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Here are the methods to calculate the bounds for the remainder in the integral test with an example. | {
"title": "191. Bounds for the Remainder in the Integral Test",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Upper bound
-Least upper bound(sup)
-Lower bound
-Greatest lower bound(inf)
-Bounded above/Bounded below
-Example | {
"title": "21. Definitions",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Method
-Recall
-Example
This is the continuous content from note 110. | {
"title": "111. Shell Method",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Differentiable at the point
-Differentiable
-The increment theorem for functions of two variables
-Corollary | {
"title": "259. Differentiability for Two Variables",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are three properties of the directional derivative, which is to evaluate the dot product in the formula. It has examples to show how to apply the property. | {
"title": "268. Properties of the Directional Derivative",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are a definition, a notation and two theorems and their proofs. Hope every readers can understand. | {
"title": "12.Absolute value of complex number",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-Other sequences: arithmetic sequence of higher-order, Cauchy sequence, Fibonacci sequence
-Recurrence relation: An equation that expresses each element of a sequence as a function of the preceding ones. | {
"title": "25. Other sequences and recurrence relation",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
-Limit(multi-dimensional case)
-Continuous(multi-dimensional case)
-Derivative(multi-dimensional case)
-Note
This time we use three-dimensional vector as example to show the definition of limit, continuous, and derivative with multi-dimensional case. | {
"title": "229. Definitions",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is a theorem which is related to Dirichlet’s Principle with its proof. | {
"title": "104. Theorem",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Definition
-Arc length formula
-Arc length parameter with base point
-Example | {
"title": "236. Arc Length Along a Space Curve",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Take trout and bass as an example:
-Model&Solution of the system
-Equilibrium point
-Trajectory direction
-Stabilization&Slope fields
-Conclusion | {
"title": "172. Competitive Hunter Model",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Natural Number(N): The numbers 1,2,3,…
-Integer(Z): The numbers…,-3,-2,-1,0,1,2,3,…
-Rational Number(Q): The number can be written as Q=p/q, where p and q are the integers.
-Irrational Number: The number which is not a rational number is called an irrational number.
-Real Number(R): The summation of the rational and irrational numbers.
-Imaginary Number: The number which is defined that i²=-1
-Complex Numer(C): The number can be expressed by x+yi, where x,y are real numbers, and x is called the real part and y is called the imaginary part. | {
"title": "1. The Number System",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
-Definition
-Notes
-Theorem
-Corollary
If you are interested in this topic, you can visit my probability notes to see more content. | {
"title": "101. C(n,r)",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
There is the definition of metric space and three properties of the distance of two points. | {
"title": "25. Metric Spaces",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-Discrete Random Variable
-Probability Mass Function(pmf)
-Notes
-Example | {
"title": "27. Discrete Random Variable",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
Republic of Retre
-----------------
### Capital
Kirham
### Offical Languages
Rovi Camber, Casterian Camber
### Religion
98% Christian2% Other
Government
----------
### Government
Blohausi Gewenari (KNGE)
### President
Botsbak Perninin
Area
----
### Land
28,227 km²
### Water
0.5%
Demographics
------------
### Population
65,774,245
### Currency
Aridoss (AR)
Info
----
### Timezone
UTC-6
### Car Code
RE
### Calling code
+54
### Internet TLD Code
.re
The Republic of Retre is a country located in north Canverland. To the north it borders the Arctic Ocean and the Retre Sea. To the east it borders Hinckhamania, to the south Shershil, to the east Ormscastheria.
Geography
---------
History
-------
The govenor of the Duchy of Retre, Venghard III. in response to the weaking of the Kingdom to Canverland, declared independence in 1616 from the kingdom starting Canverland Wars. After 2 sounding victories at Kirham and Jolonodds Retre officially gained it's independence in 1618, the first nation in Canverland to do so. In order to unite the vulnurable economies of the now broken and unstable, the President of Retre and Dunster met in Shershil and signed the Shershil Treaty, uniting Dunster and Shershil in 1814. Later in 1836, the now "Kingdom of Canverland", which in the 19th Century in reality was just made up of powerful landlords, joined the Retre Union. In 1897, the union dissolved due to disagreements. | {
"title": "Retre",
"domain": "dg-world.fandom.com",
"cats": "",
"removed": []
} |
-neighborhood
-limit point
-isolated point
-closed
-interior point
-open
-complement
-perfect
-bounded
-dense | {
"title": "27. Some definitions",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
Here are some integrals to inverse hyperbolic functions with example. | {
"title": "140. Integrals leading to inverse hyperbolic functions",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definition
-Example
This is the note from probability 21. If you want to see more relative content, you can see the probability note. | {
"title": "23. Conditional Probability",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
An orthogonal trajectory of the family of curves is a curve that intersects each curve of the family at a right angle, or orthogonally. There is an example to show this case. | {
"title": "167. Application: Orthogonal Trajectories",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are two additional theorems and proofs for the basic probability.
Note that the proof of decreasing case is similar to the nondecreasing case in the theorem1. | {
"title": "18. Additional theorem of basic probability",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
-First order differential equation
-Solution
-General solution
-Particular solution
-First order initial value problem
-Example | {
"title": "161. First Order Differential Equation",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Distribution of a variables
-Graphs: pie charts, bar graph(categorical variables), histograms, stemplots(quantitative variables) | {
"title": "2.Basic concepts",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
-Arbitrary object method
-Combine arbitrary object method with proof by contradiction
-Two examples to prove the statements involving for every
-Proof by cases: We often prove a theorem by considering various possibilities | {
"title": "10. Proofs of Statements Involving\"For Every\" and Proof by Cases",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
There is an application of RL circuits through first order linear equation form. | {
"title": "165. Application: RL Circuits",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
If a region’s bounding curves are described by functions of y, the approximating rectangles are horizontal instead of vertical and the basic formula has y in place of x.
There is an example in the picture. | {
"title": "105. Integration with Respect to y",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Use the identity (square of cosine) to eliminate the square root. Here is an example to do it at the bottom of the picture. | {
"title": "147. Eliminating Square Roots",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definition
-Theorem
-Example
If you are interested in this topic, you can visit my probability notes to see more content. | {
"title": "100. Permutation",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
Here is the rearrangement theorem for absolutely convergence test. That’s it, haha.
Summary of Tests:
-The nth-term test(note 186)
-The integral test(note 189)
-The comparison test(note 192)
-The ratio test(note 194)
-The root test(note 195)
-The alternating series test(note 196)
-The absolute convergence test(note 199) | {
"title": "200. The Rearrangement Theorem for Absolutely Convergence Test",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is a theorem which is related to Dirichlet’s Principle with its proof. | {
"title": "105. Theorem",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Least Upper Bound Completeness Axiom
-Greatest Lower Bound Completeness Axiom(with proof) | {
"title": "22. Bound Completeness Axioms",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
There is an example to compute the correlation coefficients. Also, there are two notes which need to notice. | {
"title": "17. Example",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
-Sum rule(for sequence)
-Difference rule(for sequence)
-Constant multiple rule(for sequence)
-Product rule(for sequence)
-Quotient rule(for sequence) | {
"title": "176. Theorem",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is a precise definition of a right-hand limit and a left-hand limit. There is an explanation with pictures and an example below the statement. | {
"title": "12. Right-hand limit/Left-hand limit(Precise definition)",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Eccentricity
-Recall: eccentricity in cases of parabola, ellipse, and hyperbola
-Idea
-Equivalent equation for the ellipse
-Example | {
"title": "226. Polar Equation for a Conic with Eccentricity",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-event
-complement
-subset
-union
-intersection
-disjoint
This is the note from probability 1. If you want to see more relative content, you can see the probability note. | {
"title": "21. Some definitions",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
-When we differentiate a function twice, we produce its second-order derivatives.
-Notations
-Notes
-Example | {
"title": "257. Second-Order Partial Derivatives",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Differentiable on an open interval
-Differentiable on a closed interval
-Example | {
"title": "28. Definitions",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are square and root cases of sine, cosine, and sine times cosine. | {
"title": "17. Power-reduction formula in trigonometric function",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
There is the proof that Completeness Axiom iff Least Upper Bound Completeness Axiom . | {
"title": "23. Completeness Axiom vs Least Upper Bound Completeness Axiom",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Continuous at the point
-Continuous
-Example
-Continuity of composites | {
"title": "253. Continuity for Two Variables",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are 4 examples to show how to find the limitations in the function. | {
"title": "2. Some examples",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-There are three elements to interpret it: form, direction, strength
-An example to interpret a scatterplot | {
"title": "15. Interpreting scatterplot",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
-Formula
-The Pressure-Depth Equation
-Fluid Force on a Constant-Depth Surface
-Recall
-Example | {
"title": "118. Application: The Integral for Fluid Force Against a Vertical Flat Plate",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Here is the explanation and an example of Hooke’s Law with work computation. | {
"title": "117. Application: Hooke’s Law",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Corollary(convergence of a power series)
-Radius of convergence
-Interval of convergence
-How to test a power series for convergence | {
"title": "203. The Radius of Convergence of a Power Series",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Real-valued function
-Domain
-Range
-Dependent variable/independent variable
-Input variable/output variable
-Example | {
"title": "248. Definitions",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-real number R
-two binary operations (addition, multiplication)
-binary relation(<)
-two distinct elements (zero and unity) | {
"title": "11. Real number system",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
It shows that the column and row space of matrix A are spanned by the column and row vector of matrix A. | {
"title": "18. Span of column and row vector",
"domain": "hyl.fandom.com",
"cats": "linear_algebra",
"removed": []
} |
There are four examples which are related to the four cases of permutations. | {
"title": "10.Exanples",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
There are a theorem and a corollary.
The information in the corollary tells us an important fact- all rational number is countable. | {
"title": "23. Theorem of countable sets",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-Bounded from above
-Upper bound
-Least upper bound
-Bounded from below
-Lower bound
-Greatest lower bound
-Bounded
-Unbounded
-Example | {
"title": "181. Definitions",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Velocity vector
-Direction&magnitude
-Acceleration Vector
-Unit Vector
-Example | {
"title": "230. Motion(multi-dimensional case)",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-The series multiplication theorem for power series
-Function f(x) for x in a convergent power series | {
"title": "204. Theorems",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are four steps and an example to integrate in spherical coordinates. | {
"title": "309. How to Integrate in Spherical Coordinates",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Taylor’s Formula for f(x,y) at the point (a,b)
-Taylor’s Formula for f(x,y) at the origin
-Example | {
"title": "286. Taylor’s Formula for Function of Two Variables",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-The first theorem use the definition of fields to prove it
-The second theorem is trivial | {
"title": "10.Two theroms",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-Radioactive decay
-Equations: differential equation&initial condition
-Half-time
-Example | {
"title": "134. Application: Radioactivity",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-The force of the gravitational attraction between the planet and the sun
-Combining the gravitation law with Newton’s second law, the planet is accelerated toward the sun’s center of mass at all times
-The planet moves in a fixed plane through the center of its sun | {
"title": "244. Planets Move in Planes",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Continuous(interior point)
-Continuous(end point)
-Discontinuous
-Right-Continuous
-Left-Continuous | {
"title": "14. Continuous",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Here are the derivatives for each hyperbolic function and the proof of sinhu and cschu. | {
"title": "137. Derivatives of hyperbolic functions",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definitions
-Theorem: Every infinite subset of a countable set A is countable | {
"title": "19.Sequences",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-A statement is a declarative sentence that is either true or false, but not both
-Examples | {
"title": "1. Statements",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
209. Taylor’s Theorem
-Theorem
-Convergence of Taylor series
-Example | {
"title": "209. Taylor’s Theorem",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-List the interior points of R
-List the boundary points of R
-Look through the lists for the maximum and minimum values of f
-Example | {
"title": "282. Absolute Maxima and Minima on Closed Bounded Regions",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Symmetry about the x-axis
-Symmetry about the y-axis
-Symmetry about the origin | {
"title": "221. Symmetry Test for Polar Curves",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definition
-Equations relating spherical coordinates to coordinates to cartesian and cylindrical coordinates
-Idea of integrating in spherical coordinates | {
"title": "308. Spherical Coordinates",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are three parts in this axioms: Properties of Addition, Properties of Multiplication, and The Distribution Property. | {
"title": "12. Algebraic Axioms",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
The time and the orbit’s semimajor axis are related by the equation. | {
"title": "247. Kepler’s Third Law(Time-Distance Law)",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Let A be the set of all sequences whose digits are 0 or 1. Set A is uncountable(with proof). | {
"title": "24. Theorem",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
In real-world modeling situations, a quantity y increases or decreases at a rate proportional to its size at a given t. An initial value problem can be solved, including a differential equation and initial condition. | {
"title": "131. Exponential Change",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is an intuitive definition of right hand limit/left hand limit. | {
"title": "10. Right hand limit/Left hand limit",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Principle inverses
-General cases for principle inverses
-Relationships between trigonometric functions and inverse trigonometric functions | {
"title": "20. Inverse trigonometric functions",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
-Provides a graphical representation of the five number summary&Constructed by drawing a box and two whiskers
-Example | {
"title": "11. Box Plot(Whisker Plot)",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
There are two theorems and a corollary. If you read these definitions, it can be proved easily. | {
"title": "28. Theorems",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-Level Curve
-Graph
-Example
Note these definitions are worked when the dimension is larger than two. | {
"title": "250. Definitions",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definition
-Recall
-Note: The differential formula of arc length
-Example | {
"title": "114. Area of Surface",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
We test convergence and divergence cases of p-series with the integral test. | {
"title": "190. P-Series",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Sum rule
-Difference rule
-Constant multiple rule
-Product rule
-Quotient rule
-Example | {
"title": "270. Algebra Rules for Gradients",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Suppose that w=f(x,y,…,v) is a differentiable function of the variable x,y,…,v(a finite set) and the x,y,…,v are differentiable functions of p,q,…,t(another finite set). Then w is a differentiable function of the variables p through t, and the partial derivatives of w with respect to these variables are given from the equation, which is the dot product of two vectors with components, derivatives of w with respect to the intermediate variables and derivatives of the intermediate variables with respect to the selected independent variable. The other equations are obtained by replacing p with q,…,t one at a time. | {
"title": "265. Functions of Many Variables",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is an application of mixture problems with first order differential equations. Also, there is an example to show this equation. | {
"title": "168. Application: Mixture Problems",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
An example shows that we can see delta=1 if the density is constant when we calculate the centroid(center of mass). | {
"title": "122. Example: constant density",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are five basic theorems and proofs for the basic probability in the picture. It is easy to understand the three axioms of probability. | {
"title": "17. Theorems of basic probability",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
The rate at which an object’s temperature is changing at any given time is roughly proportional to the difference between its temperature and the surrounding medium. There are formula and example in the picture. | {
"title": "135. Application: Newton’s Law of Cooling",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Normal case(by the law of cosines)
-Circle pass through the origin
-Center lies on the positive x-axis
-Center lies on the positive y-axis | {
"title": "228. Polar Equation for Circles",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are definitions of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. | {
"title": "10. Trigonometric function",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
If p and q are statements, then the statement p <=> q is read as “p if and only if q", “p is equivalent to q" or “p is a necessary and sufficient condition for q" | {
"title": "6. iff(if and only if)",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
Coterminal Angles are the points in the coordinate systems that are the same. | {
"title": "18. Multiple angles in Coterminal Angles",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
There are three steps to find limits of integration in polar coordinates. | {
"title": "297. Finding Limits of Integrations(Polar Coordinates)",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
We can solve this problem with the related identities. Here has an example in the bottom of the picture. | {
"title": "149. Product of Sines and Cosines",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is a theorem about even and odd functions with its proof and example. | {
"title": "103. Theorem",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Theorem
-Proof
-Three variables(This also works for higher variables)
-Branch diagram
-Example | {
"title": "264. A Formula for Implicit Differentiation",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Introduction
-how to make a scatterplot
-how to examine a scatterplot | {
"title": "14. Scatterplot",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
-Infinite series
-nth term
-Sequence of partial sums
-nth partial sum
-Converge(with its sum)
-Diverge | {
"title": "184. Definitions",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definition
-Idea
-Theorem(the directional derivative is a dot product)
-Example | {
"title": "267. Gradient",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Slope(at the point)
-Tangent line
-Derivative(at the point)
-Derivative(function)
-Differentiable at x
-Differentiable
-Note
-Example | {
"title": "27. Definitions",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Inductive
-The principle of mathematical induction
-Theorem: The principle of mathematical induction is equivalent to the second principle of mathematical induction. (The second principle of mathematical induction is in note 30) | {
"title": "35. The Principle of Mathematical Induction",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Tangent plane
-Normal line
-Idea
-Tangent plane to f(x,y,z)=c at P\_0(x\_0,y\_0,z\_0)
-Normal line to f(x,y,z)=c at P\_0(x\_0,y\_0,z\_0)
-Example | {
"title": "272. Tangent Plane and Normal Line",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Example(build a least-square regression)
-Cautions(With three notations) | {
"title": "20. Example&Cautions",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
There is a form of motion with resistance proportional to velocity through the first order differential equation. Also, there is an example to show this equation. | {
"title": "166. Application: Motion with Resistance Proportional to Velocity",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Subsets and Splits