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`int ` 数学手册 dx = `sum ` MathHandbook.com

Table of Contents

  1. Algebra, triangle formula and elementary function ?
  2. Elementary geometry graph computation and plot ?
  3. Algebraic equation ?
  4. Matrix · determinant · system of linear equations ?
  5. Differential calculus ?
  6. Integral calculus ?
  7. Analytic geometry and differential geometry ?
  8. Vector algorithms and tensor field and theory algorithms and Riemannian geometry ?
  9. Abstract algebraic - linear space - Functional Analysis ?
  10. Complex function ?
  11. Integral transform ?
  12. Special Function?
  13. Ordinary Differential Equations (ODE) ?
  14. Partial Differential Equations (PDE) ?
  15. Integral equations ?
  16. Statistical probability and stochastic processes ?
  17. Error theory and experimental data processing ?
  18. Optimization methods ?
  19. Finite element method ?
  20. Elementary number theory ?
  21. Set theory and general topology ?

Elementary Math
Chapter 1
Algebra, triangle formula and elementary function

Chapter 2
Elementary geometry graph computation and plot
§1 triangle and quadrangle
§2 circle and regular polygon
§3 practical geometry mapping
§4 solid figure volume, surface area, side area

Chapter 3
Algebraic equation
§1 root expression of two, three, quartic order equation

  1. Second Order Equation x^2+b*x+c=0
  2. Solve equation by solve() solve( x^2+5*x+6=0 )
  3. Numerical Solve equation by nsolve() nsolve( x^2+5*x+6=0 )
§2 algebraic equation nature
§3 special solution of algebraic equation
§4 approximate calculation of real roots

Higher Math
Chapter 4
Matrix · determinant · system of linear equations
§1 matrix and determinant
§2 matrix operation
§3 system of linear equations

Chapter 5
Differential calculus

Chapter 6
Integral calculus
  1. single variable function integral
  2. multiple integrals, curvilinear integral and surface integral
  3. integral application
  4. region function `delta(x)`
  5. Integral table `int` sin(x) dx
  6. definite integral `int_0^1` sin(x) dx
  7. Fractional integral calculus `d^-0.5/dx^-0.5` cos(x)

Chapter 7
Analytic geometry and differential geometry

Chapter 8
Vector algorithms and tensor field and theory algorithms and Riemannian geometry

Chapter 9
Abstract algebraic - linear space - Functional Analysis

Chapter 10
Complex function

Chapter 11
Integral transform

Chapter 12
Special Function

  1. Bernoulli numbers and Bernoulli polynomials
  2. Bessel function
    First kind of Bessel function J(n,x)
    Second kind of Bessel function J2(n,x)
    Third kind of Bessel function J3(n,x)
  3. Beta function Beta(a,b)
  4. beta function `beta(x)`
  5. Elliptic integral
  6. Elliptic function
  7. error function erf(x) erfi(x)
  8. eta function `eta(x)`
  9. Exponential integral Ei(x) Ein(x) En(x)
  10. Fresnel function FresnelS(x) S(x) FresnelC(x) C(x)
  11. Gamma function
    1. Gamma function `Gamma(x)`
    2. Log Gamma `logGamma(x)`
    3. Digamma function `psi(x)`
    4. polygamma function `psi^((n))(x)`
    5. Incomplete Gamma function `Gamma(a,x)`
    6. small gamma function smallgamma(a,x) `gamma(a,x)`
  12. Gaussian integral `Phi(x)`
  13. harmonic number harmonic(x) H(x)
  14. hypergeometric function
  15. Legendre function
  16. Lerch L(x,a,b)
  17. logarithmic integral li(x)
  18. sine and cosine integral si(x) ci(x)
  19. Mittag-Leffler function `E_0.5(x)`
  20. orthogonal polynomials
  21. polylog function polylog(a,x)
  22. zeta function `zeta(x)`

Chapter 13
Ordinary Differential Equations (ODE)

  1. General concept of differential equations
  2. Differential equations y' -2y = 0
  3. Solve (fractional) differential equation for y by dsolve()
    dsolve( y'-2y=0 )
  4. Test solution for (fractional) differential equation by odetest()

  5. odetest( exp(2x), `d/dx y=2y` )
  6. linear differential equation
  7. higher order differential equations
    `d^2/dx^2` y - 2y =0
  8. stability theory
  9. Numerical Solution of Ordinary Differential Equations x'=x, y'=x-y
  10. Fractional differential equation
    `d^0.5/dx^0.5` y = 2y
  11. Solve (fractional) differential equation for y by dsolve()
    dsolve( `d^0.5/dx^0.5 y=2y` )
  12. Test solution for (fractional) differential equation by test()
    test( exp(4x), `d^0.5/dx^0.5 y=2y` )
Chapter 14
Partial Differential Equations (PDE)

Chapter 15
Integral equations

  1. The general concept
    `int` y dx = 2y
  2. singular integral equation
  3. Volterra integral equations
  4. Approximate Solution of Integral Equation
  5. nonlinear integral equation
  6. Fractional integral equation
    `d^-0.5/dx^-0.5` y = 2y
  7. Solve (fractional) integral equation for y by dsolve()
    dsolve( `int` y dx = 2y )
    dsolve( `d^-0.5/dx^-0.5 y=2y` )
  8. Test solution for (fractional) integral equation by odetest()
    test( exp(1/4 x), `d^-0.5/dx^-0.5 y=2y` )
Chapter 16
Statistical probability and stochastic processes

Chapter 17
Error theory and experimental data processing

Chapter 18
Optimization methods

Chapter 19
Finite element method

Chapter 20
Elementary number theory

Chapter 21
Set theory and general topology




See Also

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