Mathematics

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Coordinate System

Cartesian Coordinate System

  1. Cartesian coordinate system
  2. Point in cartesian coordinate system
  3. Surface element in cartesian coordinate system
  4. Vector in cartesian coordinate system

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Cylindrical Coordinate System

  1. Point in cylindrical coordinate system
  2. Cylinder

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Spherical Coordinate System

  1. Point in spherical coordinate system
  2. Surface element in spherical coordinate system
  3. Sphere

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Polar Coordinate System

  1. Polar coordinate system

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Three coordinate systems

  1. Coordinate systems.doc
  2. Coordinate systems.nb
  3. Generally

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Miscellaneous

  1. Coordinate system conversion
  2. Les passages
  3. Passage des coordonnées
  4. Transformation du vecteur

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Useful and interesting link :

Coordinate Systems in 2D & 3D By Cindy You

Plane Analytic Geometry

  1. Point
  2. Midpoint
  3. Distance between two points
  4. Slope of a line segment
  5. Equation of the line passing through a point with a slope
  6. Equation of the line passing through the two given points
  7. Equation of the line that passes through the given point and is parallel to the given line
  8. Equation of the line that passes through the given point and is perpendicular to the given line
  9. Distance between point and line
  10. Distance between two parallel lines

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Single variable calculus

Intervals

  1. Les Intervalles

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Functions

  1. Fonction
  2. Injectivite
  3. Surjectivite
  4. Bijectivite
  5. Operation Sur Les Fonctions
  6. Fonction Composee
  7. Fonction Paire Et Impaire
  8. Le Sens De Variation

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Limit

  1. Limit
  2. More examples of computing limits

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Asymptote

  1. Horizontal asymptote
  2. Vertical asymptote
  3. Oblique asymptote

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Derivative

  1. Definition
  2. Derivative
  3. Derivee Des Fonctions Elementaires

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Curve

  1. Type 01

Differential

  1. Differential

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Integral

  1. Definite integral
  2. Indefinite integral

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Sequence And Series

  1. Sequence and series of numbers
  2. Taylor series for the functions
  3. Sequence and series of functions

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Function visualization

  1. Functions of two variables
  2. Plane Curves
  3. Space Curves
  4. Parametric Surfaces
  5. Vector Field
  6. Contour Plot
  7. Revolution Plot 3D - I
  8. Revolution Plot 3D - II
  9. Spherical Plot 3D
  10. Region Plot
  11. Area between two curves

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Vector calculus

Vector field

  1. Vector Field
  2. Line integral in R2
  3. Line integral in R3
  4. Integral curve in R2
  5. Integral curve in R3

Gradient

  1. Gradient in Cartesian coordinates system
  2. Gradient in Cylindrical coordinates system
  3. Gradient in Spherical coordinates system

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Divergence

  1. Divergence in Cartesian coordinates system
  2. Divergence in Cylindrical coordinates system
  3. Divergence in Spherical coordinates system

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Curl

  1. Curl in Cartesian coordinates system
  2. Curl in Cylindrical coordinates system
  3. Curl in Spherical coordinates system

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Laplacian

  1. Laplacian in Cartesian coordinates system
  2. Laplacian in Cylindrical coordinates system
  3. Laplacian in Spherical coordinates system

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Interactive visualization of Euclidean space

  1. Interactive visualization of two-dimensional Euclidean space
  2. Interactive visualization of three-dimensional Euclidean space

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Space

  1. Space R2
  2. Space R3
  3. Space Rn
  4. Space Pn
  5. Space Cn
  6. Space C[a,b]
  7. Space C*[a,b]

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Development of function

Inner product

  1. On Space Rn
  2. On Space Cn
  3. On Space Pn
  4. On Space C[a,b]
  5. On Space C*[a,b]

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Norm

  1. On Space Rn
  2. On Space Cn
  3. On Space Pn
  4. On Space C[a,b]
  5. On Space C*[a,b]

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Orthogonal Projection

  1. On Space Rn
  2. On Space Cn
  3. On Space Pn
  4. On Space C[a,b]
  5. On Space C*[a,b]

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Orthogonalization

  1. On Space Rn
  2. On Space Cn
  3. On Space Pn
  4. On Space C[a,b]
  5. On Space C*[a,b]

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Development of function

  1. On Space Rn
  2. On Space Cn
  3. On Space Pn
  4. On Space C[a,b]
  5. On Space C*[a,b]

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Classical orthogonal polynomials version 1

Les Polynomes Orthogonaux

  1. Fonctions de carré sommable
  2. Produit scalaire, normalité, orthogonalité et orthonormalité
  3. Bases de l'espace des fonctions de carré sommable
  4. Développement d'une fonction
  5. Théorème de Stone - Weierstrass
  6. La méthode de Gram-Schmidt
  7. Les polynômes orthogonaux classiques
  8. Les polynômes orthogonaux associés classiques

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Classical orthogonal polynomials version 2

  1. Classical orthogonal polynomials
  2. Legendre polynomials
  3. Legendre polynomials in polar coordinates
  4. Hermite polynomials
  5. Laguerre polynomials
  6. Chebyshev I polynomials

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Rodrigues' formula

  1. Jacobi polynomials
  2. Legendre polynomials
  3. Chebyshev I polynomials
  4. Hermite polynomials
  5. Laguerre polynomials

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Sturm–Liouville theory

Équation différentiel Sturm-Liouville (Part 1)

Équation différentiel Sturm-Liouville (Part 1)

  1. Équation différentielle de Legendre
  2. Équation différentielle de Laguerre
  3. Équations différentielles de Hermite
  4. Équations différentielles de Chebyshef I
  5. Équation différentielle de Helmholtz
  6. Équations différentielles de oscillateur harmonique
  7. Équation de Laplace en coordonnées sphérique (Symétrie Azimutale)

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Integral transforms

  1. Fourier Transform
  2. Laplace Transform

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Differential equations

Ordinary differential equation

Growth and Decay

  1. Exponential Growth
  2. Exponential Decay

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Rectilinear motion

  1. Horizontal motion
  2. Vertical projectile motion

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Curvilinear motion

  1. Angled projectile motion
  2. Curvilinear motion in polar coordinate system

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Harmonic motion

  1. Simple vertical spring-mass system
  2. Damped vertical spring-mass system
  3. Driven vertical spring-mass system

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Lagrangian Dynamics

  1. Horizontal motion
  2. Vertical motion
  3. Simple pendulum
  4. Simple pendulum with damping and external force
  5. Double pendulum
  6. Pendulum hanging from a spinning ring
  7. Horizontal mass spring system
  8. Vertical mass spring system
  9. Conical pendulum
  10. Spring-Pendulum system
  11. Pendulum on a movable support

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Helmholtz equation

  1. Helmholtz equation
  2. Helmholtz equation I
  3. Helmholtz equation II
  4. Helmholtz equation III

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Time Equations

  1. Time Equations 1
  2. Time Equations 2

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Partial differential equation

Classification of PDE

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Classical wave equations

  1. Classical wave equation V1 docx
  2. Classical wave equation V2 nb
  3. Taut string, Fixed at x = 0 and x = L
  4. Taut string, Fixed at x = 0 and free at x = L
  5. Taut string, Free at x = 0 and x = L
  6. Rectangular member

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Some Differential Equations

  1. Homogeneous 1st order linear differential equation
  2. Homogeneous 2nd order linear differential equation
  3. Non-homogeneous 2nd order linear differential equation
  4. Skydiver equation

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Linear algebra

Matrix

  1. Visualize a 2D matrix
  2. Linear operators
  3. Conjugate, Transpose, Conjugate Transpose, Hermitian Conjugate
  4. Matrices Hermitiennes v1
  5. Matrices Hermitiennes v2

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Row and column operations on matrix

  1. Delete row and column
  2. Insert row and column
  3. Swap rows and columns
  4. Swap elements
  5. Replace element
  6. Sort each row and column
  7. Sum elements along the all row and column
  8. Sum elements along the row and column
  9. Sum elements along the diagonals

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System of linear equations

  1. System of linear equations v1
  2. System of linear equations v2
  3. Characteristic polynomial of a matrix
  4. Row-Reduce form of the matrix
  5. Determine if a set of linear equations Ax=b has a solution and what type of solution

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Numerical analysis

Interpolation

  1. Polynomial interpolation
  2. Multiplication of two polynomials

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Probability

  1. Random BMP
  2. Dice
  3. Coin flipping

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Statistics

Propagation of uncertainty

  1. Propagation of uncertainty (Function of 1 variable)
  2. Propagation of uncertainty (Function of 2 variable)
  3. Propagation of uncertainty (Function of 3 variable)
  4. Propagation of uncertainty (Function of 4 variable)

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Regression analysis

  1. Linear regression

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Trigonométrie

  1. Circonférence trigonométrique
  2. Angles associés
  3. Les fonctions trigonométriques
  4. Les fonctions trigonométriques inversses

Notbooks:

  1. Radian and Degree conversion
  2. Angle and cartesian coordinate conversion
  3. Trigonometric circle
  4. Special Pairs of Angles
  5. Trigonometric Expand
  6. Trigonometric Factor
  7. Trigonometric Reduce
  8. Trigonometric equations
  9. Quadratic trigonometric equations

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Fourier analysis

  1. Numerical functions
  2. Related functions to Fourier analysis
  3. Signals
  4. Fourier Series
  5. Fourier Transforms
  6. Discrete Fourier Transforms
  7. FFT

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