƒ †. To scroll the cursor up the menu seven items, press ƒ }. Chapter 16: Programming 273
PRGM CTL (Control) InstructionsPRGM CTL MenuTo display the PRGM CTL (program control) menu, press from the program editor only.CTL I/O EXEC1: If Creates a conditional test.2: Then Executes commands when If is true.3: Else Executes commands when If is false.4: For( Creates an incrementing loop.5: While Creates a conditional loop.6: Repeat Creates a conditional loop.7: End Signifies the end of a block.8: Pause Pauses program execution.9: Lbl Defines a label.0: Goto Goes to a label.A: IS>( Increments and skips if greater than.B: DS<( Decrements and skips if less than.C: Menu( Defines menu items and branches.D: prgm Executes a program as a subroutine.E: Return Returns from a subroutine.F: Stop Stops execution.G: DelVar Deletes a variable from within program.H: GraphStyle( Designates the graph style to be drawn.I: OpenLib( No longer used.J: ExecLib( No longer used.These menu items direct the flow of an executing program. They make it easy to repeat or skip agroup of commands during program execution. When you select an item from the menu, the nameis pasted to the cursor location on a command line in the program.To return to the program editor without selecting an item, press '.Controlling Program FlowProgram control instructions tell the TI-84 Plus which command to execute next in a program. If,While, and Repeat check a defined condition to determine which command to execute next.Conditions frequently use relational or Boolean tests (Chapter 2), as in: Chapter 16: Programming 274
If A<7:A+1!AorIf N=1 and M=1:Goto ZIfUse If for testing and branching. If condition is false (zero), then the command immediately following Ifis skipped. If condition is true (nonzero), then the next command is executed. If instructions can benested.:If condition:command (if true):commandProgram OutputIf-ThenThen following an If executes a group of commands if condition is true (nonzero). End identifies theend of the group of commands.:If condition:Then:command (if true):command (if true):End:commandProgram OutputIf-Then-ElseElse following If-Then executes a group of commands if condition is false (zero). End identifies the endof the group of commands.:If condition:Then:command (if true) Chapter 16: Programming 275
:command (if true):Else:command (if false):command (if false):End:commandProgram OutputNote: In OS 2.53MP, the program name displays again when you press Í to repeat theprogram.For(For( loops and increments. It increments variable from begin to end by increment. increment is optional(default is 1) and can be negative (end<begin). end is a maximum or minimum value not to beexceeded. End identifies the end of the loop. For( loops can be nested.:For(variable,begin,end[,increment]):command (while end not exceeded):command (while end not exceeded):End:commandProgram OutputWhileWhile performs a group of commands while condition is true. condition is frequently a relational test(Chapter 2). condition is tested when While is encountered. If condition is true (nonzero), the programexecutes a group of commands. End signifies the end of the group. When condition is false (zero), theprogram executes each command following End. While instructions can be nested.:While condition:command (while condition is true):command (while condition is true) Chapter 16: Programming 276
:End:commandProgram OutputRepeatRepeat repeats a group of commands until condition is true (nonzero). It is similar to While, but conditionis tested when End is encountered; therefore, the group of commands is always executed at leastonce. Repeat instructions can be nested.:Repeat condition:command (until condition is true):command (until condition is true):End:commandProgram OutputEndEnd identifies the end of a group of commands. You must include an End instruction at the end ofeach For(, While, or Repeat loop. Also, you must paste an End instruction at the end of each If-Thengroup and each If-Then-Else group.PausePause suspends execution of the program so that you can see answers or graphs. During thepause, the pause indicator is on in the top-right corner. Press Í to resume execution.• Pause without a value temporarily pauses the program. If the DispGraph or Disp instruction has been executed, the appropriate screen is displayed.• Pause with value displays value on the current home screen. value can be scrolled. Chapter 16: Programming 277
Pause [value]Program OutputLbl, GotoLbl (label) and Goto (go to) are used together for branching.Lbl specifies the label for a command. label can be one or two characters (A through Z, 0 through99, or q).Lbl labelGoto causes the program to branch to label when Goto is encountered.Goto labelProgram Output Chapter 16: Programming 278
IS>(IS>( (increment and skip) adds 1 to variable. If the answer is > value (which can be an expression),the next command is skipped; if the answer is { value, the next command is executed. variable cannotbe a system variable.:IS>(variable,value):command (if answer value):command (if answer > value)Program OutputNote: IS>( is not a looping instruction.DS<(DS<( (decrement and skip) subtracts 1 from variable. If the answer is < value (which can be anexpression), the next command is skipped; if the answer is | value, the next command is executed.variable cannot be a system variable.:DS<(variable,value):command (if answer ' value):command (if answer < value)Program OutputNote: DS<( is not a looping instruction.Menu(Menu( sets up branching within a program. If Menu( is encountered during program execution, themenu screen is displayed with the specified menu items, the pause indicator is on, and executionpauses until you select a menu item.The menu title is enclosed in quotation marks ( " ). Up to seven pairs of menu items follow. Eachpair comprises a text item (also enclosed in quotation marks) to be displayed as a menu selection,and a label item to which to branch if you select the corresponding menu selection.Menu("title","text1",label1,"text2",label2, . . .)Program Output Chapter 16: Programming 279
The program above pauses until you select 1 or 2. If you select 2, for example, the menudisappears and the program continues execution at Lbl B.prgmUse prgm to execute other programs as subroutines. When you select prgm, it is pasted to thecursor location. Enter characters to spell a program name. Using prgm is equivalent to selectingexisting programs from the PRGM EXEC menu; however, it allows you to enter the name of aprogram that you have not yet created.prgmnameNote: You cannot directly enter the subroutine name when using RCL. You must paste the namefrom the PRGM EXEC menu.ReturnReturn quits the subroutine and returns execution to the calling program, even if encounteredwithin nested loops. Any loops are ended. An implied Return exists at the end of any program thatis called as a subroutine. Within the main program, Return stops execution and returns to thehome screen.StopStop stops execution of a program and returns to the home screen. Stop is optional at the end of aprogram.DelVarDelVar deletes from memory the contents of variable.DelVar variable Chapter 16: Programming 280
GraphStyle(GraphStyle( designates the style of the graph to be drawn. function# is the number of the Y= functionname in the current graphing mode. graphstyle is a number from 1 to 7 that corresponds to thegraph style, as shown below.1 = ç (line) 5 = ë (path)2 = è (thick) 6 = ì (animate)3 = é (shade above) 7 = í (dot)4 = ê (shade below)GraphStyle(function#,graphstyle)For example, GraphStyle(1,5) in Func mode sets the graph style for Y1 to ë (path; 5).Not all graph styles are available in all graphing modes. For a detailed description of each graphstyle, see the Graph Styles table in Chapter 3.PRGM I/O (Input/Output) InstructionsPRGM I/O MenuTo display the PRGM I/O (program input/output) menu, press ~ from within the programeditor only.CTL I/O EXEC1: Input Enters a value or uses the cursor.2: Prompt Prompts for entry of variable values.3: Disp Displays text, value, or the home screen.4: DispGraph Displays the current graph.5: DispTable Displays the current table.6: Output( Displays text at a specified position.7: getKey Checks the keyboard for a keystroke.8: ClrHome Clears the display.9: ClrTable Clears the current table.0: GetCalc( Gets a variable from another TI-84 Plus.A: Get( Gets a variable from CBL 2™ or CBR™.B: Send( Sends a variable to CBL 2 or CBR.These instructions control input to and output from a program during execution. They allow you toenter values and display answers during program execution.To return to the program editor without selecting an item, press '. Chapter 16: Programming 281
Displaying a Graph with InputInput without a variable displays the current graph. You can move the free-moving cursor, whichupdates X and Y (and R and q for PolarGC format). The pause indicator is on. Press Í toresume program execution.InputProgram OutputStoring a Variable Value with InputInput with variable displays a ? (question mark) prompt during execution. variable may be a realnumber, complex number, list, matrix, string, or Y= function. During program execution, enter avalue, which can be an expression, and then press Í. The value is evaluated and stored tovariable, and the program resumes execution.Input [variable]You can display text or the contents of Strn (a string variable) of up to 16 characters as a prompt.During program execution, enter a value after the prompt and then press Í. The value isstored to variable, and the program resumes execution.Input ["text",variable]Input [Strn,variable]Program Output Chapter 16: Programming 282
Note: When a program prompts for input of lists and Yn functions during execution, you mustinclude the braces ( { } ) around the list elements and quotation marks ( " ) around theexpressions.PromptDuring program execution, Prompt displays each variable, one at a time, followed by =?. At eachprompt, enter a value or expression for each variable, and then press Í. The values are stored,and the program resumes execution.Prompt variableA[,variableB,...,variable n]Program OutputNote: Y= functions are not valid with Prompt.Displaying the Home ScreenDisp (display) without a value displays the home screen. To view the home screen during programexecution, follow the Disp instruction with a Pause instruction.DispDisplaying Values and MessagesDisp with one or more values displays the value of each.Disp [valueA,valueB,valueC,...,value n]• If value is a variable, the current value is displayed.• If value is an expression, it is evaluated and the result is displayed on the right side of the next line.• If value is text within quotation marks, it is displayed on the left side of the current display line. ! is not valid as text.Program OutputIf Pause is encountered after Disp, the program halts temporarily so you can examine the screen.To resume execution, press Í. Chapter 16: Programming 283
Note: If a matrix or list is too large to display in its entirety, ellipses (...) are displayed in the lastcolumn, but the matrix or list cannot be scrolled. To scroll, use Pause value.DispGraphDispGraph (display graph) displays the current graph. If Pause is encountered after DispGraph, theprogram halts temporarily so you can examine the screen. Press Í to resume execution.DispTableDispTable (display table) displays the current table. The program halts temporarily so you canexamine the screen. Press Í to resume execution.Output(Output( displays text or value on the current home screen beginning at row (1 through 8) and column(1 through 16), overwriting any existing characters.Note: You may want to precede Output( with ClrHome.Expressions are evaluated and values are displayed according to the current mode settings.Matrices are displayed in entry format and wrap to the next line. ! is not valid as text.Output(row,column,"text")Output(row,column,value)Program OutputFor Output( on a Horiz split screen, the maximum value for row is 4. Chapter 16: Programming 284
getKeygetKey returns a number corresponding to the last key pressed, according to the key code diagrambelow. If no key has been pressed, getKey returns 0. Use getKey inside loops to transfer control,for example, when creating video games.Program Output Note: , Œ, , and Í were pressed during program execution.Note: You can press É at any time during execution to break the program.TI-84 Plus Key Code DiagramClrHome, ClrTableClrHome (clear home screen) clears the home screen during program execution.ClrTable (clear table) clears the values in the table during program execution.GetCalc(GetCalc( gets the contents of variable on another TI-84 Plus and stores it to variable on the receivingTI-84 Plus. variable can be a real or complex number, list element, list name, matrix element, matrixname, string, Y= variable, graph database, or picture. Chapter 16: Programming 285
GetCalc(variable[,portflag])By default, the TI-84 Plus uses the USB port if it is connected. If the USB cable is not connected, ituses the I/O port. If you want to specify either the USB or I/O port, use the following portflagnumbers:portflag=0 use USB port if connected;portflag=1 use USB port;portflag=2 use I/O portNote: GetCalc( does not work between TI.82 and TI-83 Plus or a TI.82 and TI-84 Plus calculators.Get(, Send(Get( gets data from the CBL 2™ or CBR™ and stores it to variable on the receiving TI-84 Plus.variable can be a real number, list element, list name, matrix element, matrix name, string,Y= variable, graph database, or picture.Get(variable)Note: If you transfer a program that references the Get( command to the TI-84 Plus from a TI.82,the TI-84 Plus will interpret it as the Get( described above. Use GetCalc( to get data from anotherTI-84 Plus.Send( sends the contents of variable to the CBL 2™ or CBR™. You cannot use it to send to anotherTI-84 Plus. variable can be a real number, list element, list name, matrix element, matrix name,string, Y= variable, graph database, or picture. variable can be a list of elements.Send(variable) Note: This program gets sound data and time in seconds from CBL 2™.Note: You can access Get(, Send(, and GetCalc( from the CATALOG to execute them from thehome screen (Chapter 15).Calling Other Programs as SubroutinesCalling a Program from Another ProgramOn the TI-84 Plus, any stored program can be called from another program as a subroutine. Enterthe name of the program to use as a subroutine on a line by itself.You can enter a program name on a command line in either of two ways.• Press | to display the PRGM EXEC menu and select the name of the program prgmname is pasted to the current cursor location on a command line. Chapter 16: Programming 286
• Select prgm from the PRGM CTL menu, and then enter the program name.prgmnameWhen prgmname is encountered during execution, the next command that the program executes isthe first command in the second program. It returns to the subsequent command in the firstprogram when it encounters either Return or the implied Return at the end of the second program.Program OutputSubroutine ( Notes about Calling ProgramsVariables are global.label used with Goto and Lbl is local to the program where it is located. label in one program is notrecognized by another program. You cannot use Goto to branch to a label in another program.Return exits a subroutine and returns to the calling program, even if it is encountered within nestedloops.Running an Assembly Language ProgramYou can run programs written for the TI-84 Plus in assembly language. Typically, assemblylanguage programs run much faster and provide greater control than than the keystroke programsthat you write with the built-in program editor.Note: Because an assembly langauge program has greater control over the calculator, if yourassembly language program has error(s), it may cause your calculator to reset and lose all data,programs, and applications stored in memory.When you download an assembly language program, it is stored among the other programs as aPRGM menu item. You can:• Transmit it using the TI-84 Plus communication link (Chapter 19).• Delete it using the MEM MGMT DEL screen (Chapter 18).To run an assembly Program, the syntax is: Asm(assemblyprgmname) Chapter 16: Programming 287
If you write an assembly language program, use the two instructions below from the CATALOG toidentify and compile the program.Instructions CommentsAsmComp(prgmASM1, Compiles an assembly language program written inprgmASM2) ASCII and stores the hex versionAsmPrgm Identifies an assembly language program; must be entered as the first line of an assembly language programTo compile an assembly program that you have written:1. Follow the steps for writing a program (16-4) but be sure to include AsmPrgm as the first line of your program.2. From the home screen, press y N and then select AsmComp( to paste it to the screen.3. Press to display the PRGM EXEC menu.4. Select the program you want to compile. It will be pasted to the home screen.5. Press ¢ and then select prgm from the CATALOG.6. Key in the name you have chosen for the output program. Note: This name must be unique — not a copy of an existing program name.7. Press ¤ to complete the sequence. The sequence of the arguments should be as follows: AsmComp(prgmASM1, prgmASM2)8. Press Í to compile your program and generate the output program. Chapter 16: Programming 288
Chapter 17:ActivitiesThe Quadratic FormulaNote: This example uses MathPrint™ mode for real answers and Classic mode for non-real(complex) results. You can also use the Polynomial Root Finder/Simultaneous Equation Solverapplication to solve these types of problems with a quick set-up. This application comes preloadedon your TI-84 Plus and can be downloaded from education.ti.com.Use the quadratic formula to solve the quadratic equations 2x2 N 11x + 14 = 0 and2x2 N 6x + 5 = 0.Graphing the FunctionsBefore you begin, look at the graphs of the functions to see the approximate locations of thesolutions.1. Press o to display the Y= editor.2. Press 2 " ¡ ¹ 11 " Ã 14 for Y1, and then press Í.3. Press 2 " ¡ ¹ 6 " Ã 5 for Y2.4. Press q and select 4:ZDecimal. The graph of the functions displays.You can see that the graph of the firstfunction, 2x2 N 11x + 14 = 0, crosses thex-axis, so it has a real solution. The graph ofthe second function does not cross thex-axis, so it has a complex solution. Chapter 17: Activities 289
Entering a CalculationBegin with the equation 2x2 N 11x + 14 = 0.1. Press 2 ¿ ƒ A to store the coefficient of the x2 term.2. Press ƒ [:]. The colon allows you to enter more than one instruction on a line.3. Press Ì 11 ¿ ƒ B to store the coefficient of the X term. Press ƒ [:] to enter a new instruction on the same line. Press 14 ¿ ƒ C to store the constant.4. Press Í to store the values to the variables A, B, and C.5. The last value you stored is shown on the right side of the display. The cursor moves to the next line, ready for your next entry.6. Press ƒ ^ 1 Ì ƒ B Ã y C ƒ B ¡¹ 4 ƒ A ƒ C ~~2 ƒ A to enter the expression for one of the solutions for the quadratic formula, 2 – b b – 4ac -------------------------------------- 2a7. Press Í to find one solution for the equation 2x2 N 11x + 14 = 0. The answer is shown on the right side of the display. The cursor moves to the next line, ready for you to enter the next expression.Converting to a DecimalYou can show the solution as a fraction.1. Press ƒ ^ 4 to select 4F3 4D from the FRAC shortcut menu. Chapter 17: Activities 290
2. Press Í to convert the result to a decimal.To save keystrokes, you can scroll up to find an expression you entered, copy it, and then edit it fora new calculation.3. Press } to highlight and then press Í to paste it to the entry line.4. Press | until the cursor is on the + sign in the formula. Press ¹ to edit the quadratic-formula expression to become .5. Press Í to find the other solution for the quadratic equation 2x2 N 11x + 14 = 0.Displaying Complex ResultsNow solve the equation 2x2 N 6x + 5 = 0. When you set a+bi complex number mode, the TI-84Plus displays complex results.1. Press z † † † † † † (6 times), and then press ~ to highlight a+bi. Press Í to select a+bi complex-number mode.2. Press y 5 to return to the home screen, and then press ' to clear it. Chapter 17: Activities 291
3. Press 2 ¿ ƒ A ƒ [:] Ì 6 ¿ ƒ B ƒ [:] 5 ¿ ƒ C Í. The coefficient of the x2 term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively.4. Enter the quadratic formula using Classic entry: £ Ì ƒ B à y C ƒ B ¡¹4 ƒA ƒC ~¤¥£2 ƒ A ¤. Because the solution is a complex number, you have to enter the formula using the division operation instead of using the n/d shortcut template. Complex numbers are not valid in the n/d template in input or output and will cause Error: Data Type to display.5. Press Í to find one solution for the equation 2x2 N 6x + 5 = 0.6. Press } to highlight the quadratic- formula expression, and then press Í to paste it to the entry line.7. Press | until the cursor is on the + sign in the formula. Press ¹ to edit the quadratic-formula expression to become .8. Press Í to find the other solution for the quadratic equation: 2x2 N 6x + 5 = 0. Chapter 17: Activities 292
Box with LidDefining a FunctionTake a 20 cm × 25 cm. sheet of paper and cut X × X squares from two corners. Cut X × 12½ cmrectangles from the other two corners as shown in the diagram below. Fold the paper into a boxwith a lid. What value of X would give your box the maximum volume V? Use the table and graphsto determine the solution.Begin by defining a function that describesthe volume of the box. XFrom the diagram: 20 A2X + A = 202X + 2B = 25 X B X BV = A…B…X 25Substituting:V = (20 N 2X) (25à2 N X) X1. Press o to display the Y= editor, which is where you define functions for tables and graphing.2. Press £ 20 ¹ 2 " ¤ £ 25 t ^ 1 2 ~ ¹ " ¤ " Í to define the volume function as Y1 in terms of X. " lets you enter X quickly, without having to press ƒ. The highlighted = sign indicates that Y1 is selected.Defining a Table of ValuesThe table feature of the TI-84 Plus displays numeric information about a function. You can use atable of values from the function you just defined to estimate an answer to the problem.1. Press y - to display the TABLE SETUP menu.2. Press Í to accept TblStart=0.3. Press 1 Í to define the table increment @Tbl=1. Leave Indpnt: Auto and Depend: Auto so that the table will be generated automatically. Chapter 17: Activities 293
4. Press y 0 to display the table. Notice that the maximum value for Y1 (box's volume) occurs when X is about 4, between 3 and 5.5. Press and hold † to scroll the table until a negative result for Y1 is displayed. Notice that the maximum length of X for this problem occurs where the sign of Y1 (box's volume) changes from positive to negative, between 10 and 11.6. Press y -. Notice that TblStart has changed to 5 to reflect the first line of the table as it was last displayed. (In step 5, the first value of X displayed in the table is 5.)Zooming In on the TableYou can adjust the way a table is displayed to get more information about a defined function. Withsmaller values for @Tbl, you can zoom in on the table. You can change the values on the TBLSETscreen by pressing y - or by pressing à on the TABLE screen1. Press y 0.2. Press } to move the cursor to highlight 3.3. Press Ã. The @Tbl displays on the entry line.4. Enter Ë 1 Í. The table updates, showing the changes in X in increments of 0.1. Notice that the maximum value for Y1 in this table view is 410.26, which occurs at X=3.7. Therefore, the maximum occurs where 3.6<X<3.8.5. With X=3.6 highlighted, press Ã Ë 01 Í to set @Tbl=0.01. Chapter 17: Activities 294
6. Press † and } to scroll the table. Four equivalent maximum values are shown, 410.26 at X=3.67, 3.68, 3.69, and 3.70.7. Press † or } to move the cursor to 3.67. Press ~ to move the cursor into the Y1 column. The value of Y1 at X=3.67 is displayed on the bottom line in full precision as 410.261226.8. Press † to display the other maximum. The value of Y1 at X=3.68 in full precision is 410.264064, at X=3.69 is 410.262318 and at X=3.7 is 410.256. The maximum volume of the box would occur at 3.68 if you could measure and cut the paper at .01-centimeter increments.Setting the Viewing WindowYou also can use the graphing features of the TI-84 Plus to find the maximum value of a previouslydefined function. When the graph is activated, the viewing window defines the displayed portion ofthe coordinate plane. The values of the window variables determine the size of the viewingwindow.1. Press p to display the window editor, where you can view and edit the values of the window variables. The standard window variables define the viewing window as shown. Xmin, Xmax, Ymin, and Ymax define the boundaries of the display. Xscl and Yscl define the distance between tick marks on the X and Y axes. Xres controls resolution. Chapter 17: Activities 295
2. Press 0 Í to define Xmin.3. Press 20 ¥ 2 to define Xmax using an expression. Note: For this example, the division sign is used for the calculation. However, you can use n/d entry format where fraction output can be experienced, depending on mode settings.4. Press Í. The expression is evaluated, and 10 is stored in Xmax. Press Í to accept Xscl as 1.5. Press 0 Í 500 Í 100 Í 1 Í to define the remaining window variables.Displaying and Tracing the GraphNow that you have defined the function to be graphed and the window in which to graph it, you candisplay and explore the graph. You can trace along a function using the TRACE feature.1. Press s to graph the selected function in the viewing window. The graph of Y1=(20N2X)(25à2NX)X is displayed.2. Press ~ to activate the free-moving graph cursor. The X and Y coordinate values for the position of the graph cursor are displayed on the bottom line.3. Press |, ~, }, and † to move the free- moving cursor to the apparent maximum of the function. As you move the cursor, the X and Y coordinate values are updated continually.4. Press r. The trace cursor is displayed on the Y1 function. The function that you are tracing is displayed in the top-left corner.5. Press | and ~ to trace along Y1, one X dot at a time, evaluating Y1 at each X. Chapter 17: Activities 296
You also can enter your estimate for the maximum value of X.6. Press 3 Ë 8. When you press a number key while in TRACE, the X= prompt is displayed in the bottom-left corner.7. Press Í. The trace cursor jumps to the point on the Y1 function evaluated at X=3.8.8. Press | and ~ until you are on the maximum Y value. This is the maximum of Y1(X) for the X pixel values. The actual, precise maximum may lie between pixel values.Zooming In on the GraphTo help identify maximums, minimums, roots, and intersections of functions, you can magnify theviewing window at a specific location using the ZOOM instructions.1. Press q to display the ZOOM menu. This menu is a typical TI-84 Plus menu. To select an item, you can either press the number or letter next to the item, or you can press † until the item number or letter is highlighted, and then press Í.2. Press 2 to select 2:Zoom In. The graph is displayed again. The cursor has changed to indicate that you are using a ZOOM instruction.3. With the cursor near the maximum value of the function, press Í. The new viewing window is displayed. Both XmaxNXmin and YmaxNYmin have been adjusted by factors of 4, the default values for the zoom factors.4. Press | and ~ to search for the maximum value. Chapter 17: Activities 297
5. Press p to display the new window settings. Note: To return to the previous graph, press q ~ 1:ZPrevious.Finding the Calculated MaximumYou can use a CALCULATE menu operation to calculate a local maximum of a function. To do this,pick a point to the left of where you think the maximum is on the graph. This is called the leftbound. Next, pick a point to the right of the maximum. This is called the right bound. Finally, guessthe maximum by moving the cursor to a point between the left and right bounds. With thisinformation, the maximum can be calculated by the methods programmed in the TI-84 Plus.1. Press y / to display the CALCULATE menu. Press 4 to select 4:maximum. The graph is displayed again with a Left Bound? prompt.2. Press | to trace along the curve to a point to the left of the maximum, and then press Í. A 4 at the top of the screen indicates the selected bound. A Right Bound? prompt is displayed.3. Press ~ to trace along the curve to a point to the right of the maximum, and then press Í. A 3 at the top of the screen indicates the selected bound. A Guess? prompt is displayed.4. Press | to trace to a point near the maximum, and then press Í. Chapter 17: Activities 298
Or, press 3 Ë 8, and then press Í toenter a guess for the maximum.When you press a number key in TRACE,the X= prompt is displayed in the bottom-left corner.Notice how the values for the calculatedmaximum compare with the maximumsfound with the free-moving cursor, thetrace cursor, and the table.Note: In steps 2 and 3 above, you canenter values directly for Left Bound andRight Bound, in the same way asdescribed in step 4. Chapter 17: Activities 299
Comparing Test Results Using Box PlotsProblemAn experiment found a significant difference between boys and girls pertaining to their ability toidentify objects held in their left hands, which are controlled by the right side of their brains, versustheir right hands, which are controlled by the left side of their brains. The TI Graphics teamconducted a similar test for adult men and women.The test involved 30 small objects, which participants were not allowed to see. First, they held 15of the objects one by one in their left hands and guessed what they were. Then they held the other15 objects one by one in their right hands and guessed what they were. Use box plots to comparevisually the correct-guess data from this table.Each row in the table represents the results observed for one subject. Note that 10 women and 12men were tested. Correct Guesses Women Women Men Men Left Right Left Right 8 4 7 12 9 1 8 6 12 8 7 12 11 12 5 12 10 11 7 7 8 11 8 11 12 13 11 12 7 12 4 8 9 11 10 12 11 12 14 11 13 9 5 9Procedure1. Press … 5 to select 5:SetUpEditor. Enter list names WLEFT, WRGHT, MLEFT, and MRGHT, separated by commas. Press Í. The stat list editor now contains only these four lists. (See Chapter 11: Lists for detailed instructions for using the SetUpEditor.)2. Press … 1 to select 1:Edit.3. Enter into WLEFT the number of correct guesses each woman made using her left hand (Women Left). Press ~ to move to WRGHT and enter the number of correct guesses each woman made using her right hand (Women Right).4. Likewise, enter each man's correct guesses in MLEFT (Men Left) and MRGHT (Men Right). Chapter 17: Activities 300
5. Press y ,. Select 1:Plot1. Turn on plot 1; define it as a modified box plot Õ that uses Xlist as WLEFT. Move the cursor to the top line and select Plot2. Turn on plot 2; define it as a modified box plot that uses Xlist as WRGHT. (See Chapter 12: Statistics for detailed information on using Stat Plots.)6. Press o. Turn off all functions.7. Press p. Set Xscl=1 and Yscl=0. Press q 9 to select 9:ZoomStat. This adjusts the viewing window and displays the box plots for the women's results.8. Press r. Women's left-hand data Women's right-hand data Use | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot. Notice the outlier to the women's right-hand data. What is the median for the left hand? For the right hand? With which hand were the women more accurate guessers, according to the box plots?9. Examine the men's results. Redefine plot 1 to use MLEFT, redefine plot 2 to use MRGHT. Press r. Men's left-hand data Men's right-hand data Press | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot. What difference do you see between the plots?10. Compare the left-hand results. Redefine plot 1 to use WLEFT, redefine plot 2 to use MLEFT, and then press r to examine minX, Q1, Med, Q3, and maxX for each plot. Who were the better left-hand guessers, men or women?11. Compare the right-hand results. Define plot 1 to use WRGHT, define plot 2 to use MRGHT, and then press r to examine minX, Q1, Med, Q3, and maxX for each plot. Who were the better right-hand guessers? In the original experiment boys did not guess as well with right hands, while girls guessed equally well with either hand. This is not what our box plots show for adults. Do you think that this is because adults have learned to adapt or because our sample was not large enough? Chapter 17: Activities 301
Graphing Piecewise FunctionsProblemThe fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 foreach kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66kph and above. Graph the piecewise function that describes the cost of the ticket.The fine (Y) as a function of kilometers per hour (X) is: ,which simplifies to:Procedure1. Press z. Select Func and Classic.2. Press o. Turn off all functions and stat plots. Enter the Y= function to describe the fine. Use the TEST menu operations to define the piecewise function. Set the graph style for Y1 to í (dot).3. Press p and set Xmin=L2, Xscl=10, Ymin=L5, Yscl=10 and @X=1. Ignore Xmax and Ymax; they are set in step 4. Chapter 17: Activities 302
4. Press y 5 to return to the home screen. Store 5 to @Y. @X and @Y are on the VARS Window X/Y secondary menu. @X and @Y specify the horizontal and vertical distance between the centers of adjacent pixels. Integer values for @X and @Y produce nice values for tracing.5. Press r to plot the function. At what speed does the ticket exceed 250? Chapter 17: Activities 303
Graphing InequalitiesProblemGraph the inequality 0.4x3 N 3x + 5 < 0.2x + 4. Use the TEST menu operations to explore the valuesof X where the inequality is true and where it is false.Note: You can also investigate graphing inequalities using the Inequality Graphing application. Theapplication is pre-loaded on your TI-84 Plus and can be downloaded from education.ti.com.Procedure1. Press z. Select Dot, Simul, and the default settings. Setting Dot mode changes all graph style icons to í (dot) in the Y= editor.2. Press o. Turn off all functions and stat plots. Enter the left side of the inequality as Y4 and the right side as Y5.3. Enter the statement of the inequality as Y6. This function evaluates to 1 if true or 0 if false. Note: You can use the YVARS shortcut menu to paste Y4 and Y5 in the Y= editor.4. Press q 6 to graph the inequality in the standard window.5. Press r † † to move to Y6. Then press | and ~ to trace the inequality, observing the value of Y. When you trace, you can see that Y=1 indicates that Y4<Y5 is true and that Y=0 indicates that Y4<Y5 is false.6. Press o. Turn off Y4, Y5, and Y6. Enter equations to graph only the inequality. Chapter 17: Activities 304
7. Press r. Notice that the values of Y7 and Y8 are zero where the inequality is false. You only see the intervals of the graph where Y4<Y5 because intervals that are false are multiplied by 0 (Y6†Y4 and Y6†Y5) Chapter 17: Activities 305
Solving a System of Nonlinear EquationsProblemUsing a graph, solve the equation x3N2x=2cos(x). Stated another way, solve the system of twoequations and two unknowns: y = x 3N2x and y = 2cos(x). Use ZOOM factors to control the decimalplaces displayed on the graph and use y / 5:intersect to find an approximate solution.Procedure1. Press z. Select the default mode settings. Press o. Turn off all functions and stat plots. Enter the functions.2. Press q 4 to select 4:ZDecimal. The display shows that two solutions may exist (points where the two functions appear to intersect).3. Press q ~ 4 to select 4:SetFactors from the ZOOM MEMORY menu. Set XFact=10 and YFact=10.4. Press q 2 to select 2:Zoom In. Use |, ~, }, and † to move the free-moving cursor onto the apparent intersection of the functions on the right side of the display. As you move the cursor, notice that the X and Y values have one decimal place.5. Press Í to zoom in. Move the cursor over the intersection. As you move the cursor, notice that now the X and Y values have two decimal places.6. Press Í to zoom in again. Move the free-moving cursor onto a point exactly on the intersection. Notice the number of decimal places.7. Press y / 5 to select 5:intersect. Press Í to select the first curve and Í to select the second curve. To guess, move the trace cursor near the intersection. Press Í. What are the coordinates of the intersection point?8. Press q 4 to select 4:ZDecimal to redisplay the original graph.9. Press q. Select 2:Zoom In and repeat steps 4 through 8 to explore the apparent function intersection on the left side of the display. Chapter 17: Activities 306
Using a Program to Create the Sierpinski TriangleSetting up the ProgramThis program creates a drawing of a famous fractal, the Sierpinski Triangle, and stores the drawingto a picture. To begin, press ~ ~ 1. Name the program SIERPINS, and then press Í.The program editor is displayed.Note: After you run this program, press y . † † † Í to turn on the axes in the graphscreen.ProgramPROGRAM:SIERPINS:FnOff :ClrDraw:PlotsOff:AxesOff:0!Xmin:1!Xmax Set viewing window.:0!Ymin:1!Ymax:rand!X:rand!Y:For(K,1,3000) Beginning of For group.:rand!N:If N1 à3:Then:.5X!X If/Then group:.5Y!Y:End:If 1 à3 <N and N2 à3:Then:.5(.5+X)!X If/Then group.:.5(1+Y)!Y:End:If 2 à3 <N:Then:.5(1+X)!X If/Then group.:.5Y!Y:End:Pt-On(X,Y) Draw point.:End End of For group.:StorePic 6 Store picture.After you execute the program above, you can recall and display the picture with the instructionRecallPic 6. Chapter 17: Activities 307
Chapter 17: Activities 308
Graphing Cobweb AttractorsProblemUsing Web format, you can identify points with attracting and repelling behavior in sequencegraphing.Procedure1. Press z. Select Seq and the default mode settings. Press y .. Select Web format and the default format settings.2. Press o. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y = K X(1NX). u(n)=Ku(nN1)(1Nu(nN1)) u(nMin)=.013. Press y 5 to return to the home screen, and then store 2.9 to K.4. Press p. Set the window variables. nMin=0 Xmin=0 Ymin=M.26 nMax=10 Xmax=1 Ymax=1.1 PlotStart=1 Xscl=1 Yscl=1 PlotStep=15. Press r to display the graph, and then press ~ to trace the cobweb. This is a cobweb with one attractor.6. Change K to 3.44 and trace the graph to show a cobweb with two attractors.7. Change K to 3.54 and trace the graph to show a cobweb with four attractors. Chapter 17: Activities 309
Using a Program to Guess the CoefficientsSetting Up the ProgramThis program graphs the function A sin(BX) with random integer coefficients between 1 and 10.Try to guess the coefficients and graph your guess as C sin(DX). The program continues until yourguess is correct.Note: This program changes the graph window and graph styles. After you run the program, youcan change individual settings as needed or you can press y L 7 2 2 to return to defaultsettings.Programs typically do not restore your settings in MODE, Y=, WINDOW and other locations thatwere used by the program. This is dependent on who created the program.ProgramPROGRAM:GUESS:PlotsOff :Func:FnOff :Radian:ClrHome:"Asin(BX)"!Y1 Define equations.:"Csin(DX)"!Y2:GraphStyle(1,1) Set line and path graph styles.:GraphStyle(2,5):FnOff 2:randInt(1,10)!A:randInt(1,10)!B Initialize coefficients.:0!C:0!D:L2p!Xmin:2p!Xmax:pà2!Xscl:L10!Ymin Set viewing window.:10!Ymax:1!Yscl:DispGraph:Pause Display graph.:FnOn 2:Lbl Z:Prompt C,D Prompt for guess.:DispGraph:Pause Display graph. Chapter 17: Activities 310
:If C=A:Text(1,1,"C IS OK"):If CƒA:Text(1,1,"C IS Display results.WRONG"):If D=B:Text(1,50,"D IS OK"):If DƒB:Text(1,50,"D ISWRONG"):DispGraph:Pause Display graph.:If C=A and D=B:Stop Quit if guesses are correct.:Goto ZNote: The Guess My Coefficients App is an educational game that challenges you to enter thecorrect coeffiecients for graphs of linear, quadratic and absolute value functions. This app isavailable at education.ti.com. Chapter 17: Activities 311
Graphing the Unit Circle and Trigonometric CurvesProblemUsing parametric graphing mode, graph the unit circle and the sine curve to show the relationshipbetween them.Any function that can be plotted in Func mode can be plotted in Par mode by defining the Xcomponent as T and the Y component as F(T).Procedure1. Press z. Select Par, Simul, and the default settings.2. Press p. Set the viewing window. Tmin=0 Xmin=L2 Ymin=L3 Tmax=2p Xmax=7.4 Ymax=3 Tstep=.1 Xscl=pà2 Yscl=13. Press o. Turn off all functions and stat plots. Enter the expressions to define the unit circle centered on (0,0).4. Enter the expressions to define the sine curve.5. Press r. As the graph is plotting, you may press Í to pause and Í again to resume graphing as you watch the sine function "unwrap" from the unit circle.Note:• You can generalize the unwrapping. Replace sin(T) in Y2T with any other trig function to unwrap that function. Chapter 17: Activities 312
• You can graph the functions again by turning the functions off and then turning them back on on the Y= editor or by using the FuncOFF and FuncON commands on the home screen. Chapter 17: Activities 313
Finding the Area between CurvesProblemFind the area of the region bounded by:f(x) = 300x / (x2 + 625)g(x) = 3cos(.1x)x = 75Procedure1. Press z. Select the default mode settings.2. Press p. Set the viewing window. Xmin=0 Ymin=L5 Xres=1 Xmax=100 Ymax=10 Xscl=10 Yscl=13. Press o. Turn off all functions and stat plots. Enter the upper and lower functions. Y1=300Xà(X2+625) Y2=3cos(.1X)4. Press y / 5 to select 5:Intersect. The graph is displayed. Select a first curve, second curve, and guess for the intersection toward the left side of the display. The solution is displayed, and the value of X at the intersection, which is the lower limit of the integral, is stored in Ans and X.5. Press y 5 to go to the home screen. Press y < 7 and use Shade( to see the area graphically. Shade(Y2,Y1,Ans,75)6. Press y 5 to return to the home screen. Enter the expression to evaluate the integral for the shaded region. fnInt(Y1NY2,X,Ans,75) The area is 325.839962. Chapter 17: Activities 314
Using Parametric Equations: Ferris Wheel ProblemProblemUsing two pairs of parametric equations, determine when two objects in motion are closest to eachother in the same plane.A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of onerevolution every 12 seconds. The parametric equations below describe the location of a ferriswheel passenger at time T, where a is the angle of rotation, (0,0) is the bottom center of the ferriswheel, and (10,10) is the passenger's location at the rightmost point, when T=0.X(T) = r cos a where a = 2pTs and r = dà2Y(T) = r + r sin aA person standing on the ground throws a ball to the ferris wheel passenger. The thrower's arm is atthe same height as the bottom of the ferris wheel, but 25 meters (b) to the right of the ferris wheel'slowest point (25,0). The person throws the ball with velocity (v0) of 22 meters per second at an angle(q) of 66¡ from the horizontal. The parametric equations below describe the location of the ball attime T.X(T) = b N Tv 0 cosq 2Y(T) = Tv 0 sinq N (gà2) T 2 where g = 9.8 m/secProcedure1. Press z. Select Par, Simul, and the default settings. Simul (simultaneous) mode simulates the two objects in motion over time.2. Press p. Set the viewing window. Tmin=0 Xmin=L13 Ymin=0 Tmax=12 Xmax=34 Ymax=31 Tstep=.1 Xscl=10 Yscl=103. Press o. Turn off all functions and stat plots. Enter the expressions to define the path of the ferris wheel and the path of the ball. Set the graph style for X2T to ë (path). Note: Try setting the graph styles to ë X1T and ì X2T, which simulates a chair on the ferris wheel and the ball flying through the air when you press s. Chapter 17: Activities 315
4. Press s to graph the equations. Watch closely as they are plotted. Notice that the ball and the ferris wheel passenger appear to be closest where the paths cross in the top-right quadrant of the ferris wheel.5. Press p. Change the viewing window to concentrate on this portion of the graph. Tmin=1 Xmin=0 Ymin=10 Tmax=3 Xmax=23.5 Ymax=25.5 Tstep=.03 Xscl=10 Yscl=106. Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where the paths cross. Notice the values of X, Y, and T.7. Press † to move to the path of the ball. Notice the values of X and Y (T is unchanged). Notice where the cursor is located. This is the position of the ball when the ferris wheel passenger passes the intersection. Did the ball or the passenger reach the intersection first? You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion. Chapter 17: Activities 316
Demonstrating the Fundamental Theorem of CalculusProblem 1Using the functions fnInt( and nDeriv( from the FUNC shortcut menu or the MATH menu to graphfunctions defined by integrals and derivatives demonstrates graphically that: and thatProcedure 11. Press z. Select the default settings.2. Press p. Set the viewing window. Xmin=.01 Ymin=L1.5 Xres=3 Xmax=10 Ymax=2.5 Xscl=1 Yscl=13. Press o. Turn off all functions and stat plots. Enter the numerical integral of 1àT from 1 to X and the function ln(X). Set the graph style for Y1 to ç (line) and Y2 to ë (path).4. Press r. Press |, }, ~, and † to compare the values of Y1 and Y2.5. Press o. Turn off Y1 and Y2, and then enter the numerical derivative of the integral of 1àX and the function 1àX. Set the graph style for Y3 to ç (line) and Y4 to è (thick). Chapter 17: Activities 317
6. Press r. Again, use the cursor keys to compare the values of the two graphed functions, Y3 and Y4.Problem 2Explore the functions defined by x x x – 2 t 0 t 2 t 2 2 2 y = dt, dt , and dtProcedure 21. Press o. Turn off all functions and stat plots. Use a list to define these three functions simultaneously. Store the function in Y5.2. Press q 6 to select 6:ZStandard. The graphs are displayed as each calculation of the integral and derivative occurs at the pixel point, which may take some time.3. Press r. Notice that the functions appear identical, only shifted vertically by a constant.4. Press o. Enter the numerical derivative of Y5 in Y6. Chapter 17: Activities 318
5. Press r. Notice that although the three graphs defined by Y5 are different, they share the same derivative. Chapter 17: Activities 319
Computing Areas of Regular N-Sided PolygonsProblemUse the equation solver to store a formula for the area of a regular N-sided polygon, and thensolve for each variable, given the other variables. Explore the fact that the limiting case is the areaof a circle, pr2.Consider the formula A = NB 2 sin(pàN) cos(pàN) for the area of a regular polygon with N sides ofequal length and B distance from the center to a vertex. N = 4 sides N = 8 sides N = 12 sidesProcedure1. Press t B to select B:Solver from the MATH menu. Either the equation editor or the interactive solver editor is displayed. If the interactive solver editor is displayed, press } to display the equation editor.2. Enter the formula as 0=ANNB2sin(p / N)cos(p / N), and then press Í. The interactive solver editor is displayed.3. Enter N=4 and B=6 to find the area (A) of a square with a distance (B) from center to vertex of 6 centimeters.4. Press } } to move the cursor onto A, and then press ă . The solution for A is displayed on the interactive solver editor.5. Now solve for B for a given area with various number of sides. Enter A=200 and N=6. To find the distance B, move the cursor onto B, and then press ƒ . Chapter 17: Activities 320
6. Enter N=8. To find the distance B, move the cursor onto B, and then press ƒ . Find B for N=9, and then for N=10.Find the area given B=6, and N=10, 100, 150, 1000, and 10000. Compare your results with p62 (thearea of a circle with radius 6), which is approximately 113.097.7. Enter B=6. To find the area A, move the cursor onto A, and then press ƒ . Find A for N=10, then N=100, then N=150, then N=1000, and finally N=10000. Notice that as N gets large, the area A approaches pB2.Now graph the equation to see visually how the area changes as the number of sides gets large.8. Press z. Select the default mode settings.9. Press p. Set the viewing window. Xmin=0 Ymin=0 Xres=1 Xmax=200 Ymax=150 Xscl=10 Yscl=1010. Press o. Turn off all functions and stat plots. Enter the equation for the area. Use X in place of N. Set the graph styles as shown. Chapter 17: Activities 321
11. Press r. After the graph is plotted, press 100 Í to trace to X=100. Press 150 Í. Press 188 Í. Notice that as X increases, the value of Y converges to p62, which is approximately 113.097. Y2=pB2 (the area of the circle) is a horizontal asymptote to Y1. The area of an N-sided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr 2) as N gets large. Chapter 17: Activities 322
Computing and Graphing Mortgage PaymentsProblemYou are a loan officer at a mortgage company, and you recently closed on a 30-year homemortgage at 8 percent interest with monthly payments of 800. The new home owners want to knowhow much will be applied to the interest and how much will be applied to the principal when theymake the 240th payment 20 years from now.Procedure1. Press z and set the fixed-decimal mode to 2 decimal places. Set the other mode settings to the defaults.2. Press Œ Í Í to display the TVM Solver. Enter these values. Note: Enter a positive number (800) to show PMT as a cash inflow. Payment values will be displayed as positive numbers on the graph. Enter 0 for FV, since the future value of a loan is 0 once it is paid in full. Enter PMT: END, since payment is due at the end of a period.3. Move the cursor onto the PV= prompt, and then press ƒ . The present value, or mortgage amount, of the house is displayed at the PV= prompt.Now compare the graph of the amount of interest with the graph of the amount of principal for eachpayment.4. Press z. Set Par and Simul.5. Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown. Chapter 17: Activities 323
Note: GPrn( and GInt( are located on the FINANCE menu (APPS 1:FINANCE).6. Press p. Set these window variables. Tmin=1 Xmin=0 Ymin=0 Tmax=360 Xmax=360 Ymax=1000 Tstep=12 Xscl=10 Yscl=100 Note: To increase the graph speed, change Tstep to 24.7. Press r. After the graph is drawn, press 240 Í to move the trace cursor to T=240, which is equivalent to 20 years of payments. The graph shows that for the 240th payment (X=240), 358.03 of the 800 payment is applied to principal (Y=358.03). Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800.8. Press † to move the cursor onto the function for interest defined by X2T and Y2T. Enter 240. The graph shows that for the 240th payment (X=240), 441.97 of the 800 payment is interest (Y=441.97).9. Press y 5 Œ Í 9 to paste 9:bal( to the home screen. Check the figures from the graph.At which monthly payment will the principal allocation surpass the interest allocation? Chapter 17: Activities 324
Note: Some Apps take up several App slots.Displaying the About ScreenAbout displays information about the TI-84 Plus Operating System (OS) Version, Product Number,Product Identification (ID), and Flash Application (App) Certificate Revision Number. To display theAbout screen, press y L and then select 1:About.Displays the type of Displays the Productgraphing calculator. ID. Each Flash-based graphing calculator has a unique product ID,Displays the OS which you may need ifversion. As new you contact technicalsoftware upgrades support. You can alsobecome available, use this 14 digit ID toyou can register your calculatorelectronically at education.ti.com, orupgrade your unit. identify your calculator in the event that it is lost or stolen.Displaying the MEMORY MANAGEMENT/DELETE MenuMem Mgmt/Del displays the MEMORY MANAGEMENT/DELETE menu. The two lines at the top reportthe total amount of available RAM (RAM FREE) and Archive (ARC FREE) memory. By selectingmenu items on this screen, you can see the amount of memory each variable type is using. Thisinformation can help you determine if you need to delete variables from memory to make room fornew data, such as programs or Apps.To check memory usage, follow these steps.1. Press y L to display the MEMORY menu. Note: The # and $ in the top or bottom of the left column indicate that you can scroll up or down to view more variable types.2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu. The TI-84 Plus expresses memory quantities in bytes. Chapter 18: Memory and Variable Management 326
3. Select variable types from the list to display memory usage. Notes: Real, List, Y-Vars, and Prgm variable types never reset to zero, even after memory is cleared. Apps are independent applications which are stored in Flash ROM. AppVars is a variable holder used to store variables created by Apps. You cannot edit or change variables in AppVars unless you do so through the application which created them.To leave the MEMORY MANAGEMENT/DELETE menu, press either y 5 or '. Both optionsdisplay the home screen. Chapter 18: Memory and Variable Management 327
Deleting Items from MemoryDeleting an ItemTo increase available memory by deleting the contents of any variable (real or complex number,list, matrix, Y= variable, program, Apps, AppVars, picture, graph database, or string), follow thesesteps.1. Press y L to display the MEMORY menu.2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu.3. Select the type of data you want to delete, or select 1:All for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using. For example, if you select 4:List, the LIST editor screen is displayed.4. Press } and † to move the selection cursor (4) next to the item you want to delete, and then press {. The variable is deleted from memory. You can delete individual variables one by one from this screen. No warning will be given to verify the deletion. Note: If you are deleting programs or Apps, you will receive a message asking you to confirm this delete action. Select 2:Yes to continue. To leave any variable screen without deleting anything, press y 5, which displays the home screen. You cannot delete some system variables, such as the last-answer variable Ans and the statistical variable RegEQ. Chapter 18: Memory and Variable Management 328
Clearing Entries and List ElementsClear EntriesClear Entries clears the contents of the ENTRY (last entry on home screen) storage area. To clearthe ENTRY storage area, follow these steps.1. Press y L to display the MEMORY menu.2. Select 3:Clear Entries to paste the instruction to the home screen.3. Press Í to clear the ENTRY storage area.To cancel Clear Entries, press '.Note: If you select 3:Clear Entries from within a program, the Clear Entries instruction is pasted tothe program editor, and the Entry (last entry) is cleared when the program is executed.ClrAllListsClrAllLists sets the dimension of each list in RAM to 0.To clear all elements from all lists, follow these steps.1. Press y L to display the MEMORY menu.2. Select 4:ClrAllLists to paste the instruction to the home screen.3. Press Í to set the dimension of each list in memory to 0.To cancel ClrAllLists, press '.ClrAllLists does not delete list names from memory, from the LIST NAMES menu, or from the statlist editor.Note: If you select 4:ClrAllLists from within a program, the ClrAllLists instruction is pasted to theprogram editor. The lists are cleared when the program is executed. Chapter 18: Memory and Variable Management 329
Archiving and UnArchiving VariablesArchiving and UnArchiving VariablesArchiving lets you store data, programs, or other variables to the user data archive (ARC) wherethey cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM forvariables that may require additional memory.Archived variables cannot be edited or executed. They can only be seen and unarchived. Forexample, if you archive list L1, you will see that L1 exists in memory but if you select it and pastethe name L1 to the home screen, you won't be able to see its contents or edit it.Note: Not all variables may be archived. Not all archived variables may be unarchived. Forexample, system variables including r, t, x, y, and q cannot be archived. Apps and Groups alwaysexist in Flash ROM so there is no need to archive them. Groups cannot be unarchived. However,you can ungroup or delete them. Archive? UnArchive?Variable Type Names (yes/no) (yes/no)Real numbers A, B, ... , Z yes yesComplex A, B, ... , Z yes yesnumbersMatrices [A], [B], [C], ... , [J] yes yesLists L1, L2, L3, L4, L5, L6, yes yes and user-defined namesPrograms yes yesFunctions Y1, Y2, . . . , Y9, Y0 no not applicableParametric X1T and Y1T, ... , X6T no notequations and Y6T applicablePolar functions r1, r2, r3, r4, r5, r6 no not applicableSequence u, v, w no notfunctions applicableStat plots Plot1, Plot2, Plot3 no not applicableGraph databases GDB1, GDB2,... yes yesGraph pictures Pic1, Pic2, ... , Pic9, yes yes Pic0Strings Str1, Str2, . . . Str9, Str0 yes yesTables TblStart, @Tbl, no not TblInput applicableApps Applications see Note no aboveAppVars Application variables yes yes Chapter 18: Memory and Variable Management 330
Archive? UnArchive? Variable Type Names (yes/no) (yes/no) Groups see Note no above Variables with minX, maxX, RegEQ, no not reserved names and others applicable System variables Xmin, Xmax, and others no not applicableArchiving and unarchiving can be done in two ways:• Use the 5:Archive or 6:UnArchive commands from the MEMORY menu or CATALOG.• Use a Memory Management editor screen.Before archiving or unarchiving variables, particularly those with a large byte size (such as largeprograms) use the MEMORY menu to:• Find the size of the variable.• See if there is enough free space. For: Sizes must be such that: Archive Archive free size > variable size UnArchive RAM free size > variable sizeNote: If there is not enough space, unarchive or delete variables as necessary. Be aware thatwhen you unarchive a variable, not all the memory associated with that variable in user dataarchive will be released since the system keeps track of where the variable has been and where itis now in RAM.Even if there appears to be enough free space, you may see a Garbage Collection message whenyou attempt to archive a variable. Depending on the usability of empty blocks in the user dataarchive, you may need to unarchive existing variables to create more free space.To archive or unarchive a list variable (L1) using the Archive/UnArchive options from the MEMORYmenu:1. Press y L to display the MEMORY menu.2. Select 5:Archive or 6:UnArchive to place the command in the Home screen.3. Press y d to place the L1 variable in the Home screen. Chapter 18: Memory and Variable Management 331
4. Press Í to complete the archive process.Note: An asterisk will be displayed to the left of the Archived variable name to indicate it isarchived.To archive or unarchive a list variable (L1) using a Memory Management editor:1. Press y L to display the MEMORY menu.2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu.3. Select 4:List to display the LIST menu.4. Press Í to archive L1. An asterisk will appear to the left of L1 to indicate it is an archived variable. To unarchive a variable in this screen, put the cursor next to the archived variable and press Í. The asterisk will disappear. Chapter 18: Memory and Variable Management 332
Resetting the TI-84 PlusRAM ARCHIVE ALL MenuReset displays the RAM ARCHIVE ALL menu. This menu gives you the option of resetting allmemory (including default settings) or resetting selected portions of memory while preservingother data stored in memory, such as programs and Y= functions. For instance, you can choose toreset all of RAM or just restore the default settings. Be aware that if you choose to reset RAM, alldata and programs in RAM will be erased. For archive memory, you can reset variables (Vars),applications (Apps), or both of these. Be aware that if you choose to reset Vars, all data andprograms in archive memory will be erased. If you choose to reset Apps, all applications in archivememory will be erased.When you reset defaults on the TI-84 Plus, all defaults in RAM are restored to the factory settings.Stored data and programs are not changed.These are some examples of TI-84 Plus defaults that are restored by resetting the defaults.• Mode settings such as Normal (notation); Func (graphing); Real (numbers); and Full (screen)• Y= functions off• Window variable values such as Xmin=L10, Xmax=10, Xscl=1, Yscl=1, and Xres=1• STAT PLOTS off• Format settings such as CoordOn (graphing coordinates on); AxesOn; and ExprOn (expression on)• rand seed value to 0Displaying the RAM ARCHIVE ALL MenuTo display the RAM ARCHIVE ALL menu on the TI-84 Plus, follow these steps.1. Press y L to display the MEMORY menu.2. Select 7:Reset to display the RAM ARCHIVE ALL menu.Resetting RAM MemoryResetting all RAM restores RAM system variables to factory settings and deletes all nonsystemvariables and all programs. Resetting RAM defaults restores all system variables to defaultsettings without deleting variables and programs in RAM. Resetting all RAM or resetting defaultsdoes not affect variables and applications in user data archive.Note: Before you reset all RAM memory, consider restoring sufficient available memory by deletingonly selected data. Chapter 18: Memory and Variable Management 334
To reset all RAM memory or RAM defaults on the TI-84 Plus, follow these steps.1. From the RAM ARCHIVE ALL menu, select 1:All RAM to display the RESET RAM menu or 2:Defaults to display the RESET DEFAULTS menu.2. If you are resetting RAM, read the message below the RESET RAM menu. • To cancel the reset and return to the HOME screen, press Í. • To erase RAM memory or reset defaults, select 2:Reset. Depending on your choice, the message RAM cleared or Defaults set is displayed on the home screen.Resetting Archive MemoryWhen resetting archive memory on the TI-84 Plus, you can choose to delete from user dataarchive all variables, all applications, or both variables and applications.To reset all or part of user data archive memory, follow these steps.1. From the RAM ARCHIVE ALL menu, press ~ to display the ARCHIVE menu.2. Select one of the following: 1:Vars to display the RESET ARC VARS menu. 2:Apps to display the RESET ARC APPS menu. Chapter 18: Memory and Variable Management 335
3:Both to display the RESET ARC BOTH menu.3. Read the message below the menu. • To cancel the reset and return to the HOME screen, press Í. • To continue with the reset, select 2:Reset. A message indicating the type of archive memory cleared will be displayed on the HOME screen.Resetting All MemoryWhen resetting all memory on the TI-84 Plus, RAM and user data archive memory is restored tofactory settings. All nonsystem variables, applications, and programs are deleted. All systemvariables are reset to default settings.Before you reset all memory, consider restoring sufficient available memory by deleting onlyselected data.To reset all memory on the TI-84 Plus, follow these steps.1. From the RAM ARCHIVE ALL menu, press ~ ~ to display the ALL menu.2. Select 1:All Memory to display the RESET MEMORY menu.3. Read the message below the RESET MEMORY menu. • To cancel the reset and return to the HOME screen, press Í. • To continue with the reset, select 2:Reset. The message MEM cleared is displayed on the HOME screen.When you clear memory, the contrast sometimes changes. If the screen is faded or blank, adjustthe contrast by pressing y } or †. Chapter 18: Memory and Variable Management 336
Grouping and Ungrouping VariablesGrouping VariablesGrouping allows you to make a copy of two or more variables residing in RAM and then store themas a group in user data archive. The variables in RAM are not erased. The variables must exist inRAM before they can be grouped. In other words, archived data cannot be included in a group.Once grouped, the variables can be deleted from RAM to open memory. When the variables areneeded later, they can be ungrouped for use.To create a group of variables:1. Press y L to display the MEMORY menu.2. Select 8:Group to display GROUP UNGROUP menu.3. Press Í to display the GROUP menu.4. Enter a name for the new group and press Í. Note: A group name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q.5. Select the type of data you want to group. You can select 1:All+ which shows all variables of all types available and selected. You can also select 2:All- which shows all variables of all types available but not selected. A screen is displayed listing each variable of the type you selected. Chapter 18: Memory and Variable Management 337
For example, suppose some variables have been created in RAM, and selecting 2:All- displays the following screen.6. Press } and † to move the selection cursor (4) next to the first item you want to copy into a group, and then press Í. A small square will remain to the left of all variables selected for grouping. Repeat the selection process until all variables for the new group are selected and then press ~ to display the DONE menu.7. Press Í to complete the grouping process.Note: You can only group variables in RAM. You cannot group some system variables, such as thelast-answer variable Ans and the statistical variable RegEQ.Ungrouping VariablesUngrouping allows you to make a copy of variables in a group stored in user data archive andplace them ungrouped in RAM. Chapter 18: Memory and Variable Management 338
DuplicateName MenuDuring the ungrouping action, if a duplicate variable name is detected in RAM, the DUPLICATENAME menu is displayed.DuplicateName1: Rename Prompts to rename receiving variable.2: Overwrite Overwrites data in receiving duplicate variable.3: Overwrite All Overwrites data in all receiving duplicate variables.4: Omit Skips ungrouping of sending variable.5: Quit Stops ungrouping at duplicate variable.Notes about Menu Items:• When you select 1:Rename, the Name= prompt is displayed, and alpha-lock is on. Enter a new variable name, and then press Í. Ungrouping resumes.• When you select 2:Overwrite, the unit overwrites the data of the duplicate variable name found in RAM. Ungrouping resumes.• When you select 3: Overwrite All, the unit overwrites the data of all duplicate variable names found in RAM. Ungrouping resumes.• When you select 4:Omit, the unit does not ungroup the variable in conflict with the duplicated variable name found in RAM. Ungrouping resumes with the next item.• When you select 5:Quit, ungrouping stops, and no further changes are made.To ungroup a group of variables:1. Press y L to display the MEMORY menu.2. Select 8:Group to display the GROUP UNGROUP menu.3. Press ~ to display the UNGROUP menu. Chapter 18: Memory and Variable Management 339
4. Press } and † to move the selection cursor (4) next to the group variable you want to ungroup, and then press Í. The ungroup action is completed.Note: Ungrouping does not remove the group from user data archive. You must delete the group inuser data archive to remove it. Chapter 18: Memory and Variable Management 340
Garbage CollectionGarbage Collection MessageIf you use the user data archive extensively, you may see a Garbage Collect? message. Thisoccurs if you try to archive a variable when there is not enough free contiguous archive memory.The Garbage Collect? message lets you know an archive will take longer than usual. It also alertsyou that the archive will fail if there is not enough memory.The message can also alert you when a program is caught in a loop that repetitively fills the userdata archive. Select No to cancel the garbage collection process, and then find and correct theerrors in your program.When YES is selected, the TI-84 Plus will attempt to rearrange the archived variables to makeadditional room.Responding to the Garbage Collection Message• To cancel, select 1:No.• If you select 1:No, the message ERR:ARCHIVE FULL will be displayed.• To continue archiving, select 2:Yes.• If you select 2:Yes, the process message Garbage Collecting... or Defragmenting... will be displayed.Note: The process message Defragmenting... is displayed whenever an application marked fordeletion is encountered. Garbage collection may take up to 20 minutes, depending on how muchof archive memory has been used to store variables.After garbage collection, depending on how much additional space is freed, the variable may ormay not be archived. If not, you can unarchive some variables and try again.Why Is Garbage Collection Necessary?The user data archive is divided into sectors. When you first begin archiving, variables are storedconsecutively in sector 1. This continues to the end of the sector.An archived variable is stored in a continuous block within a single sector. Unlike an applicationstored in user data archive, an archived variable cannot cross a sector boundary. If there is notenough space left in the sector, the next variable is stored at the beginning of the next sector.Typically, this leaves an empty block at the end of the previous sector. Chapter 18: Memory and Variable Management 341
variable A Sector 1 variable B Empty block variable D variable C Sector 2Depending on its size,variable D is stored in Sector 3one of these locations.Each variable that you archive is stored in the first empty block large enough to hold it.This process continues to the end of the last sector. Depending on the size of individual variables,the empty blocks may account for a significant amount of space. Garbage collection occurs whenthe variable you are archiving is larger than any empty block.How Unarchiving a Variable Affects the ProcessWhen you unarchive a variable, it is copied to RAM but it is not actually deleted from user dataarchive memory. Unarchived variables are "marked for deletion," meaning they will be deletedduring the next garbage collection. Sector 1 variable A After you unarchive variables B and C, they continue to take Sector 2 up space. variable D Sector 3If the MEMORY Screen Shows Enough Free SpaceEven if the MEMORY screen shows enough free space to archive a variable or store an application,you may still get a Garbage Collect? message or an ERR: ARCHIVE FULL message.When you unarchive a variable, the Archive free amount increases immediately, but the space isnot actually available until after the next garbage collection.If the Archive free amount shows enough available space for your variable, there probably will beenough space to archive it after garbage collection (depending on the usability of any emptyblocks). Chapter 18: Memory and Variable Management 342
The Garbage Collection ProcessThe garbage collection process:• Deletes unarchived variables Sector 1 from the user data archive. variable A• Rearranges the remaining variable D variables into consecutive blocks. Sector 2Note: Power loss during garbage collection may cause all memory (RAM and Archive) to bedeleted.Using the GarbageCollect CommandYou can reduce the number of automatic garbage collections by periodically optimizing memory.This is done by using the GarbageCollect command.To use the GarbageCollect command, follow these steps.1. From the HOME screen, press y N to display the CATALOG.2. Press † or } to scroll the CATALOG until the selection cursor points to the GarbageCollect command or press G to skip to the commands starting with the letter G.3. Press Í to paste the command to the HOME screen.4. Press Í to display the Garbage Collect? message.5. Select 2:Yes to begin garbage collection. Chapter 18: Memory and Variable Management 343
ERR:ARCHIVE FULL MessageEven if the MEMORY screen shows enoughfree space to archive a variable or store anapplication, you may still get an ERR:ARCHIVE FULL message.An ERR:ARCHIVE FULL message may be displayed:• When there is insufficient space to archive a variable within a continuous block and within a single sector.• When there is insufficient space to store an application within a continuous block of memory.When the message is displayed, it will indicate the largest single space of memory available forstoring a variable and an application.To resolve the problem, use the GarbageCollect command to optimize memory. If memory is stillinsufficient, you must delete variables or applications to increase space. Chapter 18: Memory and Variable Management 344
Chapter 19:Communication LinkGetting Started: Sending VariablesGetting Started is a fast-paced introduction. Read the chapter for details.Create and store a variable and a matrix, and then transfer them to another TI-84 Plus.1. On the home screen of the sending unit, press 5 Ë 5 ¿ ƒ Q. Press Í to store 5.5 to Q.2. Press t ` † † Í to display the 2x2 matrix template. Press 1 ~ 2 ~ 3 ~ 4 ~ to enter the values. Press ¿ y > 1 Í to store the matrix to [A].3. On the sending unit, press y L to display the MEMORY menu.4. On the sending unit, press 2 to select 2:Mem Mgmt/Del. The MEMORY MANAGEMENT menu is displayed.5. On the sending unit, press 5 to select 5:Matrix. The MATRIX editor screen is displayed.6. On the sending unit, press Í to archive [A]. An asterisk (ä) will appear, signifying that [A] is now archived.7. Connect the graphing calculators with the USB unit-to-unit cable. Push both ends in firmly.8. On the receiving unit, press y 8 ~ to display the RECEIVE menu. Press 1 to select 1:Receive. The message Waiting... is displayed and the busy indicator is on. Chapter 19: Communication Link 345
9. On the sending unit, press y 8 to display the SEND menu.10. Press 2 to select 2:AllN. The AllN SELECT screen is displayed.11. Press † until the selection cursor ( 4 ) is next to [A] MATRX. Press Í.12. Press † until the selection cursor is next to Q REAL. Press Í. A square dot next to [A] and Q indicates that each is selected to send.13. On the sending unit, press ~ to display the TRANSMIT menu.14. On the sending unit, press 1 to select 1:Transmit and begin transmission. The receiving unit displays the message Receiving....When the items are transmitted, both units display the name and type of each transmitted variable. Chapter 19: Communication Link 346
TI-84 Plus LINKThis chapter describes how to communicate with compatible TI units. The TI-84 Plus has a USBport to connect and communicate with another TI-84 Plus or TI-84 Plus Silver Edition. A USBunit-to-unit cable is included with the TI-84 Plus.The TI-84 Plus also has an I/O port using a I/O unit-to-unit cable to communicate with:• TI-83 Plus Silver Edition • TI-82• TI-83 Plus • TI-73• TI-83 • CBL 2™ or a CBR™You can send items from a calculator with an older OS to a calculator with OS 2.53MP. However,you may receive a version error if you send items from a calculator with OS 2.53MP to a calculatorwith an older OS. Transferring files between calculators works best if both calculators have thelatest operating system software installed. For example, if you send a list that contains fractions(OS 2.53MP) to a calculator with OS 2.43, a version error displays because OS 2.43 does notsupport fractions.Connecting Two Graphing Calculators with a USB Unit-to-Unit Cable or an I/O Unit-to-UnitCableUSB Unit-to-Unit CableThe TI-84 Plus USB link port is located at thetop right edge of the graphing calculator.1. Firmly insert either end of the USB unit-to-unit cable into the USB port.2. Insert the other end of the cable into the other graphing calculator's USB port.I/O Unit-to-Unit CableThe TI-84 Plus I/O link port is located at thetop left edge of the graphing calculator.1. Firmly insert either end of the I/O unit-to-unit cable into the port.2. Insert the other end of the cable into the other graphing calculator's I/O port. Chapter 19: Communication Link 347
TI-84 Plus to a TI-83 Plus using I/O Unit-to-Unit CableThe TI-84 Plus I/O link port is located at thetop left edge of the graphing calculator. TheTI-83 Plus I/O link port is located at thebottom edge of the graphing calculator.3. Firmly insert either end of the I/O unit-to-unit cable into the port.4. Insert the other end of the cable into the other graphing calculator's I/O port.Linking to the CBL/CBR SystemThe CBL 2™ system and the CBR™ system are optional accessories that also connect to a TI-84Plus with the I/O unit-to-unit cable. With a CBL 2™ system or CBR™ system and a TI-84 Plus, youcan collect and analyze real-world data.Linking to a ComputerWith TI Connect™ software and the USB computer cable that is included with your TI-84 Plus, youcan link the graphing calculator to a personal computer. Chapter 19: Communication Link 348
2. Select the menu item that describes the data type to send. The corresponding SELECT screen is displayed.3. Press } and † to move the selection cursor ( 4 ) to an item you want to select or deselect.4. Press Í to select or deselect the item. Selected names are marked with a 0. Note: An asterisk (ä) to the left of an item indicates the item is archived.5. Repeat steps 3 and 4 to select or deselect additional items.Sending the Selected ItemsAfter you have selected items to send on the sending unit and set the receiving unit to receive,follow these steps to transmit the items. To set the receiving unit, see Receiving Items.1. Press ~ on the sending unit to display the TRANSMIT menu.2. Confirm that Waiting... is displayed on the receiving unit, which indicates it is set to receive.3. Press Í to select 1:Transmit. The name and type of each item are displayed line-by-line on the sending unit as the item is queued for transmission, and then on the receiving unit as each item is accepted. Note: Items sent from the RAM of the sending unit are transmitted to the RAM of the receiving unit. Items sent from user data archive (flash) of the sending unit are transmitted to user data archive (flash) of the receiving unit.After all selected items have been transmitted, the message Done is displayed on both calculators.Press } and † to scroll through the names.Sending to a TI-84 Plus Silver Edition or TI-84 PlusYou can transfer variables (all types), programs, and Flash applications to another TI-84 PlusSilver Edition or TI-84 Plus. You can also backup the RAM memory of one unit to another.Note: Keep in mind that the TI-84 Plus has less Flash memory than the TI-84 Plus Silver Edition. Chapter 19: Communication Link 350
• Variables stored in RAM on the sending TI-84 Plus Silver Edition will be sent to the RAM of the receiving TI-84 Plus Silver Edition or TI-84 Plus.• Variables and applications stored in the user data archive of the sending TI-84 Plus Silver Edition will be sent to the user data archive of the receiving TI-84 Plus Silver Edition or TI-84 Plus.After sending or receiving data, you can repeat the same transmission to additional TI-84 PlusSilver Edition or TI-84 Plus units—from either the sending unit or the receiving unit—withouthaving to reselect data to send. The current items remain selected. However, you cannot repeattransmission if you selected All+ or All..To send data to an additional TI-84 Plus Silver Edition or a TI-84 Plus:1. Use a USB unit-to-unit cable to link two units together.2. On the sending unit press y 8 and select a data type and items to SEND.3. Press ~ on the sending unit to display the TRANSMIT menu.4. On the other unit, press y 8 ~ to display the RECEIVE menu.5. Press Í on the receiving unit.6. Press Í on the sending unit. A copy of the selected item(s) is sent to the receiving unit.7. Disconnect the link cable only from the receiving unit and connect it to another unit.8. Press y 8 on the sending unit.9. Select only the data type. For example, if the unit just sent a list, select 4:LIST. Note: The item(s) you want to send are pre-selected from the last transmission. Do not select or deselect any items. If you select or deselect an item, all selections or deselections from the last transmission are cleared.10. Press ~ on the sending unit to display the TRANSMIT menu.11. On the new receiving unit, press y 8 ~ to display the RECEIVE menu.12. Press Í on the receiving unit.13. Press Í on the sending unit. A copy of the selected item(s) is sent to the receiving unit.14. Repeat steps 7 through 13 until the items are sent to all additional units.Sending to a TI-83 Plus or TI-83 Plus Silver EditionYou can send all variables from a TI-84 Plus to a TI-83 Plus or TI-83 Plus Silver Edition exceptFlash applications with new features, or programs with new features in them.If archived variables on the TI-84 Plus are variable types recognized and used on the TI-83 Plus orTI-83 Plus Silver Edition, you can send these variables to the TI-83 Plus or TI-83 Plus SilverEdition. They will be automatically sent to the RAM of the TI-83 Plus or TI-83 Plus Silver Editionduring the transfer process. It will send to archive if the item is from archive.To send data to a TI-83 Plus or TI-83 Plus Silver Edition:1. Use an I/O unit-to-unit cable to link the two units together.2. Set the TI-83 Plus or TI-83 Plus Silver Edition to receive. Chapter 19: Communication Link 351
3. Press y 8 on the sending TI-84 Plus to display the LINK SEND menu.4. Select the menu of the items you want to transmit.5. Press ~ on the sending TI-84 Plus to display the LINK TRANSMIT menu.6. Confirm that the receiving unit is set to receive.7. Press Í on the sending TI-84 Plus to select 1:Transmit and begin transmitting. Chapter 19: Communication Link 352
Receiving ItemsLINK RECEIVE MenuTo display the LINK RECEIVE menu, press y 8 ~.SEND RECEIVE1: Receive Sets unit to receive data transmission.Receiving UnitWhen you select 1:Receive from the LINK RECEIVE menu on the receiving unit, the messageWaiting... and the busy indicator are displayed. The receiving unit is ready to receive transmitteditems. To exit the receive mode without receiving items, press É, and then select 1:Quit from theError in Xmit menu.When transmission is complete, the unit exits the receive mode. You can select 1:Receive again toreceive more items. The receiving unit then displays a list of items received. Press y 5 to exitthe receive mode.DuplicateName MenuDuring transmission, if a variable name is duplicated, the DuplicateName menu is displayed on thereceiving unit.DuplicateName1: Rename Prompts to rename receiving variable.2: Overwrite Overwrites data in receiving variable.3: Omit Skips transmission of sending variable.4: Quit Stops transmission at duplicate variable.When you select 1:Rename, the Name= prompt is displayed, and alpha-lock is on. Enter a newvariable name, and then press Í. Transmission resumes.When you select 2:Overwrite, the sending unit's data overwrites the existing data stored on thereceiving unit. Transmission resumes.When you select 3:Omit, the sending unit does not send the data in the duplicated variable name.Transmission resumes with the next item.When you select 4:Quit, transmission stops, and the receiving unit exits receive mode. Chapter 19: Communication Link 353
Receiving from a TI-84 Plus Silver Edition or TI-84 PlusThe TI-84 Plus Silver Edition and the TI-84 Plus are totally compatible. Keep in mind, however thatthe TI-84 Plus has less Flash memory than a TI-84 Plus Silver Edition.You cannot send memory backups between the TI-84 Plus product family and the TI-83 Plusproduct family.Receiving from a TI-83 Plus Silver Edition or TI-83 PlusThe TI-84 Plus product family and the TI-83 Plus product family are compatible with a fewexceptions.Receiving from a TI-83You can transfer all variables and programs from a TI-83 to a TI-84 Plus if they fit in the RAM of theTI-84 Plus. The RAM of the TI-84 Plus is slightly less than the RAM of the TI-83. Chapter 19: Communication Link 354
Backing Up RAM MemoryWarning: H:Back Up overwrites the RAM memory and mode settings in the receiving unit. Allinformation in the RAM memory of the receiving unit is lost.Note: Archived items on the receiving unit are not overwritten.You can backup the contents of RAM memory and mode settings (no Flash applications orarchived items) to another TI-84 Plus Silver Edition. You can also backup RAM memory and modesettings to a TI-84 Plus. The backup calculator must also have OS 2.53MP installed.To perform a RAM memory backup:1. Use a USB unit-to-unit cable to link two TI-84 Plus units, or a TI-84 Plus and a TI-84 Plus Silver Edition together.2. On the sending unit press y 8 and select H:Back Up. The MEMORYBACKUP screen displays.3. On the receiving unit, press y 8 ~ to display the RECEIVE menu.4. Press Í on the receiving unit.5. Press Í on the sending unit. A WARNING — Backup message displays on the receiving unit.6. Press Í on the receiving unit to continue the backup. — or — Press 2:Quit on the receiving unit to cancel the backup and return to the LINK SEND menu Note: If a transmission error is returned during a backup, the receiving unit is reset.Memory Backup CompleteWhen the backup is complete, both the sending graphing calculator and receiving graphingcalculator display a confirmation screen. Chapter 19: Communication Link 355
Error ConditionsA transmission error occurs after one or two seconds if:• A cable is not attached to the sending unit.• A cable is not attached to the receiving unit. Note: If the cable is attached, push it in firmly and try again.• The receiving unit is not set to receive transmission.• You attempt a backup between a TI-73, TI-82, TI-83, TI-83 Plus, or TI-83 Plus Silver Edition.• You attempt a data transfer from a TI-84 Plus to a TI-83 Plus, TI-83 Plus Silver Edition, TI-83, TI-82, or TI-73 with variables or features not recognized by the TI-83 Plus, TI-83 Plus Silver Edition, TI-83, TI-82, or TI-73. New variable types and features not recognized by the TI-83, TI-83 Plus, TI-82, or TI-73 include applications, application variables, grouped variables, new variable types, or programs with new features in them such as Archive, UnArchive, SendID, SendOS, Asm(, AsmComp(, AsmPrgm, checkTmr(, ClockOff, ClockOn, dayOfWk(, getDate, getDtFmt, getDtStr(, getTime, getTmFmt, getTmStr, isClockOn, randIntNoRep(, setDate(, setDtFmt(, setTime(, setTmFmt(, startTmr, summation(, timeCnv and fractions.• You attempt a data transfer from a TI-84 Plus to a TI-82 with data other than real lists L1 through L6 or without using menu item 5:Lists to TI82.• You attempt a data transfer from a TI-84 Plus to a TI-73 with data other than real numbers, pics, real lists L1 through L6 or named lists with q as part of the name.Although a transmission error does not occur, these two conditions may prevent successfultransmission.• You try to use Get( with a graphing calculator instead of a CBL 2™ system or CBR™ system.• You try to use GetCalc( with a TI-83 instead of a TI-84 Plus or TI-84 Plus Silver Edition.Insufficient Memory in Receiving Unit• During transmission, if the receiving unit does not have sufficient memory to receive an item, the Memory Full menu is displayed on the receiving unit.• To skip this item for the current transmission, select 1:Omit. Transmission resumes with the next item.• To cancel the transmission and exit receive mode, select 2:Quit. Chapter 19: Communication Link 356
Appendix A:Functions and InstructionsFunctions return a value, list, or matrix. You can use functions in an expression. Instructions initiatean action. Some functions and instructions have arguments. Optional arguments and accompanyingcommas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptionsand restrictions, turn to the page listed on the right side of the table.From the CATALOG, you can paste any function or instruction to the home screen or to a commandline in the program editor. However, some functions and instructions are not valid on the homescreen. The items in this table appear in the same order as they appear in the CATALOG.† indicates either keystrokes that are valid in the program editor only or ones that paste certaininstructions when you are in the program editor. Some keystrokes display menus that are availableonly in the program editor. Others paste mode, format, or table-set instructions only when you arein the program editor.Function or Key orInstruction/Arguments Result Keys/Menu or Screen/Itemabs(value) Returns the absolute value of a real number, expression, list, or matrix. NUM 1:abs(abs(complex value) Returns the magnitude of a complex number or list. CPX 5:abs(valueA and valueB Returns 1 if both valueA and valueB are ƒ 0. valueA and y: valueB can be real numbers, expressions, or lists. LOGIC 1:andangle(value) Returns the polar angle of a complex number or list of complex numbers. CPX 4:angle(ANOVA(list1,list2 Performs a one-way analysis of variance for comparing the …[,list3,...,list20]) means of two to 20 populations. TESTS H:ANOVA(Ans Returns the last answer. yZArchive Moves the specified variables from RAM to the user data yL archive memory. 5:ArchiveAsm(assemblyprgmname) Executes an assembly language program. yN Asm(AsmComp(prgmASM1, Compiles an assembly language program written in ASCII y NprgmASM2) and stores the hex version. AsmComp(AsmPrgm Must be used as the first line of an assembly language yN program. AsmPrgmaugment(matrixA, Returns a matrix, which is matrixB appended to matrixA as y>matrixB) new columns. MATH 7:augment( Appendix A: Functions and Instructions 357
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/Itemaugment(listA,listB) Returns a list, which is listB concatenated to the end of y9 listA. OPS 9:augment(AUTO Answer Displays answers in a similar format as the input. z Answers: AUTOAxesOff Turns off the graph axes. †y. AxesOffAxesOn Turns on the graph axes. †y. AxesOna+bi Sets the mode to rectangular complex number mode †z (a+bi). a+bibal(npmt[,roundvalue]) Computes the balance at npmt for an amortization Œ 1:Finance schedule using stored values for PV, æ, and PMT and CALC rounds the computation to roundvalue. 9:bal(binomcdf(numtrials,p Computes a cumulative probability at x for the discrete y=[,x]) binomial distribution with the specified numtrials and DISTR probability p of success on each trial. B:binomcdf(binompdf(numtrials,p Computes a probability at x for the discrete binomial y=[,x]) distribution with the specified numtrials and probability p of DISTR success on each trial. A:binompdf(checkTmr(starttime) Returns the number of seconds since you used startTmr yN to start the timer. The starttime is the value displayed by checkTmr( startTmr.c2cdf(lowerbound, Computes the c2 distribution probability between y=upperbound,df) lowerbound and upperbound for the specified degrees of DISTR freedom df. 8:c2cdf(c2pdf(x,df) Computes the probability density function (pdf) for the c2 y = distribution at a specified x value for the specified degrees DISTR of freedom df. 7:c2pdf(c2LTest(observedmatrix, Performs a chi-square test. drawflag=1 draws results; †…expectedmatrix drawflag=0 calculates results. TESTS[,drawflag]) C:c2LTest(c2GOF-Test(observedlist, Performs a test to confirm that sample data is from a †…expectedlist,df) population that conforms to a specified distribution. TESTS D:c2GOFLTest(Circle(X,Y,radius) Draws a circle with center (X,Y) and radius. y< DRAW 9:Circle(CLASSIC Displays inputs and outputs on a single line, such as z 1/2+3/4. CLASSIC Appendix A: Functions and Instructions 358
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/ItemcumSum(list) Returns a list of the cumulative sums of the elements in y9 list, starting with the first element. OPS 6:cumSum(cumSum(matrix) Returns a matrix of the cumulative sums of matrix y> elements. Each element in the returned matrix is a MATH cumulative sum of a matrix column from top to bottom. 0:cumSum(dayOfWk(year,month, Returns an integer from 1 to 7, with each integer yNday) representing a day of the week. Use dayOfWk( to dayOfWk( determine on which day of the week a particular date 1:Sunday would occur. The year must be 4 digits; month and day can 2:Monday be 1 or 2 digit. 3:Tuesday...dbd(date1,date2) Calculates the number of days between date1 and date2 Œ 1:Finance using the actual-day-count method. CALC D:dbd(DEC Answers Displays answers as integers or decimal numbers. z Answers: DECvalue4Dec Displays a real or complex number, expression, list, or matrix in decimal format. MATH 2:4DecDegree Sets degree angle mode. †z DegreeDelVar variable Deletes from memory the contents of variable. † CTL G:DelVarDependAsk Sets table to ask for dependent-variable values. †y- Depend: AskDependAuto Sets table to generate dependent-variable values †y- automatically. Depend: Autodet(matrix) Returns determinant of matrix. y> MATH 1:det(DiagnosticOff Sets diagnostics-off mode; r, r2, and R2 are not displayed yN as regression model results. DiagnosticOffDiagnosticOn Sets diagnostics-on mode; r, r2, and R2 are displayed as yN regression model results. DiagnosticOndim(listname) Returns the dimension of listname. y9 OPS 3:dim(dim(matrixname) Returns the dimension of matrixname as a list. y> MATH 3:dim( Appendix A: Functions and Instructions 360
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/Itemgeometcdf(p,x) Computes a cumulative probability at x, the number of the y= trial on which the first success occurs, for the discrete DISTR geometric distribution with the specified probability of F:geometcdf( success p.geometpdf(p,x) Computes a probability at x, the number of the trial on which y = the first success occurs, for the discrete geometric DISTR distribution with the specified probability of success p. E:geometpdf(Get(variable) Gets data from the CBL 2™ or CBR™ System and stores it † in variable. I/O A:Get(GetCalc(variable Gets contents of variable on another TI-84 Plus and stores it † [,portflag]) to variable on the receiving TI-84 Plus. By default, the TI-84 I/O Plus uses the USB port if it is connected. If the USB cable 0:GetCalc( is not connected, it uses the I/O port. portflag=0 use USB port if connected; portflag=1 use USB port; portflag=2 use I/O port.getDate Returns a list giving the date according to the current value y N of the clock. The list is in {year,month,day} format. getDategetDtFmt Returns an integer representing the date format that is yN currently set on the device. getDtFmt 1 = M/D/Y 2 = D/M/Y 3 = Y/M/DgetDtStr(integer) Returns a string of the current date in the format specified yN by integer, where: getDtStr( 1 = M/D/Y 2 = D/M/Y 3 = Y/M/DgetTime Returns a list giving the time according to the current value y N of the clock. The list is in {hour,minute,second} format. The getTime time is returned in the 24 hour format.getTmFmt Returns an integer representing the clock time format that yN is currently set on the device. getTmFmt 12 = 12 hour format 24 = 24 hour formatgetTmStr(integer) Returns a string of the current clock time in the format yN specified by integer, where: getTmStr( 12 = 12 hour format 24 = 24 hour formatgetKey Returns the key code for the current keystroke, or 0, if no † key is pressed. I/O 7:getKeyGoto label Transfers control to label. † CTL 0:Goto Appendix A: Functions and Instructions 364
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/ItemInput [variable] Prompts for value to store to variable. †Input ["text",variable] I/O 1:InputInput [Strn,variable] Displays Strn and stores entered value to variable. † I/O 1:InputinString(string,substring Returns the character position in string of the first yN[,start]) character of substring beginning at start. inString(int(value) Returns the largest integer a real or complex number, expression, list, or matrix. NUM 5:int(GInt(pmt1,pmt2 Computes the sum, rounded to roundvalue, of the interest Œ 1:Finance[,roundvalue]) amount between pmt1 and pmt2 for an amortization CALC schedule. A:GInt(invNorm(area[,m,s]) Computes the inverse cumulative normal distribution y= function for a given area under the normal distribution DISTR curve specified by m and s. 3:invNorm(invT(area,df) Computes the inverse cumulative student-t probability y= function specified by degree of freedom, df for a given area DISTR under the curve. 4:invT(iPart(value) Returns the integer part of a real or complex number, expression, list, or matrix. NUM 3:iPart(irr(CF0,CFList[,CFFreq]) Returns the interest rate at which the net present value of Œ 1:Finance the cash flow is equal to zero. CALC 8:irr(isClockOn Identifies if clock is ON or OFF. Returns 1 if the clock is yN ON. Returns 0 if the clock is OFF. isClockOn:IS>(variable,value) Increments variable by 1; skips commandA if variable>value. † :commandA CTL:commands A:IS>(Ùlistname Identifies the next one to five characters as a user-created y 9 list name. OPS B:ÙLabelOff Turns off axes labels. †y. LabelOffLabelOn Turns on axes labels. †y. LabelOnLbl label Creates a label of one or two characters. † CTL 9:Lbl Appendix A: Functions and Instructions 366
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/Itemlcm(valueA,valueB) Returns the least common multiple of valueA and valueB, which can be real numbers or lists. NUM 8:lcm(length(string) Returns the number of characters in string. yN length(Line(X1,Y1,X2,Y2) Draws a line from (X1,Y1) to (X2,Y2). y< DRAW 2:Line(Line(X1,Y1,X2,Y2,0) Erases a line from (X1,Y1) to (X2,Y2). y< DRAW 2:Line(LinReg(a+bx 8:LinReg(a+bx)LinReg(ax+b 4:LinReg(ax+b)LinRegTInt [Xlistname, Performs a linear regression and computes the t †…Ylistname,freqlist, confidence interval for the slope coefficient b. TESTSconfidence level, regequ] G:LinRegTIntLinRegTTest [Xlistname, Performs a linear regression and a t-test. alternative=L1 is †…Ylistname,freqlist, <; alternative=0 is ƒ; alternative=1 is >. TESTSalternative,regequ] F:LinRegTTest@List(list) Returns a list containing the differences between y9 consecutive elements in list. OPS 7:@List(List 4 matr(listname1,..., Fills matrixname column by column with the elements from y9listname n,matrixname) each specified listname. OPS 0:List 4 matr(ln(value) Returns the natural logarithm of a real or complex number, μ expression, or list.LnReg [Xlistname, Fits a logarithmic regression model to Xlistname and …Ylistname,freqlist, Ylistname with frequency freqlist, and stores the regression CALCregequ] equation to regequ. 9:LnReglog(value) Returns logarithm of a real or complex number, « expression, or list.logBASE(value, base) Returns the logarithm of a specifed value determined from a specified base: logBASE(value, base). A: logBASELogistic [Xlistname, Fits a logistic regression model to Xlistname and Ylistname …Ylistname,freqlist, with frequency freqlist, and stores the regression equation CALCregequ] to regequ. B:Logistic Appendix A: Functions and Instructions 367
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/ItemManual-Fit equname Fits a linear equation to a scatter plot. … CALC D:Manual-FitMATHPRINT Displays most entries and answers the way they are z displayed in textbooks, such as . MATHPRINTMatr4list(matrix, Fills each listname with elements from each column in y9listnameA,...,listname n) matrix. OPS A:Matr4list(Matr4list(matrix, Fills a listname with elements from a specified column# in y9column#,listname) matrix. OPS A:Matr4list(max(valueA,valueB) Returns the larger of valueA and valueB. NUM 7:max(max(list) Returns largest real or complex element in list. y9 MATH 2:max(max(listA,listB) Returns a real or complex list of the larger of each pair of y9 elements in listA and listB. MATH 2:max(max(value,list) Returns a real or complex list of the larger of value or each y9 list element. MATH 2:max(mean(list[,freqlist]) Returns the mean of list with frequency freqlist. y9 MATH 3:mean(median(list[,freqlist]) Returns the median of list with frequency freqlist. y9 MATH 4:median(Med-Med [Xlistname, Fits a median-median model to Xlistname and Ylistname …Ylistname,freqlist, with frequency freqlist, and stores the regression equation CALCregequ] to regequ. 3:Med-MedMenu("title","text1", Generates a menu of up to seven items during program †label1[,...,"text7",label7]) execution. CTL C:Menu(min(valueA,valueB) Returns smaller of valueA and valueB. NUM 6:min(min(list) Returns smallest real or complex element in list. y9 MATH 1:min( Appendix A: Functions and Instructions 368
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/Itemmin(listA,listB) Returns real or complex list of the smaller of each pair of y9 elements in listA and listB. MATH 1:min(min(value,list) Returns a real or complex list of the smaller of value or y9 each list element. MATH 1:min(valueA nCr valueB Returns the number of combinations of valueA taken valueB at a time. PRB 3:nCrvalue nCr list Returns a list of the combinations of value taken each element in list at a time. PRB 3:nCrlist nCr value Returns a list of the combinations of each element in list taken value at a time. PRB 3:nCrlistA nCr listB Returns a list of the combinations of each element in listA taken each element in listB at a time. PRB 3:nCrn/d Displays results as a simple fraction. t^ 1: n/d or NUM D: n/dnDeriv(expression, Returns approximate numerical derivative of expression variable,value[,H]) with respect to variable at value, with specified H. MATH 8:nDeriv(4 n/d 3 4 Un/d Converts the results from a fraction to mixed number or t^ from a mixed number to a fraction, if applicable. 3: 4 n/d 3 4 Un/d or NUM A: 4 n/d 3 4 Un/d4Nom(effective rate, Computes the nominal interest rate. Œ 1:Financecompounding periods) CALC B:4Nom(Normal Sets normal display mode. †z Normalnormalcdf(lowerbound, Computes the normal distribution probability between y=upperbound[,m,s]) lowerbound and upperbound for the specified m and s. DISTR 2:normalcdf( Appendix A: Functions and Instructions 369
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/Itemnormalpdf(x[,m,s]) Computes the probability density function for the normal y= distribution at a specified x value for the specified m and s. DISTR 1:normalpdf(not(value) Returns 0 if value is ƒ 0. value can be a real number, y: expression, or list. LOGIC 4:not(valueA nPr valueB Returns the number of permutations of valueA taken valueB at a time. PRB 2:nPrvalue nPr list Returns a list of the permutations of value taken each element in list at a time. PRB 2:nPrlist nPr value Returns a list of the permutations of each element in list taken value at a time. PRB 2:nPrlistA nPr listB Returns a list of the permutations of each element in listA taken each element in listB at a time. PRB 2:nPrnpv(interest rate,CF0, Computes the sum of the present values for cash inflows Œ 1:FinanceCFList[,CFFreq]) and outflows. CALC 7:npv(valueA or valueB Returns 1 if valueA or valueB is ƒ 0. valueA and valueB can y: be real numbers, expressions, or lists. LOGIC 2:orOutput(row,column, Displays text beginning at specified row and column. †"text") I/O 6:Output(Output(row,column, Displays value beginning at specified row and column. †value) I/O 6:Output(Param Sets parametric graphing mode. †z ParPause Suspends program execution until you press Í. † CTL 8:PausePause [value] Displays value; suspends program execution until you press † Í. CTL 8:PausePlot#(type,Xlistname, Defines Plot# (1, 2, or 3) of type Scatter or xyLine for †y,Ylistname,mark) Xlistname and Ylistname using mark. STAT PLOTS 1:Plot1- 2:Plot2- 3:Plot3- Appendix A: Functions and Instructions 370
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/Itempxl-Test(row,column) Returns 1 if pixel (row, column) is on, 0 if it is off; y< 0 row 62 and 0 column 94. POINTS 7:pxl-Test(P4Rx(r,q) Returns X, given polar coordinates r and q or a list of polar y ; coordinates. ANGLE 7:P4Rx(P4Ry(r,q) Returns Y, given polar coordinates r and q or a list of polar y ; coordinates. ANGLE 8:P4Ry(QuadReg [Xlistname, Fits a quadratic regression model to Xlistname and …Ylistname,freqlist, Ylistname with frequency freqlist, and stores the regression CALCregequ] equation to regequ. 5:QuadRegQuartReg [Xlistname, Fits a quartic regression model to Xlistname and Ylistname …Ylistname,freqlist, with frequency freqlist, and stores the regression equation CALCregequ] to regequ. 7:QuartRegRadian Sets radian angle mode. †z Radianrand[(numtrials)] Returns a random number between 0 and 1 for a specified number of trials numtrials. PRB 1:randrandBin(numtrials,prob Generates and displays a random real number from a [,numsimulations]) specified Binomial distribution. PRB 7:randBin(randInt( lower,upper Generates and displays a random integer within a range [,numtrials]) specified by lower and upper integer bounds for a specified PRB number of trials numtrials. 5:randInt(randIntNoRep(lowerint, Returns a random ordered list of integers from a lower upperint) integer to an upper integer which may include the lower PRB integer and upper integer. 8:randIntNoRep(randM(rows,columns) Returns a random matrix of rows (1-99) × columns (1-99). y> MATH 6:randM(randNorm(m,s Generates and displays a random real number from a [,numtrials]) specified Normal distribution specified by m and s for a PRB specified number of trials numtrials. 6:randNorm(re^qi Sets the mode to polar complex number mode (re^qi). †z re^qiReal Sets mode to display complex results only when you enter † z complex numbers. Realreal(value) Returns the real part of a complex number or list of complex numbers. CPX 2:real( Appendix A: Functions and Instructions 373
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/ItemRecallGDB n Restores all settings stored in the graph database variable y < GDBn. STO 4:RecallGDBRecallPic n Displays the graph and adds the picture stored in Picn. y< STO 2:RecallPiccomplex value 4Rect Displays complex value or list in rectangular format. CPX 6:4RectRectGC Sets rectangular graphing coordinates format. †y. RectGCref(matrix) Returns the row-echelon form of a matrix. y> MATH A:ref(remainder(dividend, Reports the remainder as a whole number from a division divisor) of two whole numbers where the divisor is not zero. NUM 0:remainder(remainder(list, divisor) Reports the remainder as a whole number from a division of two lists where the divisor is not zero. NUM 0:remainder(remainder(dividend, list) Reports the remainder as a whole number from a division of two whole numbers where the divisor is a list. NUM 0:remainder(remainder(list, list) Reports the remainder as a whole number from a division of two lists. NUM 0:remainder(:Repeat condition Executes commands until condition is true. †:commands CTL:End 6:Repeat:commandsReturn Returns to the calling program. † CTL E:Returnround(value[,#decimals]) Returns a number, expression, list, or matrix rounded to #decimals ( 9). NUM 2:round(ärow(value,matrix,row) Returns a matrix with row of matrix multiplied by value and y> stored in row. MATH E:ärow(row+(matrix,rowA,rowB) Returns a matrix with rowA of matrix added to rowB and y> stored in rowB. MATH D:row+( Appendix A: Functions and Instructions 374
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/ItemSetUpEditor Removes all list names from the stat list editor, and then … restores list names L1 through L6 to columns 1 through 6. EDIT 5:SetUpEditorSetUpEditor listname1 Removes all list names from the stat list editor, then sets it …[,listname2,..., up to display one or more listnames in the specified order, EDITlistname20] starting with column 1. 5:SetUpEditorShade(lowerfunc, Draws lowerfunc and upperfunc in terms of X on the current y <upperfunc[,Xleft,Xright, graph and uses pattern and patres to shade the area DRAWpattern,patres]) bounded by lowerfunc, upperfunc, Xleft, and Xright. 7:Shade(Shadec2(lowerbound, Draws the density function for the c2 distribution specified y =upperbound,df) by degrees of freedom df and shades the area between DRAW lowerbound and upperbound. 3:Shadec2(ShadeÜ(lowerbound, Draws the density function for the Û distribution specified y=upperbound, by numerator df and denominator df and shades the area DRAWnumerator df, between lowerbound and upperbound. 4:ShadeÜ(denominator df)ShadeNorm(lowerbound, Draws the normal density function specified by m and s y=upperbound[,m,s]) and shades the area between lowerbound and upperbound. DRAW 1:ShadeNorm(Shade_t(lowerbound, Draws the density function for the Student-t distribution y=upperbound,df) specified by degrees of freedom df, and shades the area DRAW between lowerbound and upperbound. 2:Shade_t(Simul Sets mode to graph functions simultaneously. †z Simulsin(value) Returns the sine of a real number, expression, or list. ˜sinL1(value) Returns the arcsine of a real number, expression, or list. y?sinh(value) Returns the hyperbolic sine of a real number, expression, yN or list. sinh(sinhL1 (value) Returns the hyperbolic arcsine of a real number, yN expression, or list. sinhL1(SinReg [iterations, Attempts iterations times to fit a sinusoidal regression model …Xlistname,Ylistname, to Xlistname and Ylistname using a period guess, and stores CALCperiod,regequ] the regression equation to regequ. C:SinRegsolve(expression, Solves expression for variable, given an initial guess and †variable,guess, lower and upper bounds within which the solution is sought. MATH{lower,upper}) 0:solve(SortA(listname) Sorts elements of listname in ascending order. y9 OPS 1:SortA(SortA(keylistname, Sorts elements of keylistname in ascending order, then y9dependlist1[,dependlist2, sorts each dependlist as a dependent list. OPS...,dependlist n]) 1:SortA( Appendix A: Functions and Instructions 377
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/ItemSortD(listname) Sorts elements of listname in descending order. y9 OPS 2:SortD(SortD(keylistname,dependl Sorts elements of keylistname in descending order, then y9ist1[,dependlist2, sorts each dependlist as a dependent list. OPS..., dependlist n]) 2:SortD(startTmr Starts the clock timer. Store or note the displayed value, yN and use it as the argument for checkTmr( ) to check the startTmr elapsed time.stdDev(list[,freqlist]) Returns the standard deviation of the elements in list with y9 frequency freqlist. MATH 7:stdDev(Stop Ends program execution; returns to home screen. † CTL F:StopStore: value!variable Stores value in variable. ¿StoreGDB n Stores current graph in database GDBn. y< STO 3:StoreGDBStorePic n Stores current picture in picture Picn. y< STO 1:StorePicString4Equ(string,Y= var) Converts string into an equation and stores it in Y= var. yN String4Equ(sub(string,begin,length) Returns a string that is a subset of another string, from yN begin to length. sub(sum(list[,start,end]) Returns the sum of elements of list from start to end. y9 MATH 5:sum(summation G(expression Displays the MathPrint™ summation entry template and [,start,end]) returns the sum of elements of list from start to end, where NUM start <= end. 0: summation G(tan(value) Returns the tangent of a real number, expression, or list. štanL1(value) Returns the arctangent of a real number, expression, or yA list.Tangent(expression, Draws a line tangent to expression at X=value. y<value) DRAW 5:Tangent(tanh(value) Returns hyperbolic tangent of a real number, expression, or y N list. tanh(tanhL1(value) Returns the hyperbolic arctangent of a real number, yN expression, or list. tanhL1( Appendix A: Functions and Instructions 378
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/Itemtvm_PV[(Ú,æ,PMT,FV, Computes the present value. Œ 1:FinanceP/Y,C/Y)] CALC 4:tvm_PVUnArchive Moves the specified variables from the user data archive yL memory to RAM. 6:UnArchive To archive variables, use Archive.Un/d Displays results as a mixed number, if applicable. NUM C: Un/duvAxes Sets sequence graphs to plot u(n) on the x-axis and v(n) †y. on the y-axis. uvuwAxes Sets sequence graphs to plot u(n) on the x-axis and w(n) †y. on the y-axis. uw1-Var Stats [Xlistname, Performs one-variable analysis on the data in Xlistname …freqlist] with frequency freqlist. CALC 1:1-Var Stats2-Var Stats [Xlistname, Performs two-variable analysis on the data in Xlistname …Ylistname,freqlist] and Ylistname with frequency freqlist. CALC 2:2-Var Statsvariance(list[,freqlist]) Returns the variance of the elements in list with frequency y 9 freqlist. MATH 8:variance(Vertical x Draws a vertical line at x. y< DRAW 4:VerticalvwAxes Sets sequence graphs to plot v(n) on the x-axis and w(n) †y. on the y-axis. vwWeb Sets sequence graphs to trace as webs. †y. Web:While condition Executes commands while condition is true. †:commands CTL:End 5:While:commandvalueA xor valueB Returns 1 if only valueA or valueB = 0. valueA and valueB y: can be real numbers, expressions, or lists. LOGIC 3:xorZBox Displays a graph, lets you draw a box that defines a new †q viewing window, and updates the window. ZOOM 1:ZBoxZDecimal Adjusts the viewing window so that @X=0.1 and @Y=0.1, †q and displays the graph screen with the origin centered on ZOOM the screen. 4:ZDecimal Appendix A: Functions and Instructions 380
Function or Key orInstruction/Arguments Result Keys/Menu or Screen/ItemZFrac 1/2 Sets the window variables so that you can trace in q increments of , if possible. Sets @X and @Y to . ZOOM B:ZFrac1/2ZFrac 1/3 Sets the window variables so that you can trace in q increments of , if possible. Sets @X and @Y to . ZOOM C:ZFrac1/3ZFrac 1/4 Sets the window variables so that you can trace in q increments of , if possible. Sets @X and @Y to . ZOOM D:ZFrac1/4ZFrac 1/5 Sets the window variables so that you can trace in q increments of , if possible. Sets @X and @Y to . ZOOM E:ZFrac1/5ZFrac 1/8 Sets the window variables so that you can trace in q increments of , if possible. Sets @X and @Y to . ZOOM F:ZFrac1/8ZFrac 1/10 Sets the window variables so that you can trace in q increments of , if possible. Sets @X and @Y to . ZOOM G:ZFrac1/10ZInteger Redefines the viewing window using these dimensions: †q @X=1 Xscl=10 ZOOM @Y=1 Yscl=10 8:ZIntegerZInterval s[,listname, Computes a z confidence interval. †…freqlist,confidence level] TESTS(Data list input) 7:ZIntervalZInterval s,v,n Computes a z confidence interval. †…[,confidence level] TESTS(Summary stats input) 7:ZIntervalZoom In Magnifies the part of the graph that surrounds the cursor †q location. ZOOM 2:Zoom InZoom Out Displays a greater portion of the graph, centered on the †q cursor location. ZOOM 3:Zoom OutZoomFit Recalculates Ymin and Ymax to include the minimum and † q maximum Y values, between Xmin and Xmax, of the ZOOM selected functions and replots the functions. 0:ZoomFitZoomRcl Graphs the selected functions in a user-defined viewing †q window. MEMORY 3:ZoomRclZoomStat Redefines the viewing window so that all statistical data †q points are displayed. ZOOM 9:ZoomStat Appendix A: Functions and Instructions 381
Appendix B:Reference InformationVariablesUser VariablesThe TI-84 Plus uses the variables listed below in various ways. Some variables are restricted tospecific data types.The variables A through Z and q are defined as real or complex numbers. You may store to them.The TI-84 Plus can update X, Y, R, q, and T during graphing, so you may want to avoid using thesevariables to store nongraphing data.The variables (list names) L1 through L6 are restricted to lists; you cannot store another type ofdata to them.The variables (matrix names) [A] through [J] are restricted to matrices; you cannot store anothertype of data to them.The variables Pic1 through Pic9 and Pic0 are restricted to pictures; you cannot store another typeof data to them.The variables GDB1 through GDB9 and GDB0 are restricted to graph databases; you cannot storeanother type of data to them.The variables Str1 through Str9 and Str0 are restricted to strings; you cannot store another type ofdata to them.Except for system variables, you can store any string of characters, functions, instructions, orvariables to the functions Yn, (1 through 9, and 0), XnT/YnT (1 through 6), rn (1 through 6), u(n), v(n),and w(n) directly or through the Y= editor. The validity of the string is determined when the function isevaluated.Archive VariablesYou can store data, programs or any variable from RAM to user data archive memory where theycannot be edited or deleted inadvertantly. Archiving also allows you to free up RAM for variables thatmay require additional memory. The names of archived variables are preceded by an asterisk (*)indicating they are in user data archive.System VariablesThe variables below must be real numbers. You may store to them. Since the TI-84 Plus canupdate some of them, as the result of a ZOOM, for example, you may want to avoid using thesevariables to store nongraphing data.• Xmin, Xmax, Xscl, @X, XFact, Tstep, PlotStart, nMin, and other window variables. Appendix B: Reference Information 386
CP = compounding periods Nom = nominal rateDays between DatesWith the dbd( function, you can enter or compute a date within the range Jan. 1, 1950, throughDec. 31, 2049.Actual/actual day-count method (assumes actual number of days per month and actual numberof days per year):dbd( (days between dates) = Number of Days II - Number of Days I Number of Days I = (Y1-YB) 365 + (number of days MB to M1) + DT1 + Y1 – YB ------------------------ 4 Number of Days II = (Y2-YB) 365 + (number of days MB to M2) + DT2 + Y2 – YB ------------------------ 4where: M1 = month of first date DT1 = day of first date Y1 = year of first date M2 = month of second date DT2 = day of second date Y2 = year of second date MB = base month (January) DB = base day (1) YB = base year (first year after leap year) Appendix B: Reference Information 395
Important Things You Need to Know About Your TI-84 PlusTI-84 Plus ResultsThere may be a number of reasons that your TI-84 Plus is not displaying the expected results;however, the most common solutions involve order of operations or mode settings. Your calculatoruses an Equation Operating System™ (EOS™) which evaluates the functions in an expression inthe following order:1. Functions that precede the argument, such as square root, sin(, or log(2. Functions that are entered after the argument, such as exponents, factorial, r, ¡, and conversions3. Powers and roots, such as 2^5, or 5*square root(32)4. Permutations (nPr) and combinations (nCr)5. Multiplication, implied multiplication, and division6. Addition and subtraction7. Relational functions, such as > or <8. Logic operator and9. Logic operators or and xorRemember that EOS™ evaluates from left to right and calculations within parentheses areevaluated first. You should use parentheses where the rules of algebra may not be clear. In OS2.53 MP, parentheses may be pasted in an expression to indicate how the input is interpreted.If you are using trigonometric functions or performing polar and rectangular conversions, theunexpected results may be caused by an angle mode setting. The Radian and Degree angle modesettings control how the TI-84 Plus interprets angle values.To change the angle mode settings, follow these steps:1. Press z to display the Mode settings.2. Select Degree or Radian.3. Press Í to save the angle mode setting.ERR:DIM MISMATCH ErrorYour TI-84 Plus displays the ERR:DIM MISMATCH error if you are trying to perform an operationthat references one or more lists or matrices whose dimensions do not match. For example,multiplying L1*L2, where L1={1,2,3,4,5} and L2={1,2} produces an ERR:DIM MISMATCH errorbecause the number of elements in L1 and L2 do not match. Appendix B: Reference Information 396
ERR:INVALID DIM ErrorThe ERR:INVALID DIM error message may occur if you are trying to graph a function that does notinvolve the stat plot features. The error can be corrected by turning off the stat plots. To turn thestat plots off, press y , and then select 4:PlotsOff.Link-Receive L1 (or any file) to Restore MessageYour TI-84 Plus displays the Link-Receive L1 (or any file) to Restore message if it has been disabledfor testing, and not re-enabled. To restore your calculator to full functionality after testing, link toanother TI-84 Plus and transfer any file to the disabled calculator, or use TI Connect™ software todownload a file from your computer to your TI-84 Plus.To transfer a file from another TI-84 Plus:1. On the receiving unit, press y 8 and then select RECEIVE.2. On the sending calculator, Press y 8.3. Select a file to send by selecting a category, and then selecting a file to send.4. Select TRANSMIT to send the file.Contrast FeatureIf the contrast setting is too dark (set to 9) or too dim (set to 0) the unit may appear as if it ismalfunctioning or turned off. To adjust the contrast, press and release y, and then press and hold} or †.TI-84 Plus Identification CodeYour graphing calculator has a unique identification (ID) code that you should record and keep.You can use this 14 digit ID to register your calculator at education.ti.com or identify your calculatorin the event that it is lost or stolen. A valid ID includes numbers 0 through 9 and the letters Athrough F. Appendix B: Reference Information 397
You can view the calculator's Operating System, Product Number, ID, and Certificate RevisionNumber from the About screen. To display the About screen, press y L and then select1:About.Your unique product ID code: _____________________________BackupsYour TI-84 Plus is similar to a computer, in that it stores files and Apps that are important to you. Itis always a good idea to back up your graphing calculator device files and Apps using theTI Connect™ software and a USB computer cable. You can find the specific procedures forbacking up your calculator's device files and Apps in the TI Connect™ Help file.AppsTI-84 Plus Software Applications (Apps) is software that you can add to your calculator in thesame way you would add software to your computer. Apps let you customize your calculator forpeak performance in specific areas of study. You can find apps for the TI-84 Plus ateducation.ti.com.TI-Cares KnowledgeBaseThe TI-Cares KnowledgeBase provides 24-hour access through the Web to find answers tofrequently asked questions. The TI-Cares KnowledgeBase searches its repository of knownsolutions and presents you with the solutions that are most likely to solve your problem. You cansearch the TI-Cares KnowledgeBase at education.ti.com/support. Appendix B: Reference Information 398
Error ConditionsWhen the TI-84 Plus detects an error, it returns an error message as a menu title, such asERR:SYNTAX or ERR:DOMAIN. This table contains each error type, possible causes, andsuggestions for correction. The error types listed in this table are each preceded by ERR: on yourgraphing calculator display. For example, you will see ERR:ARCHIVED as a menu title when yourgraphing calculator detects an ARCHIVED error type.Error Type Possible Causes and Suggested RemediesARCHIVED You have attempted to use, edit, or delete an archived variable. For example, the expression dim(L1) produces an error if L1 is archived.ARCHIVE FULL You have attempted to archive a variable and there is not enough space in archive to receive it.ARGUMENT A function or instruction does not have the correct number of arguments. See Appendix A for function and instruction syntax, stdDev(list[,freqlist]) might be entered as stdDev(L1) or stdDev(L1,L2) since the frequency list or freqlist is optional.BAD ADDRESS You have attempted to send or receive an application and an error (e.g. electrical interference) has occurred in the transmission.BAD GUESS • In a CALC operation, you specified a Guess that is not between Left Bound and Right Bound. • For the solve( function or the equation solver, you specified a guess that is not between lower and upper. • Your guess and several points around it are undefined. Examine a graph of the function. If the equation has a solution, change the bounds and/or the initial guess.BOUND • In a CALC operation or with Select(, you defined Left Bound > Right Bound. • In fMin(, fMax(, solve(, or the equation solver, you entered lower ' upper.BREAK You pressed the É key to break execution of a program, to halt a DRAW instruction, or to stop evaluation of an expression. Appendix B: Reference Information 399
Error Type Possible Causes and Suggested RemediesDATA TYPE You entered a value or variable that is the wrong data type. • For a function (including implied multiplication) or an instruction, you entered an argument that is an invalid data type, such as a complex number where a real number is required. See Appendix A and the appropriate chapter. • In an editor, you entered a type that is not allowed, such as a matrix entered as an element in the stat list editor. See the appropriate chapter. • You attempted to store an incorrect data type, such as a matrix, to a list.DIM MISMATCH Your calculator displays the ERR:DIM MISMATCH error if you are trying to perform an operation that references one or more lists or matrices whose dimensions do not match. For example, multiplying L1*L2, where L1={1,2,3,4,5} and L2={1,2} produces an ERR:DIM MISMATCH error because the number of elements in L1 and L2 do not match.DIVIDE BY 0 • You attempted to divide by zero. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph. • You attempted a linear regression with a vertical line.DOMAIN • You specified an argument to a function or instruction outside the valid range. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph. See Appendix A. • You attempted a logarithmic or power regression with a LX or an exponential or power regression with a LY. • You attempted to compute GPrn( or GInt( with pmt2 < pmt1.DUPLICATE You attempted to create a duplicate group name.Duplicate Name A variable you attempted to transmit cannot be transmitted because a variable with that name already exists in the receiving unit.EXPIRED You have attempted to run an application with a limited trial period which has expired.Error in Xmit • The TI-84 Plus was unable to transmit an item. Check to see that the cable is firmly connected to both units and that the receiving unit is in receive mode. • You pressed É to break during transmission. • You attempted to perform a backup from a TI.82 to a TI-84 Plus. • You attempted to transfer data (other than L1 through L6) from a TI-84 Plus to a TI.82. • You attempted to transfer L1 through L6 from a TI-84 Plus to a TI.82 without using 5:Lists to TI82 on the LINK SEND menu. Appendix B: Reference Information 400
Error Type Possible Causes and Suggested RemediesID NOT FOUND This error occurs when the SendID command is executed but the proper graphing calculator ID cannot be found.ILLEGAL NEST • You attempted to use an invalid function in an argument to a function, such as seq( within expression for seq(.INCREMENT • The increment in seq( is 0 or has the wrong sign. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph. • The increment in a For( loop is 0.INVALID • You attempted to reference a variable or use a function where it is not valid. For example, Yn cannot reference Y, Xmin, @X, or TblStart. • You attempted to reference a variable or function that was transferred from the TI.82 and is not valid for the TI-84 Plus For example, you may have transferred UnN1 to the TI-84 Plus from the TI.82 and then tried to reference it. • In Seq mode, you attempted to graph a phase plot without defining both equations of the phase plot. • In Seq mode, you attempted to graph a recursive sequence without having input the correct number of initial conditions. • In Seq mode, you attempted to reference terms other than (nN1) or (nN2). • You attempted to designate a graph style that is invalid within the current graph mode. • You attempted to use Select( without having selected (turned on) at least one xyLine or scatter plot.INVALID DIM • The ERR:INVALID DIM error message may occur if you are trying to graph a function that does not involve the stat plot features. The error can be corrected by turning off the stat plots. To turn the stat plots off, press y , and then select 4:PlotsOff. • You specified a list dimension as something other than an integer between 1 and 999. • You specified a matrix dimension as something other than an integer between 1 and 99. • You attempted to invert a matrix that is not square.ITERATIONS • The solve( function or the equation solver has exceeded the maximum number of permitted iterations. Examine a graph of the function. If the equation has a solution, change the bounds, or the initial guess, or both. • irr( has exceeded the maximum number of permitted iterations. • When computing æ, the maximum number of iterations was exceeded. Appendix B: Reference Information 401
Error Type Possible Causes and Suggested RemediesLABEL The label in the Goto instruction is not defined with a Lbl instruction in the program.LINK L1 (or any The calculator has been disabled for testing. To restoreother file) to full functionality, use TI Connect™ software toRestore download a file to your calculator from your computer, or transfer any file to your calculator from another TI-84 Plus. (See the instructions under Important Things to Know about your TI-84 Plus, earlier in this chapter.)MEMORY Memory is insufficient to perform the instruction or function. You must delete items from memory before executing the instruction or function. Recursive problems return this error; for example, graphing the equation Y1=Y1. Branching out of an If/Then, For(, While, or Repeat loop with a Goto also can return this error because the End statement that terminates the loop is never reached.MemoryFull • You are unable to transmit an item because the receiving unit's available memory is insufficient. You may skip the item or exit receive mode. • During a memory backup, the receiving unit's available memory is insufficient to receive all items in the sending unit's memory. A message indicates the number of bytes the sending unit must delete to do the memory backup. Delete items and try again.MODE You attempted to store to a window variable in another graphing mode or to perform an instruction while in the wrong mode; for example, DrawInv in a graphing mode other than Func.NO SIGN CHNG • The solve( function or the equation solver did not detect a sign change. • You attempted to compute æ when FV, (Ú…PMT), and PV are all ' 0, or when FV, (Ú…PMT), and PV are all _ 0. • You attempted to compute irr( when neither CFList nor CFO is > 0, or when neither CFList nor CFO is < 0.NONREAL ANS In Real mode, the result of a calculation yielded a complex result. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph.OVERFLOW You attempted to enter, or you have calculated, a number that is beyond the range of the graphing calculator. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph.RESERVED You attempted to use a system variable inappropriately. See Appendix A. Appendix B: Reference Information 402
Error Type Possible Causes and Suggested RemediesSINGULAR MAT • A singular matrix (determinant = 0) is not valid as the argument for L1. • The SinReg instruction or a polynomial regression generated a singular matrix (determinant = 0) because it could not find a solution, or a solution does not exist. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph.SINGULARITY expression in the solve( function or the equation solver contains a singularity (a point at which the function is not defined). Examine a graph of the function. If the equation has a solution, change the bounds or the initial guess or both.STAT You attempted a stat calculation with lists that are not appropriate. • Statistical analyses must have at least two data points. • Med-Med must have at least three points in each partition. • When you use a frequency list, its elements must be ' 0. • (Xmax N Xmin) à Xscl must be' 47 for a histogram.STAT PLOT You attempted to display a graph when a stat plot that uses an undefined list is turned on.SYNTAX The command contains a syntax error. Look for misplaced functions, arguments, parentheses, or commas stdDev(list[,freqlist]) might be entered as stdDev(L1) or stdDev(L1,L2) since the frequency list or freqlist is optional.TOL NOT MET You requested a tolerance to which the algorithm cannot return an accurate result.UNDEFINED You referenced a variable that is not currently defined. For example, you referenced a stat variable when there is no current calculation because a list has been edited, or you referenced a variable when the variable is not valid for the current calculation, such as a after Med-Med.VALIDATION Electrical interference caused a link to fail or this graphing calculator is not authorized to run the application. Appendix B: Reference Information 403
Error Type Possible Causes and Suggested RemediesVARIABLE You have tried to archive a variable that cannot be archived or you have tried to unarchive an application or group. Examples of variables that cannot be archived include: • Real numbers LRESID, R, T, X, Y, Theta, Statistic variables under Vars, STATISTICS menu, Yvars, and the AppIdList.VERSION You have attempted to receive an incompatible variable version from another graphing calculator.WINDOW A problem exists with the window variables.RANGE • You defined Xmax Xmin or Ymax Ymin. • You defined qmax qmin and qstep > 0 (or vice versa). • You attempted to define Tstep=0. • You defined Tmax Tmin and Tstep > 0 (or vice versa). • Window variables are too small or too large to graph correctly. You may have attempted to zoom in or zoom out to a point that exceeds the TI-84 Plus's numerical range.ZOOM • A point or a line, instead of a box, is defined in ZBox. • A ZOOM operation returned a math error. Appendix B: Reference Information 404
Accuracy InformationComputational AccuracyTo maximize accuracy, the TI-84 Plus carries more digits internally than it displays. Values arestored in memory using up to 14 digits with a two-digit exponent.• You can store a value in the window variables using up to 10 digits (12 for Xscl, Yscl, Tstep, and qstep).• Displayed values are rounded as specified by the mode setting with a maximum of 10 digits and a two-digit exponent.• RegEQ displays up to 14 digits in Float mode. Using a fixed-decimal setting other than Float causes RegEQ results to be rounded and stored with the specified number of decimal places.Xmin is the center of the leftmost pixel, Xmax is the center of the next-to-the-rightmost pixel. (Therightmost pixel is reserved for the busy indicator.) @X is the distance between the centers of twoadjacent pixels.• In Full screen mode, @X is calculated as (Xmax N Xmin) à 94. In G-T split-screen mode, @X is calculated as (Xmax N Xmin) à 46.• If you enter a value for @X from the home screen or a program in Full screen mode, Xmax is calculated as Xmin + @X É… 94. In G-T split-screen mode, Xmax is calculated as Xmin + @X É… 46.Ymin is the center of the next-to-the-bottom pixel; Ymax is the center of the top pixel. @Y is thedistance between the centers of two adjacent pixels.• In Full screen mode, @Y is calculated as (Ymax N Ymin) à 62. In Horiz split-screen mode, @Y is calculated as (Ymax N Ymin) à 30. In G-T split-screen mode, @Y is calculated as (Ymax N Ymin) à 50.• If you enter a value for @Y from the home screen or a program in Full screen mode, Ymax is calculated as Ymin + @Y É… 62. In Horiz split-screen mode, Ymax is calculated as Ymin + @Y … 30. In G-T split-screen mode, Ymax is calculated as Ymin + @Y É … 50.Cursor coordinates are displayed as eight-character numbers (which may include a negative sign,decimal point, and exponent) when Float mode is selected. X and Y are updated with a maximumaccuracy of eight digits.minimum and maximum on the CALCULATE menu are calculated with a tolerance of 1âL5; ‰f(x)dx iscalculated at 1âL3. Therefore, the result displayed may not be accurate to all eight displayed digits.For most functions, at least five accurate digits exist. For fMin(, fMax(, and fnInt( on the MATH menuand solve( in the CATALOG, the tolerance can be specified.Function LimitsFunction Range of Input Valuessin x, cos x, tan x 0 |x| < 10 12 (radian or degree) Appendix B: Reference Information 405
Appendix C:Service and Warranty InformationTexas Instruments Support and ServiceFor general informationHome Page: education.ti.comKnowledgeBase and education.ti.com/supporte-mail inquiries:Phone: (800) TI-CARES / (800) 842-2737 For U.S., Canada, Mexico, Puerto Rico, and Virgin Islands onlyInternational education.ti.com/internationalinformation:For product (hardware) serviceCustomers in the U.S., Canada, Mexico, Puerto Rico and Virgin Islands: Always contact TexasInstruments Customer Support before returning a product for service.All other customers: Refer to the leaflet enclosed with this product (hardware) or contact your localTexas Instruments retailer/distributor.Battery InformationWhen to Replace the BatteriesThe TI-84 Plus uses five batteries: four AAA alkaline batteries and one button cell backup battery.The backup battery provides auxiliary power to retain memory while you replace the AAAbatteries.When the battery voltage level drops below a usable level, the TI-84 Plus: Displays this message when Displays this message when you attempt you turn on the unit. to download an application. Message A Message B Appendix C: Service and Warranty Information 407
After Message A is first displayed, you can expect the batteries to function for about one or twoweeks, depending on usage. (This one-week to two-week period is based on tests with alkalinebatteries; the performance of other types of batteries may vary.)If Message B is displayed, you must replace the batteries immediately to successfully download anapplication.Effects of Replacing the BatteriesDo not remove both types of batteries (AAA and backup ) at the same time. Do not allow thebatteries to lose power completely. If you follow these guidelines and the steps for replacingbatteries, you can replace either type of battery without losing any information in memory.Battery PrecautionsTake these precautions when replacing batteries.• Do not leave batteries within reach of children• Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries.• Do not mix rechargeable and nonrechargeable batteries.• Install batteries according to polarity (+ and N) diagrams.• Do not place nonrechargeable batteries in a battery recharger.• Properly dispose of used batteries immediately. Do not leave them within the reach of children.• Do not incinerate or dismantle batteries.Disposing of used batteries safely and properlyDo not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode,releasing hazardous chemicals. Discard used batteries according to local regulations.Replacing the BatteriesTo replace the batteries, follow these steps.1. Turn off the graphing calculator. Replace the slide cover over the keyboard to avoid inadvertently turning on the graphing calculator. Turn the back of the unit toward you.2. Hold the graphing calculator upright, push downward on the latch on the top of the battery cover, and then pull the cover toward you. Note: To avoid loss of information stored in memory, you must turn off the graphing calculator. Do not remove the AAA batteries and the backup battery simultaneously.3. Replace all four AAA alkaline batteries simultaneously. Or, replace the backup battery. • To replace the AAA alkaline batteries, remove all four discharged AAA batteries and install new ones according to the polarity (+ and N) diagram in the battery compartment. Appendix C: Service and Warranty Information 408
• To replace the backup battery, remove the screw from the backup battery cover, and then remove the cover. Install the new battery, + side up. Replace the cover and secure it with the screw.4. Replace the battery compartment cover. Turn the graphing calculator on and adjust the display contrast, if necessary, by pressing y } or †. Appendix C: Service and Warranty Information 409
In Case of DifficultyHandling a DifficultyTo handle a difficulty, follow these steps.1. If you cannot see anything on the screen, you may need to adjust the graphing calculator contrast. To darken the screen, press and release y, and then press and hold } until the display is sufficiently dark. To lighten the screen, press and release y, and then press and hold † until the display is sufficiently light.2. If an error menu is displayed, follow these steps: • Note the error type (ERR:error type). • Select 2:GOTO, if it is available. The previous screen is displayed with the cursor at or near the error location. • Deteremine the error. • Correct the expression. Refer to the Error Conditions table for details about specific errors, if necessary.3. If the busy indicator (dotted line) is displayed, a graph or program has been paused; the TI-84 Plus is waiting for input. Press Í to continue or press É to break.4. If a checkerboard cursor ( # ) is displayed, then either you have entered the maximum number of characters in a prompt, or memory is full. If memory is full: • Press y L 2 to display the MEMORY MANAGEMENT / DELETE menu. • Select the type of data you want to delete, or select 1:All for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using. • Press } and † to move the selection cursor (4) next to the item you want to delete, and then press {.5. If the graphing calculator does not seem to work at all, be sure the alkaline batteries are fresh and that they are installed properly.6. If the TI-84 Plus does not function even though you are sure that the batteries are fresh, you can try manually resetting it. • Remove all of the AAA batteries from the graphing calculator. • Press and hold the É key for ten seconds. • Replace the batteries. • Turn on the unit. When you reset your graphing calculator, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast by pressing y and releasing } or †.7. If the above solutions do not work you can reset all of the memory. The RAM, user data archive memory, and system variables are restored to factory settings when you reset all memory. All nonsystem variables, applications (Apps), and programs are deleted. Appendix C: Service and Warranty Information 410
• Press y L to display the MEMORY menu.• Select 7:Reset to display the RAM ARCHIVE ALL menu.• Press ~ ~ to display the ALL menu.• Select 1:All Memory to display the RESET MEMORY menu.• To continue with the reset, select 2:Reset. The message Mem cleared is displayed on the home screen. Appendix C: Service and Warranty Information 411
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Customer Reviews
Mathematics for the TradesAugust 2, 2011 by Myles Dalquist
This is not a complicated, in depth, advanced algebra textbook. This textbook contains the simple, common sense skills that you will need in any job. It has easy-to-follow-lessons and plenty of practice problems. This textbook is very well priced compared to similar textbooks. It is an easy read that is straight to the point and easy to understand.
The authors interviewed trades workers, apprentices, teachers, and training program directors to ensure realistic problems and applications and added over 100 new exercises to this edition. Geometry, triangle trigonometry, and advanced algebra. For individuals who will need technical math skills to succeed in a wide variety of trades.
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Each subtopic below contains a
lesson page, an interactive student practice page, and a
teacher resource page. Sections denoted with * have Graphing Calculator references.
Note: Certain topics in the NYS Learning Standards cross
strands, such as "parabolas" occurring under both the Algebra and Geometry
strands. This site presents such topics in only one location.
The materials (text,
graphics, video clips, etc) from this Integrated Algebra website are
protected by copyright law.
The materials are for classroom or personal use only.
The materials are not to be publically distributed in part or whole.
The materials are not to be reposted to the internet in part or
whole. Thank you.
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The elementary functions (sine, cosine, tan,
exponentials,
and logarithms) are the most commonly used mathematical functions in
science
and engineering. Computing these functions quickly and accurately is a
major goal in computer arithmetic.
This new book gives the concepts and
background
necessary to understand and build algorithms for computing these
functions,
presenting and structuring the algorithms (hardware-oriented as well as
software-oriented), and discusses issues related to the accurate
floating-point
implementation.
The purpose is not to give "cookbook recipes"
that allow one to implement some given function, but to provide the
reader
with the knowledge that is necessary to build, or adapt, algorithms to
their specific computing environment.
Topics and Features
Background material reviewed in Chapter 2,
Computer
Arithmetic
Polynomial and rational approximations
Table based methods
Shift-and-add algorithms thoroughly covered
in
part two
The CORDIC algorithm
Range reduction and accuracy covered in part
three
The book provides an up-to-date presentation of
the
information needed to understand and accurately use mathematical
functions
and algorithms in computational work and design. Graduates,
professionals
and researchers in scientific computing, software engineering and
computer
engineering will find the book a useful reference and resource.
This fascinating book describes the techniques used by high level
compilers and by pocket book calculators to generate values of the
common
elementary mathematical functions. Both the theory and the
implementation
details of the algorithms are explained in sufficient detail to satisfy
the curious or to inform the professional. ASLIB Book Guide
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This book presents a broad overview of computer graphics (CG), its history, and the hardware tools it employs. Covering a substantial number of concepts and algorithms, the text describes the techniques, approaches, and algorithms at the core of this field.
This book focuses on five hot research directions in 3D model analysis and processing in computer science: compression, feature extraction, content-based retrieval, irreversible watermarking and reversible watermarking.
Transformations and Projections in Computer Graphics provides a thorough background, discussing the mathematics of perspective in a detailed, yet accessible style. It also reviews nonlinear projections in depth, including fisheye, panorama, and map projections frequently used to enhance digital images.
An ideal course book for mathematics undergraduates and graduates alike, this is a complete introduction to vector analysis/ Each topic covered is given a practical application within computer graphics.
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Preface Linearalgebra has in recent years become an essential part of the mathematical background required by mathematicians and mathematics teachers, engineers, computer scientists, physicists, economists, and
Schaums Outline of LinearAlgebra (4th edition) by Seymour Lipschutz and Marc Lipson. (This is an exercise textbook in case you liked to ex your LinearAlgebra muscles). Prerequisites: Calculus I (Math-UA:0121) with a C or higher (or the equivalent).
SCHAUM'S OUTLINE OF Theory and Problems of COLLEGE MATHEMATICS THIRDEDITION Algebra DiscreteMathematics Precalculus IntroductiontoCalculus FRANKAYRES,Jr.,Ph.D. Formerly Professor andHead ... This is a linear function and its graph is a straight line.For this graph only two points are necessary.
The Schaum's Outline of LinearAlgebra contains 1. useful summaries of the most important material and a large number of solved problems covering a wide range of topics. Consequently, it is an excellent tool for reviewing and practicing course material.
LinearAlgebra. Notation R,R+,Rn realnumbers,realsgreaterthan0,n-tuplesofreals N,C naturalnumbersf0;1;2;:::g,complexnumbers (a::b),[a::b] openinterval,closedinterval ... Algebra course is an ideal spot to work on this transition to more rigor. It
Schaum'sOutlineofLinearAlgebra, fourth edition, by Lipschutz and Lipson, McGraw-Hill. Prerequisites: Calculus 1 and 2 with a grade of C or higher. ... to linearalgebra, an introduction to ordinary differential equations, and the application of
Use the vocabulary of linearalgebra to discuss these statements. Abstract algebra skills, including ... Schaum's Outline of Linare Algebra The material of the course is standard; any textbook titled linearalgebra will cover the computational
† From LinearAlgebra and Vector Calculus at Texas A&M: { Sections 1.1{1.2 † From Schaum's Outline of Beginning LinearAlgebra: { Sections 2.1{2.9 Required problems. Turn in a solution for each of the following problems. 1. Find all solutions to the following system of linear equations:
SCHAUM'S SOLVED PROBLEMS SERIES l 3000 SOLVED PROBLEMS IN PRECALCULUS Philip Schmidt, Ph.D. State University of New York at New Paltz ... of a Function / 3.4 Step Functions and Continuity / 3.5 Linear Functions / 3.6 The Algebra of Functions
Also recommended are Schaum's Outline Linear Algebraby Lipschutz, and LinearAlgebra by Gilbert Strang. You may not use the electronic form in class, as such readers are usually wifi capable, and that is not allowed during class time.
Schaum's Outlines, McGraw-Hill, 2009 ... linearalgebra well. As well as basic complex variables and (some) probability. The goal of this course is not to teach fundamental concepts of linearalgebra (which you are assumed to
Schaum's Outlines, McGraw-Hill, 2009 ... linearalgebra, the course reading and homework will not be assigned in the order of presentation given in the textbook. 6 Assumed Programming Skills ! It is assumed that students know Matlab or an equivalent
• Schaum's Outline of LinearAlgebra, Seymour Lipschutz and Marc Lipson, 3rd Ed., McGraw-Hill, 2000, ISBN 0-071-36200-2 All books are available at and at Fast and free shipping, and discounts are available.
Additional resources: Schaum's Outlines: LinearAlgebra by S. Lipschutz and M. Lipson is a cheap, helpful book. In addition, the following textbooks are on reserve in the Mathematics Library: LinearAlgebra with Applications by Steven Leon.
To introduce the basic topics of linearalgebra such as matrices, vector spaces, linear transformations, bases and dimension. To develop the ... Theory and problems of LinearAlgebra. Schaum's Outline Series, 2000. Author: 00012123 Created Date:
Schaum's Outline of College Algebra is a complete, concise guide to college algebra, for studen ts ... LinearAlgebra, Arithmetic and Topics in Algebra, or Functions and Graphs. Features • Outline format supplies a concise guide to the standard college course in college algebra
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Elementary Algebra for College Students - 8th edition
Summary: Today's students are visual learners, and Angel/Runde offers a visual presentation to help them succeed in math. Visual examples and diagrams are used to explain concepts and procedures. New Understanding Algebra boxes and an innovative color coding system for variables and notation keep students focused. Short, clear sentences reinforce the presentation of each topic and help students overcome language barriers to learn math. Real Numbers; Solving Linear Equations and Inequalities; ...show moreApplications of Algebra; Exponents and Polynomials; Factoring; Rational Expressions and Equations; Graphing Linear Equations; Systems of Linear Equations; Roots and Radicals; Quadratic Equations For all readers interested in algebraALL ANSWERS INCLUDED.Identical to student edition.Black tape on cover. NO CD OR ACCESS CODE.SHIPS FAST!! SAME DAY OR W/N 24 HOURS.EXPEDITED SHIPPING AVAILABLE TOO!!
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…
To learn and understand mathematics, students must engage in the process of doing mathematics. Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and howBuilding on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology.
The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and …
This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory …
Through many examples and real-world applications, Practical Linear Algebra: A Geometry Toolbox, Third Edition teaches undergraduate-level linear algebra in a comprehensive, geometric, and algorithmic way. Designed for a one-semester linear algebra course at the undergraduate level, the book gives …
Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic …
Near Rings, Fuzzy Ideals, and Graph Theory explores the relationship between near rings and fuzzy sets and between near rings and graph theory. It covers topics from recent literature along with several characterizations.
After introducing all of the necessary fundamentals of algebraic systems, the …
Topology is a large subject with many branches broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad variety of mathematical disciplines. Algebraic topology serves as a powerful tool for studying the problems in …
Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group
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Book Description: This accessible text is designed to help readers help themselves to excel. The content is organized into two parts: (1) A Library of Elementary Functions (Chapters 1–2) and (2) Calculus (Chapters 3–9). The book's overall approach, refined by the authors' experience with large sections of college freshmen, addresses the challenges of teaching and learning when readers' prerequisite knowledge varies greatly. Reader-friendly features such as Matched Problems, Explore & Discuss questions, and Conceptual Insights, together with the motivating and ample applications, make this text a popular choice for today's students and instructors
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$138.679The History of MathematicsAugust 7, 2011 by Jacki Leach
The minute I got this textbook I fell in love with it and I was reading it every day. The problems at the end of the chapters are so cool. I would recommend this textbook for a course any day in the history and development of mathematics for those who have had some experience with mathematical proofs. Burton did a wonderful job on this book.
The History of Mathematics: An Introduction:
5 out of
5
stars based on
1 user reviews.
Summary
The History of Mathematics: An Introduction, Seventh Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools.
Elegantly written in David Burton's imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics' greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Seventh Edition a valuable resource that teachers and students will want as part of a permanent library.
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Offering the most geometric presentation available, Linear Algebra with Applications, Fourth Edition emphasizes linear transformations as a unifying ...Show synopsisOffering the most geometric presentation available, Linear Algebra with Applications, Fourth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the many techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Extensive problem sets keep students involved in the material, while genuine applications for a broad range of sciences prepares them for the methods and models of contemporary scientists. In addition, the wealth and variety of exercise sets enable instructors to design a course to best suit the goals and needs of their students. This revision reflects careful review and appropriate changes to the wording of each idea, while preserving the content structure of the previous
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simple, concise and useful book, explaining MATLAB for freshmen in engineering. MATLAB is presently a globally available standard computational tool for engineers and scientists. The terminology, syntax and the use of the programming language are well defined and the organisation of the material makes it easy to locate information and navigate through the textbook. This new text emphasises that students do not need to write loops to solve many problems. The MATLAB "find" command with its relational and logical operators can be used instead of loops in many cases. This was mentioned in Palm's previous MATLAB texts, but receives more emphasis in this MATLAB 6 edition, starting with Chapter 1, and re-emphasised in Chapter 4.
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Still baffled by the Building Regs? Confused by codes of practice? Mystified by materials and puzzled by planning permission? Then look no further! This is an ideal guide to glance at when you need a quick, precise answer to the requirements of the Building Regulations.
1001 Basic Math & Pre- Algebra Practice Problems For Dummies Practice makes perfect-and helps deepen your understanding of basic math and pre-algebra by solving problems 1001 Basic Math & Pre-Algebra Practice Problems For Dummies, with free access to online practice problems, takes you beyond the instruction and guidance offered in Basic Math & Pre-Algebra For Dummies, giving you 1,001 opportunities to practice solving problems from the major topics in your math course. You begin with some basic arithmetic practice, move on to fractions, decimals, and percents, tackle story problems, and finish up with basic algebra. Every practice question includes not only a solution but a step-by-step explanation. From the book, go online and find:Many Light Water Reactors (LWRs) are in operation worldwide and others are in construction. Analysis techniques and their validation are needed to provide assurances for licensing and for safe reactor operation.
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MTH60 Introductory Algebra- 1st Term
Introduction to algebraic concepts and processes with a focus on linear equations and inequalities in one and two variables. Applications, graphs, functions, formulas, and proper mathematical notation are emphasized throughout the course. A scientific calculator is required. The TI-30X II is recommended. Prerequisites: MTH 20 and RD 80 (or ESOL 250). Audit available.
(For detailed information, see the Course Content and Outcome Guide ).
MTH 60 is a first term beginning algebra course that focuses on the symbolic algebra skills needed for further course work in mathematics and science.
In this telecourse, you will watch lessons on Comcast Cable channel 27 (Portland area only), on your computer via youtube, or on VHS tapes that can be viewed at the library. Each week you will be expected to watch two lessons. Hopefully, you'll find the lessons thorough and comprehensive. Nonetheless, it will be important that you also read the corresponding sections of your textbook and do the suggested practice problems. You will also need to log in to Desire2Learn several times a week as I send announcements via Desire2Learn. The youtube links will also be available in Desire2Learn.
You need to purchase the text at the Sylvania bookstore.
THOUGHTS ABOUT DISTANCE LEARNING AND MATHEMATICS:
It is not easy to learn mathematics via pre-recorded lessons. The time you would spend in class will instead be spent watching the lessons, reading and studying mathematics in your textbook. To be successful in this class, you must be an independent learner.
This course, like other math courses, is time-intensive. Classes like this one typically require about five hours each week watching, pausing and reviewing the lessons (just like attending class) and an additional eight to twelve hours reading the textbook, doing homework, and studying.
Please assess your situation, and determine if you will be able to commit this kind of time to the class. Also think about the type of learner you are. Teleweb courses are a terrific option, especially for independent, self-motivated learners. If this does not describe you, consider why it is you are thinking about taking this type of class, and if it really is a medium that will give you the best chance to succeed. DO NOT TAKE MTH 60 via TELEWEB BECAUSE YOU THINK IT WILL BE EASIER THAN AN ON-CAMPUS CLASS. For many students, it is HARDER via teleweb than on-campus. This is not a self-paced course. There are specific due dates and I do not accept late work.
Course Specific Requirements:
IMPORTANT DETAILS:
There are three proctored paper-and-pencil, no-notes, no-books, no calculator exams (two midterms and a final). There will be scheduled times to take those exams at the Sylvania Campus, but if you live out of town, you can make arrangements with me to take the exam at an approved college testing center. If you live in the Portland area, you must take the exam at the Sylvania Campus. I do not offer testing at the other PCC campuses. Otherwise, the entire course can be completed from home. The five graded worksheets can be mailed.
Students with disabilities should notify their instructor if accommodations are needed to take this class. For information about technologies that help people with disabilities in taking Web based distance learning classes please visit the Office for Students with Disabilities website.
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Description:
"Do not worry about your difficulties in mathematics, I assure you that mine are greater." Einstein, Albert (1879-1955). If you are not Einstein, or are actually having difficulties with mathematics, let this website help. The page contains a wealth of online math resources. Some of these include: basic math, everyday math, pre-algebra, algebra, geometry, trigonometry, statistics, calculus, advanced topics, and math tutoring.
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Every year, hundreds of the most beautiful people in the world come to New York to become models. At age fourteen, Cheryl Diamond was one of them. Living on her own in a run-down apartment, Cheryl spent her days on go-sees, runways, and shoots, surviving hand-to-mouth, while taking in everything she could about the tough and sleazy modeling industry. She watched other girls make mistakes, and swore she wouldn't be a victim. . . until a career-altering event changed her life and nearly ruined her shot at her dream. This is the riveting, true account of Cheryl's triumphant rise, disastrous fall, and phoenix-like comeback in one of the hottest and most demanding industries in the world.
An innovative course that offers students an exciting new perspective on mathematics,Modeling With Mathematicsexplores how mathematics can help explore problems real people encounter in their jobs and lives. Mathematical modeling and a data-driven approach to exploring functions helps students deepen their mathematical skills and maturity. Modeling With Mathematics: A Bridge To Algebra IIhas been designed for students who have completed Algebra I or Algebra I and Geometry but need review practice and motivation to succeed in Algebra II. In addition the course gives students a look ahead to many Algebra II topics. Modeling With Mathematics: A Bridge To Algebra II list serv whfreeman. com/bridgelistserv. pdf As a service to instructors usingModeling With Mathematics: A Bridge To Algebra II, a listserv has been designed as a forum to share ideas, ask questions and learn new ways to enhance the learning experience for their students.The world we live in is complex and diverse. It contains the hardness of steel and the softness of cotton, the brilliance of diamonds and the blackness of coal, the heat of flames and the chill of ice, the tranquility of a slow moving river and the din of a busy city street. All the colors, textures, objects, animals, and plants that exist are too numerous to count. Yet scientists have learned that there are approximately 90 different ingredients, or elements, that make up all the material things we see and experience.
Explore the world around you with pages of colorful photos, helpful illustrations, detailed Sample Problems, and hands-on activities using everyday materials. Learn how chemistry concepts are connected to your everyday life.Modern Livestock and Poultry Production, seventh edition is the textbook students and instructors turn to for thorough coverage of the animal agriculture industry. For each of the many species discussed in the text, students will find essential information about the breeds, selection of breeding stock, feeding and species management, diseases and parasites common to the species and marketing. Material is derived from the latest research and most current information about animal genetics, breeding, nutrition, biotechnology and product promotion. The text provides complete coverage of such major farm animal enterprises as beef cattle, swine, sheep, goats, horses, poultry and dairy cattle. Minor animal enterprises addressed include rabbits, bison, ratites, llamas and alpacas. Students will gain a comprehensive understanding of the livestock industry, including career opportunities.
Modern Residential Wiring provides essential information about the tools, materials, equipment, and processes encountered in the electrical trade. The 2008 edition of this comprehensive textbook includes the latest information on installation and repair techniques, as well as recentdevelopments in wiring systems, personal protection equipment, and computer wiring. References to the 2008 National Electrical CodeRG are made throughout this text to reinforce the importance of installing residential wiring in a safe and professional manner. Apprentices, vocational students, andanyone interested in electrical wiring will find Modern Residential Wiring a valuable aid in learning how electrical systems are designed, installed, and maintained. Experienced electricians who want to review basic wiring techniques or study the recent developments in the electrical field will alsofind this book helpful. Based on the 2008 National Electrical CodeRG.
Modern Welding is a comprehensive text that has long been the standard for teaching the theory, fundamentals, equipment, and techniques of welding technology. In addition to covering a very wide range of welding and cutting processes, the text includes thorough coverage of welding symbols, testing and inspection, and getting a job in the welding industryIn to better themselves and
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Discrete Mathematics
9780130890085
ISBN:
0130890081
Edition: 5 Pub Date: 2000 Publisher: Prentice Hall PTR
Summary: For one or two term introductory courses in discrete mathematics. This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has woven techniques of proofs into the text as a running theme. Each chapter has a problem-solving corner that shows students how to attack and solve problems.
Johnsonbaug...h, Richard is the author of Discrete Mathematics, published 2000 under ISBN 9780130890085 and 0130890081. Fifty seven Discrete Mathematics textbooks are available for sale on ValoreBooks.com, fifty four used from the cheapest price of $0.76, or buy new starting at $40
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More About
This Textbook
Overview
Very little prior mathematical knowledge is assumed, other than the rudiments of algebra and geometry, so the book may be used as a source of enrichment material and project work for college students. A chapter on games using goldpoint tiles is included at the end, and it can provide much material for stimulating mathematical activities involving geometric puzzles of a combinatoric
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MIST Academy's Advanced Problem Solving program is aimed at
students with very strong problem solving skills.
It is suggested that
students taking this class be confident in their ability to qualify for
the American Invitational Mathematics Examination (AIME).
Little
time will be spent on traditional curriculum, except to extend and
generalize important concepts.
Topics covered will include synthetic
geometry, the pigeonhole principle, the principle of
inclusion-exclusion, mathematical induction, and many others.
Some class time will be spent developing students' abilities to write rigorous proofs.
The
Advanced Problem Solving course is listed for grades 9 through 12,
but MIST Academy actually places students in classes by ability, not
age or grade.
The grade range has more to do with the competitions that
make up some of the focus of this course.
Problems and lessons are
taken from many sources including the AMC 12, the Mandelbrot
competition, Mu Alpha Theta, the AIME, ARML, and even sometimes from Olympiad competitions such as the USA Mathematical Olympiad.
The theme of the Spring Advanced Problem Solving class is Inequalities and Optimization.
Topics include tactics and strategies for solving inequalities, the Power Mean inequality chain, the Cauchy Schwarz inequality, geometric inequalities, and much more.
Much of
the class will be aimed at the levels of problems seen at ARML, and on the AIME and
USA Mathematical Olympiad (USAJMO/USAMO) exams.
This material should also be
helpful for
students competing in Alabama math team events, or the Alabama ARML team.
Additional course information, instructor information, and a complete schedule can be found here.
Cost of enrollment in this course is $420.
To enroll or ask questions about class, please contact us.
The theme of the Summer Advanced Problem Solving class is Number Theory.
Topics include Diophantine equations, modular arithmetic, Fermat's Little Theorem, Euler's Theorem, Pell equations, and much more.
Part of the goal of this class will be to teach a rigorous development of these topics, including proofs of many famous and useful results.
Another goal will be to prepare students for the kinds of problem solving techniques helpful to a wide variety of analytical disciplines such as those seen on the AIME and
USA Mathematical Olympiad (USAMO) exams.
This material should also be
helpful for
students competing in Alabama math team events, or the Alabama ARML team.
More information can be found here.
Cost of enrollment in
the two-week course is $640, which includes all fees, materials, and
registration.
To enroll, please contact us.
The theme of the Fall Advanced Problem Solving class is Geometry.
Topics include advanced problems involving triangles and other polygons, 3D geometry, symmetries, centers of triangles, locuses, transformations, and much more.
Some of the class focuses on learning to develop better proof writing skills.
Much of
the class will be aimed at the levels of problems seen on the AIME and
USA Mathematical Olympiad (USAMO) exams.
This material should also be
helpful for
students competing in Alabama math team events,
or the Alabama ARML team.
Click here for the Fall schedule.
Cost of enrollment in
the ten-week course is $420, which includes all fees, materials, and
registration.
To enroll, please contact us.
The theme of the Winter Advanced Problem Solving class is Combinatorics.
Topics include advanced problems involving generating functions, discrete and continuous probability, recursion, set theory, graph theory, and much more.
Much of
the class will be aimed at the levels of problems seen on the AIME and
USA Mathematical Olympiad (USAJMO/USAMO) exams.
This material should also be
helpful for
students competing in Alabama math team events,
or the Alabama ARML team.
A complete schedule can be found here.
Cost of enrollment in
the ten-week course is $420, which includes all fees, materials, and
registration.
To enroll, please contact us.
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Curriculum and Assessment (5 ECTS): In this module, students examine principles, theories and international trends in curriculum and assessment and engage in the curriculum planning process with a particular focus on contemporary issues in Irish curriculum policy and practice.
Practical Teaching Programme: Special Educational Needs (5 ECTS): Student teachers will complete 20hrs in the classroom with a focus on issues of catering for diverse learners and accommodating students with special educational needs. Tasks will engage student teachers in designing learning activities and creating resources and materials to support a variety of learning needs.
History of Mathematics (5 ECTS): A selection of topics concerned with the ancient and recent history of mathematical thinking, and the development of modern mathematics. Topics will include the history of number theory, the history of geometry, the history of calculus, and major developments in the last century.
Discrete Mathematics (5 ECTS): This module offers an introduction to combinatorial mathematics, including the following topics: enumeration techniques, permutations and combinations, graph theory, algorithms and applications.
Semester 2:
Professional Studies: Integrated Project (5 ECTS): In this module, students draw from learning throughout the programme to design their own summer programme. In a collaborative effort, they consider important issues of school organisation, administration, curriculum design and teaching and learning to develop a two-week mathematics enrichment programme for local second-level pupils. On an administrative level, students create a programme handbook, outlining its aims, structure and policies. They design the curriculum based on the potential pupils, advertise their programme and offer it during the summer as part of their Practical Teaching Programme.
Mathematical Software (5 ECTS): The aim of this module will be to introduce students to the many software packages that are available to mathematicians for various purposes including research, learning, teaching, preparation of presentations and mathematical typesetting.
Complex Variables (5 ECTS): This module entails a detailed study of the theory of complex numbers including their arithmetic properties and an introduction to the analysis of functions of one complex variable. Topics to be covered include : De Moivre's theorem, roots of unity, analytic functions and the Cauchy-Riemann equations, Cauchy's Integral Theorem, the Residue Theorem and applications.
Full-Year Modules:
Psychology, Sociology and Catering for Diversity (10 ECTS): This module presents a range of theoretical perspectives in Psychology and Sociology and offers practical support for both meeting diverse educational needs and managing important variables such as social class, race and ethnicity in the context of the post-primary school. The focus is on preparation for promoting educational inclusion in diverse settings and developing strategies for supporting the needs of diverse learners in the mainstream classroom.
Applied Mathematics: Mathematical Modeling (10 ECTS): In these modules students will investigate applications of mathematical and statistical theory and uses of mathematical models in diverse fields.
Summer Session:
Practical Teaching Programme: Mathematics Enrichment Programme (5 ECTS): This programme will run during the summer following Year 3. Student teachers are notified of this component from Year 1 so that they can plan for it in advance; however, in the case that someone is unable to participate outside of the University's regular academic timetable, s/he may petition for completion of an alternative placement during the semester but must still partake in all planning and preparation efforts throughout the semester Thursday, April 22, 2010
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Math Inductive And Deductive Reasoning Pdf
Inductive Versus Deductive Reasoning - University of Houston although inductive reasoning can sometimes lead to false conclusions it can often be a useful first step in the process of applying deductive reasoning to determine Inductive Versus Deductive Reasoning - University of Houston
House and Holmes A Guide to Deductive and Inductive Reasoning house and holmes a guide to deductive and inductive reasoning summary maybe youve seen dr house in action figuring things out from what seem like totally House and Holmes A Guide to Deductive and Inductive Reasoning
1 2 An Application of Inductive Reasoning Number Patterns 1 2 an application of inductive reasoning number patterns 15 figure 5 example 3 use the formulas to find each of the following a the seventh triangular 1 2 An Application of Inductive Reasoning Number Patterns
5TH GRADE MATH SCOPE AND SEQUENCE - Cleveland 5th grade math scope and sequence july 2008 early third quarter number number sense and operations e use order of operations including use of 5TH GRADE MATH SCOPE AND SEQUENCE - Cleveland
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Intermediate Algebra - 9th edition
Summary: The new edition of INTERMEDIATE ALGEBRA is an exciting and innovative revision that takes an already successful text and makes it more compelling for today's instructor and student. The new edition has been thoroughly updated with a new interior design and other pedagogical features that make the user both easier to read and easier to use. Known for its clear writing and an engaging, accessible approach that makes algebra relevant, INTERMEDIATE ALGEBRA helps users to develop problem-...show moresolving skills and strategies that they can use in their everyday lives. The new edition welcomes two new co-authors Rosemary Karr and Marilyn Massey who along with David Gustafson have developed a learning plan to help users succeed in Intermediate Algebra and transition to the next level in their coursework46 +$3.99 s/h
Acceptable
Borgasorus Books, Inc. MO Wentzville, MO
Hardcover Fair 049583142520.28 +$3.99 s/h
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Synopses & Reviews
Publisher Comments:
Mathematics: Applications and Concepts is a three-text Middle School series intended to bridge the gap from Elementary Mathematics to High School Mathematics. The program is designed to motivate middle school students, enable them to see the usefulness of mathematics in the world around them, enhance their fluency in the language of mathematics, and prepare them for success in Algebra and Geometry
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Mathematics
Page Content
The Georgia Performance Standards Mathematics curriculum is designed to achieve a balance among concepts, skills, and problem solving. The curriculum stresses rigorous concept development, presents realistic and relevant tasks, and maintains a strong emphasis on computational and procedural skills. At all grades, the curriculum encourages students to reason mathematically, to evaluate mathematical arguments both formally and informally, to use the language of mathematics to communicate ideas and information precisely, and to make connections among mathematical topics and to other disciplines.
Mathematics CCGPS
In 2010, the Georgia State School Board of Education adopted a new set of standards known as CCGPS for Mathematics to be implemented in kindergarten through grade nine in school year 2012-2013. The CCGPS for Mathematics was finalized after multiple rounds of development and feedback from states and national organizations. Representatives from Georgia provided feedback at each round. The Georgia Performance Standards (GPS) Mathematics curriculum was one of the state curricula used to inform the creation of the CCGPS for Mathematics. The rigor and relevance, as well as the balance of skills, concepts, and problem solving, found in GPS mathematics is mirrored in the CCGPS.
The CCGPS, like the GPS, is evidence and/or research based, vertically aligned, and internationally benchmarked so that all students are prepared to succeed in our global economy and society. Although some content may be in different grade levels, all of the standards addressed in the CCGPS are also addressed in GPS mathematics. Most importantly, our work with GPS has prepared Georgia for the implementation of the CCGPS. It is appropriate that the name given to Georgia's CCGPS Mathematics reflect the influence of the GPS in the teaching and learning of mathematics. Therefore, Georgia's Mathematics curriculum is called CCGPS.
Information for Parents and Students
CCGPS Mathematics information is available at the GaDOE Parent Information Webpage.
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Do the Math: Secrets, Lies, and Algebra
In the eighth grade, 1 math whiz < 1 popular boy, according to Tess's calculations. That is, until she has to factor in a few more variables, like:
1 stolen test (x),
3 cheaters (y),
and 2 best friends (z) who can't keep a secret.
Oh, and she can't forget the winter dance (d)!
Then there's the suspicious guy Tess's parents know, but that's a whole different problem—
Sydney (Fair Oaks Ranch, TX)
Do the Math: Secrets, Lies, and Algebra by Wendy Lichtman was awesome! I really enjoyed the various chacters and the fast paced plot! I might have learned some math along the way too! :) I rate this book an 8/10!
—
Allie (Forest Hill, MD)
This was a very interesting book. It had a new way of looking at life: through math. As the main character discovers, math is so logical that it can often help to solve problems in real life--and she has some big ones. Any math lover would instantly love this book, and anyone else would love it also for its unique perspective on life. I would highly recommend it to anyone, even those who think math is useless (maybe this will change their minds).
—
Molly (Agua Dulce, CA)
This wonderful, witty book puts things in a refreshingly new perspective, relating everyday things to math in a way that will have you thinking. This book evokes an interest in math without being a textbook and also allows us to enter the world of a typical teenage girl. This book combines typical teenage life and math in a way that will make you excited for math class
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Introduction to Teaching Mathematics at the College Level
college mathematics can be a daunting task, indeed. It's nice for seasoned professionals and others to have a solid primer on the subject and this guide from Professor Suzanne Kelton is quite useful. The 54-page guide is divided into four chapters that cover documenting teaching practices, classroom basics, course policies, and discussion sections. Each of these chapters has additional subsections, such as syllabi, pace, and proofs. As a bonus, the document has an appendix that covers graphing techniques. The language of the document is jargon-free and accessible, which is a welcome departure from other guides. Visitors will want to share this item with friends in the field and even those who are teaching in other disciplines.Fri, 8 Nov 2013 14:43:31 -0600Lessons in Electric Circuits Vol V Reference USEFUL EQUATIONS AND CONVERSION FACTORS Chapter 2: COLOR CODES Chapter 3: CONDUCTOR AND INSULATOR TABLES Chapter 4: ALGEBRA REFERENCE Chapter 5: TRIGONOMETRY REFERENCE Chapter 6: CALCULUS REFERENCE Chapter 7: USING THE SPICE CIRCUIT SIMULATION PROGRAM Chapter 8: TROUBLESHOOTING -- THEORY AND PRACTICE Chapter 9: CIRCUIT SCHEMATIC SYMBOLS Chapter 10: PERIODIC TABLE OF THE ELEMENTSFri, 14 Jun 2013 13:21:33 -0500Webmath
from Discovery Education, provides help for mathematics students. Categories include general mathematics, K-8 math, algebra, geometry, trigonometry and calculus. The site covers everything you need to know, whether you need help with a specific topic or are looking to brush up on some math skills.Mon, 10 Jun 2013 13:23:38 -0500National Security Agency: High School Concept Development Units
National Security Agency (NSA) has worked to craft these educational materials they are calling "concept development units" (CDUs). The units are divided into 11 sections, including Algebra, Calculus, and Data Analysis. Clicking on each of these sections will bring up a complete list of all the CDUs currently available. Each list offers a paragraph-long description of each activity, along with an indication of the appropriate grade level for each activity. Some of the activities include "Understanding Proportions and Scale Drawings," "Scatter Brained," "Fashion Sense and Dollar Wise" and "Squares in the Light." These are all terrific resources for educators, and the site also contains links to information about the Math and Related Sciences Camp (MARS) sponsored by the National Security Agency and links to other educational centers.Fri, 15 Feb 2013 10:50:45 -0600Bates College Online Resources for Calculus and Linear Algebra
College in Maine has worked diligently to bring together this set of mathematical resources to the public, and it's a nice find. The materials here are drawn from four courses at the school: Math 105, Math 106, Math 205, and Math 206. The first couple of resources in each section contain past quizzes and exams from each course, complete with information on each topic. Additionally, each area contains drill problems, tutorials, and a fun "Find the Error!" feature. The topics covered here include linear algebra, quadric surfaces, functions, and abstract vector spaces. Moving on, the site also includes links to external sites from Harvey Mudd College and the University of California-Davis that address advanced math topics. For those persons interested in learning more about the mathematics department at Bates College, there's a link to its official website at the bottom of the page.Mon, 25 Jun 2012 10:53:18Do the Math
by staff members at the University of Arizona's Center for Recruitment & Retention of Mathematics Teachers (CRR), Do the Math is a weekly cable television show that features mathematics teachers explaining key mathematical concepts. Recently, the folks at CRR decided to create a "best of" playlist that offers segments from this popular program. Here visitors will find 18 segments that last between 26 and 38 minutes. Some of the subjects covered include geometry, advanced algebra, and calculus. Visitors may be interested in the materials on the left-hand side of the page, such as an AP Calculus practice exam, information about the related academic programs offered at the University of Arizona, and more. Also, the site contains a listserv for mathematics teachers and information on upcoming conferences that may be of interest.Thu, 15 Mar 2012 03:00:05 -0500AP Central: AP Calculus AB Course Home Page
Educational Testing Service (ETS) and the AP College Board have a number of excellent resources at their disposal, and this site provides a cornucopia of materials about teaching and learning calculus. First up is the information about the actual AP Calculus AB course, which may be most useful to those teaching the course at the high school level. Most visitors will want to take their time looking over the "Classroom Instruction and Resources" area. Here visitors will find special focus materials on approximation and differential equations, along with sample lesson plans and curriculum modules. The modules cover extrema, motion, and reasoning from tabular data. History of mathematics-types shouldn't miss the "History of Calculus" area, as it is quite a pip.Fri, 17 Jun 2011 22:36:41Precalculus
Wed, 22 Dec 2010 03:00:02Vector Calculus
is a series of lectures, authored by Chris Tisdell of the University of New South Wales, for MATH2111 "Higher Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney. This playlist provides a shapshot of some lectures presented in Session 1, 2009. These lectures focus on presenting vector calculus in an applied and engineering context, while maintaining mathematical rigour. Thus, this playlist may be useful to students of mathematics, but also to those of engineering, physics and the applied sciences. There is an emphasis on examples and also on proofs.Thu, 16 Dec 2010 03:00:01 presented by MIT and taught by Professor Denis Auroux, presents multivariable calculus. It is intended for use in a freshman calculus course. It includes material relating to vectors and matrices, partial derivatives, double and triple integrals and vector calculus in 2 and 3-space. The material includes video lectures, lecture notes, exams (with solutions) and student assignments (without solutions). MIT presents OpenCourseWare as free educational material online. No registration or enrollment is required to use the materials.Fri, 10 Dec 2010 03:00:02 -0600
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A seminar course required as a culminating experience for mathematics majors. Students prepare and present a portfolio following departmental guidelines to document achievement of the learning goals for the mathematics major. Additionally, students present a lecture on a topic not covered in core courses in consultation with the instructor and take the Major Field Test for Mathematics. Grade of C or higher required. Prerequisite: Senior standing.
Prerequisite(s) / Corequisite(s):
Senior standing.
Course Rotation for Day Program:
Offered Fall and Spring.
Text(s):
Course Objectives
To understand the theory and application of algebra and analysis.
To write a computer program in a high-level language to solve a mathematical problem.
To identify and apply appropriate technologies to solve mathematical problems.
To write rigorous mathematical proofs.
To solve real-world problems from a variety of disciplines using mathematical techniques.
To approach a topic in calculus from the four perspectives: numerical, graphical, analytical, and verbal.
Measurable Learning Outcomes:
Demonstrate a fluency in the language of mathematics and with the fundamental results of analysis and algebra.
Topical Outline:
The Major Field Test in Mathematics will be administered and students will make the following presentations (all materials will be archived in the students' portfolios):
Write a computer program to implement a mathematical algorithm
Demonstrate an example of solving a mathematical problem using technology
Present a summary and critique of a selection of proofs written for the core courses of Linear Algebra, Abstract Algebra, Probability Theory, and Advanced Calculus
Present a lecture on a topic not covered in core courses in consultation with the instructor
Present three examples of solving problems in other disciplines using mathematics
Present a topic from analysis demonstrated from the four viewpoints
Culminating Experience Statement:
Material from this course may be tested on the History Assessment Test (HAT) administered during the Culminating Experience course for the degree.
During this course the ETS Proficiency Profile may be administered. This 40-minute standardized test measures learning in general education courses. The results of the tests are used by faculty to improve the general education curriculum at the College
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1992, I had the honor and the pleasure of working with numerous students and realized the need for prep books that can simply explain the fundamentals of mathematics. This book is built on many years of research and experience in this field. Most importantly, the questions in this book focus on building a solid understanding of basic mathematical concepts. Without understanding these solid foundations, it will be difficult to score well on these exams. This book emphasizes that any difficult math question can all be solved with a solid understanding of basic concepts. "Perfect Tips and 8 full length practice tests (4 AP Calculus AB and 4 AP Calculus BC)"
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College Algebra
Our popular College Algebra course provides a working knowledge of college-level algebra and its applications. Emphasis is placed upon the solution and the application of linear and quadratic equations, word problems, polynomials, and rational and radical equations. Students perform operations on real numbers and polynomials and simplify algebraic, rational, and radical expressions.
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Yes, the course is fast-paced, and
it will be difficult to catch up with some aspects of math (such as
trigonometry) during the semester.You
need your focus to master the problem-solving that physics challenges you to
do.
Yes, it often does help to have
had physics in high school before. But it is no guarantee for success, nor do
you need to worry about failure if you did not have physics before. There is
really no clear correlation.
And no – even with physics in high
school I guarantee you that you will be challenged.
If you are concerned whether you are
prepared enough before the course, below
are some things you can do to put yourself into a good position before the
semester. They are arranged in order of decreasing significance, with the last
one still being pretty significant. You may also refer to appendix B in your
text book to see examples of what mathematically lies ahead of you.
1.Review trigonometry and geometry!
Mastering these is more important for your comfort in this class than
remembering some calculus. Most of the semester, we will spend representing all
sorts of physical phenomena using vectors. Those little arrow symbols combine
in triangles and polygons on the paper. Once you have drawn them, you will use
the drawings to calculate unknown lengths, angles, etc. which means: there is
geometry and trigonometry everywhere. Often we need to draw from every trick in
the math book to solve the problem.
d.Big
one: be able to solve
a system of equations for multiple variables. In this semster,
we will usually have two or three equations and two or three variables.
Mathematics has equipped you with several tools to deal with a system of
equations, the simplest one being repeated substitution.
3.Review a few rules for integration
and differentiation!
We will use differentiation and integration in some well-defined places,
and use mostly very simple examples. The lecture and the text book will
introduce these places in a way similar to what you may have seen in your
calculus course. However, after the introduction, you will sometimes be
confronted just to "do" a derivative or integral of some function, and for that
it is useful to remember a few simple rules.
4.Enjoy reading a few physics-related
texts other than the text book– and
that one is really up to you. You may wonder about the rules governing the
motion of satellites, or why your tires spin on snow (easier the more you push
the gas), or why your bike does not tip over when it is moving. Why is this
penny speeding up on its way down the wishing well? Why do the Australians not
hang upside down, and how does this go together with our image of "gravity
constant and down"? Why is there a gap between the top of the steam vent and
the white cloud, and why is it rising? Where will this birthday balloon land if
the wind from the west is increasing in speed and turning SW with height above
the ground? Look around and wonder about things that you are taking for granted
every day, and bring those thoughts to class …
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Why Take Math in High School
Do you want to travel to Mars?
Design houses or create computer software?
Do you want to discover a cure to cancer or protect rivers and oceans from pollution?
If you do, be sure to take lots of math in school.
Many challenging and rewarding careers - not just engineering - demand a strong background in math. Classes like algebra, geometry, and trigonometry may be difficult, but they will open the doors to many exciting opportunities in your future. Of course, you can catch up on your math when you get to college, but like a language it is much easier to really learn it when you are young, and you'll have a hard time catching up in college without taking extra years if you don't at least have the basics. Since you have to take most math class in a particular order, it's also important to start early so that you are prepared to take the right classes when you need them.
Besides the inherent beauty in mathematics there are lots of other reasons to take as much math as you can, even if you don't want to be an engineer. For one, math can actually make you smarter! It's like endurance training for your brain. Learning to think critically and focus on a problem is important for any career.
You may also want to take math so you can make and save more money. On average, people who understand math have higher paying careers. That may not always be the case, but you'll certainly increase your odds by understanding as much as you can. And when all your friends are losing their last dime on the latest crazy scheme that doesn't make mathematical sense, you might actually have the forethought to sit back and crunch the numbers before jumping in.
Having a solid background in math is very much like understanding a very useful and universal language. It is important to start early to be completely fluent, and you'll be able to communicate difficult concepts with a few simple equations. People in many other countries know the importance of math and work very hard to master it from an early age. Considering the increasing globalization of the economy, you shouldn't be surprised that you will be competing with many of those hard-working students for jobs by the time you get out of college.
And speaking of college, you may want to consider taking extra math just to help make sure you get into the right college. A compelling essay will go a long way on your college entrance applications, but so will a solid background in mathematics. And once you get to college, you won't have to take loads of remedial math courses just to catch up.
And finally, you should take math because you're cool! You won't need to explain away why you don't do numbers for the rest of your life. You'll be able to help your kids with their math homework, and you will be the one people turn to when they need some creative problem-solving.
So now that you know all the great reasons to study math in high school, here are some math classes that you will want to take:
Algebra
Algebra is extremely useful for solving problems. Algebra uses basic arithmetic rules to describe and group things and to discover the value of something unknown (usually represented by a letter in an equation). Algebra is the foundation for many other math subjects.
Geometry
Geometry is the study of the properties of and relationships between points, lines, angles, and surfaces. Geometry uses logic and mathematical laws to describe the physical world and will give you several other important problem solving tools.
Trigonometry
In trigonometry, you study triangles and trigonometric functions like sine, cosine, and tangent. Trigonometry has real world applications dealing with everything from radio waves and electricity to telescopes and ship navigation.
Calculus
With calculus, you combine everything you've learned about math and take the next step. Calculus uses special symbols and logic to do difficult calculations, like determining the orbit of a space vehicle, or predicting the time it takes a car to stop on a wet road. Calculus is a very powerful tool for solving complex problems.
What about you?
So do you have a favorite math class? Can you think of other great reasons for taking math? Tell us in the comments below.
I love math! I understood and understand why math is so important now in life. I want to go far in life and be a pediatric neurosurgeon and I know it would take alot. I realize math is important in life and I should continue to study math.
I really love math and now I know that it can really help me get more opportunities for career choices. Even though it is my favorite subject I still need to pay close attention and take all the math classes that I can.
I really strong but math is not my forte. After reading this article i realize now that math is necessary.Even though i don't like it but i realize in the distant future i may be able to enjoy math. Thank you for this informative read
i am pretty weak at math like in 60s. this is because i ignore math when i was in elementary school. now i really want math to become an engineer. how can i learn basic math that i have missed in one year. pls help!!!!!!
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Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
| 677.169 | 1 |
Introductory Algebra: Applied Approach - 8th edition
Summary: As in previous editions, the focus in INTRODUCTORY ALGEBRA remains on the Aufmann Interactive Method (AIM). Users are encouraged to be active participants in the classroom and in their own studies as they work through the How To examples and the paired Examples and You Try It problems. The role of "active participant" is crucial to success. Presenting students with worked examples, and then providing them with the opportunity to immediately work similar pro...show moreblems, helps them build their confidence and eventuallyFair Book has excessive shelf or use wear. Bent corners and/or dinged edges. May have torn covers, but cover is intact. We ship all books within 24hrs. Books purchased on the weekend ship first thin...show moreg Monday morning. Safe and Secure Bubble Mailer! ...show less
$52.3352.39 +$3.99 s/h
VeryGood
Cloud 9 Books FL West Palm Beach, FL
PAPERBACK Very Good 1439046042 Very Good Condition. Ships within 24 hours and all purchases are guaranteed or your money back.
$57.569798
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NumericalMethods in Engineering with MATLAB® is a text for engineering students and a reference for practicing engineers. The choice of numericalmethods was based on their relevance to engineering problems. Every method is discussed thoroughly and illustrated with problems involving both hand computation and programming. MATLAB M-files accompany each method and are available on the book website. This code is made simple and easy to understand by avoiding complex book-keeping schemes, while maintaining the essential features of the method.
This book presents an introduction to MATLAB and its applications in engineering problem solving. The book is designed as an introductory course in MATLAB for engineers. The classical methods of electrical circuits, control systems, numericalmethods, optimization, direct numerical integration methods, engineering mechanics and mechanical vibrations are covered using MATLAB software.
This is a unique monograph on numerical conformal mapping that gives a comprehensive account of the theoretical, computational and application aspects of the problems of determining conformal modules of quadrilaterals and of mapping conformally onto a rectangle. It contains a detailed study of the theory and application of a domain decomposition method for computing the modules and associated conformal mappings of elongated quadrilaterals, of the type that occur in engineering applications.
This book will interest researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modeling and computer simulation. Although it represents only a small sample of the research activity on numerical simulations, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. It will be useful to encourage further experimental and theoretical researches in the above mentioned areas of numerical simulation.
Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numericalmethods and shows how to develop, analyze, and use them.
STATISTICAL METHODS FOR ENGINEERS offers a balanced, streamlined one-semester introduction to Engineering Statistics that emphasizes the statistical tools most needed by practicing engineers. Using real engineering problems with real data based on actual journals and consulting experience in the field, users see how statistics fits within the methods of engineering problem solving. The book teaches users how to think like an engineer at analyzing real data and planning a project the same way they will in their careers.
Written as both a textbook and a handy reference, this text deliberately avoids complex mathematics assuming only basic familiarity with geodynamic theory and calculus. Here, the authors have brought together the key numerical techniques for geodynamic modeling, demonstrations of how to solve problems including lithospheric deformation, mantle convection and the geodynamo. Building from a discussion of the fundamental principles of mathematical and numerical modeling, the text moves into critical examinations of each of the different techniques before concluding with a detailed analysis of specific geodynamic applications
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