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| meta
dict |
|---|---|
Continuity tests:
-c lies in the domain f
-f has a limit as x approaches c
-The limit equals the function value
Some kinds of discontinuity:
-removable
-jump discontinuity
-infinite discontinuity
-oscillating discontinuity | {
"title": "15. Continuity test/Some kinds of discontinuity",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-member(element) in a set
– member(element) not in a set
-subset
-empty set
-equal sets | {
"title": "1. Some definitions:",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-The six trigonometric functions can be defined as coordinate values of points on the Euclidean plane that are related to the unit circle, which is the circle of radius one centered at the origin O of this coordinate system.
-Two pictures below illustrate the positive or negative value of each trigonometric function in each quadrant. | {
"title": "11. Unit-circle definition in trigonometric function",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
(1).(a+b)²=a²+2ab+b²
(2).(a-b)²=a²-2ab+b²
(3).(a+b)(a-b)=a²-b²
(4).(a+b+c)²=a²+b²+c²+2ab+2bc+2ac
(5).(a+b)³=a³+3a²b+3ab²+b³
(6).(a-b)³=a³-3a²b+3ab²-b³
(7).(a+b)(a²-ab+b²)=a³=b³
(8).(a-b)(a²+ab+b²)=a³-b³ | {
"title": "4. Multiplication Formula:",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
– Commutative law
– Association law
– Distributive law(with proof)
– 4 properties | {
"title": "21. Three laws of sets&properties",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
There is the formula and its idea of the general solution of Euler Equation with an example. | {
"title": "364. The General Solution of Euler Equation",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Read the problem
-Draw a picture
-Introduce variables
-Write an equation for the unknown quantity
-Test the critical points and endpoints in the domain of the unknown
-Example | {
"title": "81. Solving Applied Optimization Problems",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
The power-series method for solving a second-order homogeneous differential equation consists of finding the coefficients of a power series which solves the equation. There is an example to show how to solve the equation with power-series. | {
"title": "365. Power-Series Solution",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
This method for finding a particular solution to the nonhomogeneous equation applies to the special cases for which G(x) is a sum of terms of various polynomials multiplying an exponential with possibly sine or cosine factors.
-Example
-The table of the method of undetermined coefficients for selected equations | {
"title": "358. The Method of Undetermined Coefficients",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-The positive square root of the variance
-Sample standard deviation vs Population standard deviation
-Example | {
"title": "8.Standard Deviation",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
A set E is open iff its complement is closed.
It also shows the proof and a corollary, which is similar to the theorem: A set F is closed iff its complement is open. | {
"title": "31. Theorem(Mathematical Analysis)",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
There is a corollary which is extended from the corollary of the last note. | {
"title": "69. Corollary",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Here is an example that shows the case of cycloids with parametric equations. | {
"title": "215. Cycloids",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
If a piecewise smooth curve C is made by joining a finite number of smooth curves end to end, then the integral of a function over C is the sum of the integrals over the curves that make it up.
There is a note and example in the end of this part. | {
"title": "313. Additivity",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is the corollary and its proof which is extended from the Mean Value Theorem. | {
"title": "68. Corollary",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definition
-Find absolute value on a finite closed interval
-Example | {
"title": "65. Critical Point",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Second-order linear differential equation
-Homogeneous&Nonhomogeneous
-The superposition principle
-Note | {
"title": "351. Second-Order Linear Equations",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are five different cases of parabola functions, with conditions of a, focus point, focal length, semi-latus rectum, vertex, directrix, and the tangent line. | {
"title": "41. Some facts of the parabola function",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
-Expected value(for continuous random variable)
-Variance(for continuous random variable)
-Example | {
"title": "39. Definition",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
(1). There will be established between one of three: a<b,a=b, and a>b
(2).If a<b and b<c, then a<c
(3).If a<b, then a+c<b+c
(4).If a<b and c>0, then ac<bc;If a<b and c<o, then ac>bc
(5).a²≥ 0, and a² only establishes when a=0. | {
"title": "2. Some properties of the real number",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
-Constant multiple
-Sum and Difference
-Domination
-Additivity
-Example | {
"title": "293. Properties of Double Integrals",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Surface area differential
-Differential formula for surface area
-Example | {
"title": "335. Surface Area Differential for a Parameterized Surface",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Member(element)
-Not a member
-Union
-Intersection
-Difference
-Family of sets
-Notes | {
"title": "31. Definitions",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-zero polynomial
-degree 0 polynomial
-degree 1 polynomial(linear function)
-degree 2 polynomial(quadratic function)
-degree 3 polynomial(cubic function)
-high degree polynomial | {
"title": "34. Polynomial functions&graphs",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
A function f(x,y) can have partial derivatives with respect to both x, and y at a point without the function being continuous there. | {
"title": "256. Partial Derivatives and Continuity",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Diophantine equations
-Linear diophantine in two variables
-Theorem | {
"title": "48. Diophantine Equations",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
There are two theorems and their proofs. There also has a corollary in the end of the picture. | {
"title": "47. Theorems",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Addition
-Scalar multiplication
-Transposition
-Matrix multiplication
-Example | {
"title": "74. Basic operation of matrix",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
It is the extreme value theorem. You can see the proof in the mathematical analysis notes. | {
"title": "62. The Extreme Value Theorem",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are some properties to calculate the probability with cdf. Also, there is an example to show how to calculate the probability with these properties.
This is the note from statistics 29. If you want to see more relative content, you can see the statistics note. | {
"title": "34. Some Properties",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
-The midpoint of the distribution
-The number such that half of the observation are smaller and the other half are larger
-Find the median of distribution
-Example | {
"title": "5.Median",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
Here is an example to show whether the sets are open, close, perfect, and bounded. If you understand those definitions, you can answer this example easily. | {
"title": "29. Example",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
Here are the idea of double integrals over rectangles and double integral as volumes. | {
"title": "289. Double Integrals over Rectangles",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Here is De Morgan’s Law and its general cases(including infinite and finite cases). | {
"title": "34. De Morgan’s Law",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
There is a theorem with its proof. Also, there also have a corollary with its proof as well. | {
"title": "39. Theorem",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
There is the formula and its idea of vibrations based on second-order linear equations. | {
"title": "360. Application: Vibrations",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are three theorems about partition and equivalence relation. That’s it, haha. | {
"title": "57. Theorem",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Definition
-Example
Note that it is a special case of the polynomial remainder theorem. | {
"title": "53. Factor Theorem",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
-Euclidean space
-Matrix space
-Polynomial space
-n-th polynomial space
-Function space
-Space of continuous function | {
"title": "3. Some different kinds of vector spaces",
"domain": "hyl.fandom.com",
"cats": "linear_algebra",
"removed": []
} |
There are four steps and an example to integrate in cylindrical coordinates. | {
"title": "307. How to Integrate in Cylindrical Coordinates",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Three dimensional solid(about x-axis, y-axis, z-axis, a line)
-Two dimensional plate(about x-axis, y-axis, a line, the origin)
-Idea
-Example | {
"title": "305. Moments of Inertia(Second Moments) Formulas",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definition
-Notes
-Idea
-Calculating flux across a smooth closed plane curve
-Example | {
"title": "322. Flux Across a Simple Plane Curve",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definition
-idea
-Different ways to write the work integral
-Example | {
"title": "320. Application:Work Done by a Force over a Curve in Space",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Here is the explanation of arrow diagrams which are shown as an example. | {
"title": "288. Arrow Diagram",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definition
-Example
Both definitions and examples are shown with pictures. | {
"title": "7. Definition of limit",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-general case
-Definition: Suppose we have n objects, then there are n! different permutations.
-Two examples of permutations | {
"title": "6.Permutations(1)",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
-and: If p,q are true, then"p and q" is true, and otherwise it is false
-or: If at least one of p,q is true, then"p or q" is true. If both p,q are false, then"p or q" is false. | {
"title": "4.And, Or",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
There are three steps to find limits of integration. Both vertical cross-section and horizontal cross-section methods are similar. | {
"title": "292. Finding Limits of Integration",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is a theorem with its proof. Also, there also have a corollary with its proof as well. | {
"title": "40.Theorem",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-Inverse
-Symmetric
-Proposition
-Example: show the inverse, symmetric, and the propositions as Cartesian graphs and directed graphs | {
"title": "53. Inverse&Symmetric",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Discrete Random Variable
-Probability Mass Function(pmf)
-Notes
-Example
This is the note from statistics 27. If you want to see more relative content, you can see the statistics note. | {
"title": "32. Discrete Random Variable",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
There is a method to approximate the differential error with proof. | {
"title": "59. Error in Differential Approximation",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Parallel
-Linear combination
-Unit vector
-Section formula
-Collinearity | {
"title": "64. Some properties of vector",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
Here use two examples to show how to prove with induction and recursion methods. | {
"title": "40. Induction and Recursion",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
The distance between the original point O and the point in the number line A(a), denoted by |a|, the absolute value of a.
Here are some properties:
(1). If a≥0, then |a|=a; If a<0, then |a|=-a
(2).The distance between two points A(a), B(b) in the number line is |a-b|=|b-a|
(3).|a|≥ 0
(4).|a|=|-a|
(5).|a|²=|a²|
(6).|a||b|=|ab|
(7).|a|/|b|=|a/b|, b is not equal to 0
(8).|a| ≤|b| is equivalent to a² ≤b²
(9).Triangle Equality:|a+b|≤|a|+|b| | {
"title": "5. Absolute Value",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
There is a proposition related to binomial random variable and its proof. | {
"title": "40. Proposition",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
-Definition
-pmf
-Note(relation between Bernoulli random variable and binomial random variable)
-Example
-Expected value(with proof)
-Variance(with proof) | {
"title": "39. Binomial Random Variable",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
Here are the mass and moment formulas for coil springs, wires, and then rods lying along a smooth curve C in space:
-Mass
-First moments about the coordinate planes
-Coordinates of the center of mass
-Moments of inertia about axes and other lines
There is an example in the end of this part. | {
"title": "314. Mass and Moment Calculations",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Here are some examples about counting principles. (The last example is “how many numbers do not have 3 between 1 to 1000“: the word with color is miss in the picture) | {
"title": "5.Some Examples",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
-General case
-Cylindrical Coordinates
-Spherical coordinates
-Example | {
"title": "311.Substitutions in Triple Integrals",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is a theorem with its proof. The hidden part in the right side shows “comparison”. | {
"title": "72. Theorem",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
There are two steps to change cartesian integrals into polar integrals. | {
"title": "299. Changing Cartesian Integrals into Polar Integrals",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
These are some properties of field with some proved. Readers can also try to prove the second part of the properties! | {
"title": "5.Some properties of field",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
This conception is combined conditional probability and independence. | {
"title": "29. Conditionally independent",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
-Definition
-pmf
-Note(relation between Bernoulli random variable and binomial random variable)
-Example | {
"title": "33. Binomial Random Variable",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
**Welcome to the Discord Championship Wiki!**
DCC!!
DCC (Discord Championship) is a collaborative community event where 10 teams of 4 compete in minigames to take first place! Here you'll find each event and player ever in DCC history! See who the best is! See which teams were stacked! Stay tuned for updates!!
(started by ItsLunaForever)
Important articles
------------------
PlaceholderA Main CharacterPlaceholderThe First EpisodePlaceholderAn Important LocationPlaceholderA Key EventPlaceholderA Crucial ItemSaltEater
*Need help building out this community?*
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You can also be part of the larger Fandom family of communities. Visit Fandom's Community Central!
*Community Founders*: Write a good and paragraph-length description for your welcome section about your topic. Let your readers know what your topic is about and add some general information about it. Then you should visit the admin dashboard for more tips. | {
"title": "Discord Championship Wiki",
"domain": "discord-championship.fandom.com",
"cats": "discord_championship_wiki",
"removed": []
} |
-Definition: If we want to choose K form N different things for permutation, it will have N!/(N-K)! different ways.(K<N)
-One example for this case | {
"title": "7.Permutations(2)",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
-Comparable
-Chain
-Linear order&Linear order set
-Well-order set
-Example
-Theorem | {
"title": "75. Definition",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
Suppose S is an ordered set with the least-upper-bound property. Let the set B belong to set S. B is not empty and is bounded below. Let the set L be the set of all lower bounds of B. Then alpha=supL=infB belong to S.
The picture under the theorem is the explanation of the theorem. | {
"title": "3.Theorem",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-Definition
-Center
-Major axis
-Minor axis
-Distance a
-Distance b
-Focal distance(distance c)
-Eccentricity
-Notation | {
"title": "42. Ellipse",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
-Triangle area(two dimensions)
-Cross product
-Triangle area(three dimensions)
-Parallelopiped volume
-Inverse matrix | {
"title": "83. Applications of determinant",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
GoodAtEverything
----------------
### Joined
DCC I (Dec 12, 2021)
### Times Played
3
Statistics
----------
### Wins
1
### Best Individual Placement
17th (DCC I)
### Coins Average
915
**GoodAtEverything** is a player in Discord Championship. They made their debut in DCC I.
Tournament History
------------------
| Event
| Team
| Teammates
| Team Result
| Individual Result
| Dodgebolt Result |
--- | --- | --- | --- | --- | --- |
| Discord Championship 1 | | Radstuner21, Camaron08, & BoggledToggo | **5th** (9,906)
| **17th** (1,342)
| N/A |
Discord Championship 3 | | Jasoom, cwnnr, & dGc | **8th** (9,641)
| **38th** (789)
| N/A |
Discord Championship 5 | | dGc, iljone, & Pinnacles | **2nd** (13,667)
| **38th** (615)
| **Won**(2-1)
| | {
"title": "GoodAtEverything",
"domain": "discord-championship.fandom.com",
"cats": "",
"removed": []
} |
-Limits of polynomials
-Limits of rational functions
-Notation
-Two examples | {
"title": "4. Two theorems",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Proof of exhaustion
-Multiplication principle
-Addition principle
-Note:goal of multiplication and addition principle | {
"title": "4.Counting Principles",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
If f has derivative at x=c, then f is continuous at x=c.
There is the proof under the theorem statement. | {
"title": "29. Theorem",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-There exists a ordered field R which has the least-upper bound property. Moreover, R contains Q as a subfield.
(The word in the picture which is blocked is “Moreover")
By this theorem, we.can get these two outcomes:
-archimedean of R
-Q is dense in R
The description and proof of these two outcomes are in the picture. | {
"title": "7.Some theories",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-Three forms
-Each coefficient(standard form)
-Exact roots
-Intersection(between f(x) and x-axis) | {
"title": "30. Quadratic function",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
There is a definition of the random variable. Also, there is an example to understand the meaning of the random variable.
This is the note from statistics 26. If you want to see more relative content, you can see the statistics note. | {
"title": "31. Random Variable",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
-Sum rule
-Difference rule
-Constant multiple rule
-Product rule
-Quotient rule
-Power rule
-Root rule
-An example: show how to apply those rules | {
"title": "3. Limit laws",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is the theorem of general solution to the nonhomogeneous case and its idea. | {
"title": "357. General Solution to the Nonhomogeneous Case",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There are the theorem and five examples. The proof of the theorem will be shown later. | {
"title": "78. L’Hopital’s Rule",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
At a production level yielding maximum profit, marginal revenue equals marginal cost. | {
"title": "83. Application: Economics",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Measured in terms of square of the original units of measurement
-Sample variance vs Population variance
Error: The first denominator of sample variance is n-1 | {
"title": "7.Variance",
"domain": "hyl.fandom.com",
"cats": "statistics",
"removed": []
} |
To be a ordered field, It must have ordered sets and fields properties. | {
"title": "6. Definition and Properties of ordered field",
"domain": "hyl.fandom.com",
"cats": "mathematical_analysis",
"removed": []
} |
-The extended principle of mathematical induction
-Theorem: The principle of mathematical induction implies the extended principle mathematical induction
-Example | {
"title": "36. The Extended Principle of Mathematical Induction",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
There is the introduction and the definition of the 2\*2 and 3\*3 cases. | {
"title": "80. Determinant",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
Here is the definition of the greatest common divisor, denoted as gcd. | {
"title": "41. Greatest Common Divisor",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Components(voltage source, resistor, inductor, capactor)
-Symbols
-Ohm’s law
-The voltage drops across an inductor and a capacitor
-Kirchhoff’s law(with second-order differential equation) | {
"title": "363. Application: Electric Circuits",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
-Definition
-Basic equation
Error: In the picture, the distance between the point on the parabola and focus is the same as the distance between the point on the parabola and directrix, not the x-axis. | {
"title": "40. Parabola",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
Trevor Trixz
------------
### Affiliation
Hinto
### Occupation
Leader of Hinto Gang
Biographical information
------------------------
### Place of birth
United Kingdom
Physical description
--------------------
### Gender
Male
Appearances
-----------
### Debut
CIMcity BETA
Portrayed by TrixzOnline
Biography
--------- | {
"title": "TREVOR TRIXZ",
"domain": "cimcity-rp.fandom.com",
"cats": "characters",
"removed": []
} |
-Mass
-First moments about the coordinate planes
-Coordinates of center of mass
-Momentd of inertia about coordinate axes
-Example | {
"title": "340. Mass and Moments of Thin Shells",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
Here are the explanations and examples to show what are Cartesian graphs and directed graphs. | {
"title": "52. Cartesian Graphs&Directed Graphs",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Definition
-Center
-Major axis
-Distance a
-Focal distance(distance c)
-Eccentricity
-Asymptotes
-Conjugate axis | {
"title": "44. Hyperbola",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
There is the flux-divergence or normal form of Green’s Theorem. It tells the outward flux equals the divergence integral. | {
"title": "331. Green’s Theorem: Flux-Divergence or Normal Form",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is the formula and its idea of simple harmonic motion based on second-order linear equations. | {
"title": "361. Application: Simple Harmonic Motion",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is a theorem with its proof. The hidden part in the right side shows “S^-1°R^-1”. | {
"title": "71. Theorem",
"domain": "hyl.fandom.com",
"cats": "foundational_mathematics",
"removed": []
} |
-Definition
-Note(discrete case)
-Example
This is the note from statistics 28. If you want to see more relative content, you can see the statistics note. | {
"title": "33. Cumulative Distribution Function(cdf)",
"domain": "hyl.fandom.com",
"cats": "probability",
"removed": []
} |
-Monotonically increasing
-Monotonically decreasing
-Monotone function
-Strictly increasing
-Strictly decreasing
-Strict monotone
-Local maximum/minimum
-Tangent line
-Absolute maximum/minimum
-Inflection point | {
"title": "32. Some definitions",
"domain": "hyl.fandom.com",
"cats": "high_school_mathematics",
"removed": []
} |
There are six steps to solve the problem of the related rates problem with an example. | {
"title": "55. Related Rates Problems",
"domain": "hyl.fandom.com",
"cats": "calculus",
"removed": []
} |
There is a Theorem about subspace. The Corollary is the general case of the Theorem. | {
"title": "8. Theorem",
"domain": "hyl.fandom.com",
"cats": "linear_algebra",
"removed": []
} |
Subsets and Splits