Fractional Calculus Computer Algebra System math software Home | list | math | function | calculator | handbook | help | forum | index | 中文
+ + =



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

  • math handbook (Russian)
  • Handbook of Special Functions

    Content 2 - Content 3 - Content 4

    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 `int` cos(x) `(dx)^0.5`

    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 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 digamma(x) `psi(x)`
      4. trigamma function trigamma(x) `psi^((1))(x)`
      5. polygamma function polygamma(n,x) `psi^((n))(x)`
      6. Incomplete Gamma function `Gamma(a,x)`
      7. 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. linear differential equation
    4. higher order and a system of differential equations
      `d^2/dx^2` y - 4y =0
      `dx/dt=x, dy/dt=x-y`
    5. stability theory
    6. Numerical Solution of Ordinary Differential Equations
    7. Solve (fractional) differential equation for y by dsolve()
      dsolve( y'-2y=0 )
    8. Test solution for (fractional) differential equation by test()

    9. test( exp(2x), `d/dx y=2y` )
    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