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

Content 1 - Content 2 - Content 3 - Content 4 - Index

Content 2

  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 ?

初等数学 Elementary math

第一章 Chapter 1
代数三角公式与初等 函数 Algebra, triangle formula and elementary function
第二章 Chapter 2
初等几何图形的计算与作图 Elementary geometry graph computation and plot

第三章 Chapter 3
代数方程 Algebraic equation

高等数学 Higher Math

第四章 Chapter 4
矩阵 · 行列式 · 线性方程组 Matrix · determinant · system of linear equations

第五章 Chapter 5
微分学 Differential calculus

  1. 序列与函数的极限 sequence and function limit
  2. 级数的收敛与运算 seres restraining and operation
  3. 微分 differential `d/dx` sin(x)
  4. 隐函数 explicit differential
  5. 微分的应用 application of derivative
  6. 分数阶微积分 fractional calculus `d^1.5/dx^1.5` cos(x)
第六章 Chapter 6
积分学 Integral calculus
  1. 单变量函数的积分 integral of single variable function
  2. 定积分的求法 method of indefinite integral
  3. 多重积分、曲线积分与曲面积分 Multiple integrals, curve integrals and surface integrals
  4. 积分的应用 integral application
  5. 区域函数 region function `delta(x)`
  6. 分数阶积分 fractional integral `int sin(x) \ (dx)^(1/2)`
第七章 Chapter 7
解析几何与微分几何 Analytic geometry and differential geometry

第八章 Chapter 8
矢量算法与场论·张量算法与黎曼几何 Vector algorithms and field theory * tensor algorithms and Riemannian geometry

第九章 Chapter 9
抽象代数·线性空间·泛函分析 Abstract algebraic - linear space - Functional Analysis

第十章 Chapter 10
复变函数 Complex function

第十一章 Chapter 11
积分变换 Integral transform

第十二章 Chapter 12
特殊函数 Special function

第十三章 Chapter 13
常微分方程 Ordinary Differential Equation (ODE)

  1. 微分方程的一般概念 General concept of differential equations
  2. 一阶微分方程 First order differential equation y' -2y = 0
  3. 线性微分方程 linear differential equation
  4. 高阶微分方程与微分方程组 higher order differential equations and system of differential equations
  5. 稳定性理论大意 stability theory
  6. 常微分方程的数值解法 Numerical Solution of Ordinary Differential Equations
  7. 分数阶微分方程 Fractional differential equation
    `d^0.5/dx^0.5` y = 2y
  8. 解微分方程 solve differential equation by dsolve()
    dsolve( `d^0.5/dx^0.5 y=2y` )
  9. 验证微分方程的解 test solution for differential equation by test()
    test( exp(4x), `d^0.5/dx^0.5 y=2y` )
  10. 常微分方程2000题 2000 examples of ODE

第十四章 Chapter 14
偏微分方程 Partial Differential Equation (PDE)

第十五章 Chapter 15
积分方程 Integral equation

  1. 积分方程一般概念与弗雷德霍姆方程 The general concept
  2. 奇异积分方程 Singular integral equation
  3. 沃尔泰拉积分方程 Volterra integral equation
  4. 积分方程的近似解法 Approximate Solution of Integral Equation
  5. 非线性积分方程 nonlinear integral equation
  6. 分数阶积分方程 Fractional integral equation
    `d^-0.5/dx^-0.5` y = 2y
  7. 解积分方程 solve integral equation by dsolve()
    dsolve( `int` y dx = 2y )
    dsolve( `d^-0.5/dx^-0.5 y=2y` )
  8. 验证积分方程的解 test solution for integral equation by test()
    test( exp(1/4 x), `d^-0.5/dx^-0.5 y=2y` )

第十六章 Chapter 16
概率统计与随机过程 Statistical probability and stochastic processes

第十七章 Chapter 17
误差理论与实验数据处理 Error theory and experimental data processing

第十八章 Chapter 18
最优化方法 Optimization methods

第十九章 Chapter 19
有限元法 Finite element method

第二十章 Chapter 20
初等数论 Elementary number theory

第二十一章 Chapter 21
集论与一般拓扑学 Set theory and general topology

  • Index 

    Reference

  • Digital Library of Mathematical Functions
  • math handbook (Russian)
  • Handbook of Special Functions
    
    See Also

    
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