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


Table of Contents

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 preliminary tensor field theory algorithms and Riemannian preliminary

Chapter 9
Abstract algebraic linear space - Functional Analysis

Chapter 10
Complex function

Chapter 11
Fourier series and integral transform

Chapter 12
Special Function

  1. beta function `beta(a,x)`
  2. Bessel function
  3. Bernoulli numbers and Bernoulli polynomials
  4. Elliptic function
  5. error function erf(x) erfi(x)
  6. eta function `eta(x)`
  7. exponential integral ei(x)
  8. Fresnel function FresnelS(x) FresnelC(x)
  9. Gamma function `Gamma(x)`
  10. Gaussian integral gaussi(x)
  11. harmonic number harmonic(x)
  12. hypergeometric function
  13. Legendre function
  14. Lerch Phi `Phi(x,a,b)`
  15. logarithmic integral li(x)
  16. sine and cosine integral si(x) ci(x)
  17. Mittag-Leffler function `E_0.5(x)`
  18. polylog polylog(a,x)
  19. orthogonal polynomials
  20. zeta function `zeta(x)`

Chapter 13
Ordinary Differential Equations

  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
  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 odetest()
    odetest( exp(4x), `d^0.5/dx^0.5 y=2y` )
Chapter 14
Partial Differential Equations

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()
    odetest( 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

Symbol
Function




See Also

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