Contents
Chapter 1 Solution of Nonlinear Equations f (x)= 0
非线性方程f (x) = 0的解法
1.1 Iteration for Solving x = g(x)
求解x = g(x)的迭代法
1.2 Bracketing Methods for Locating a Root
定位一个根的分类方法
1.3 Newton-Raphson and Secant Methods
牛顿-拉夫森法和割线法
Chapter 2 Solution of Linear Systems AX = B
线性方程组AX = B的数值解法
2.1 Upper-Triangular Linear Systems
上三角线性方程组
2.2 Gaussian Elimination and Pivoting
高斯消去法和选主元
2.3 Triangular Factorization
三角分解法
2.4 Iterative Methods for Linear Systems
求解线性方程组的迭代法
2.5 Iteration for Nonlinear Systems (Optional)
非线性方程组的迭代法(选读)
Chapter 3 Interpolation and Polynomial Approximation
插值与多项式逼近
3.1 Taylor Series and Calculation of Functions
泰勒级数和函数计算
3.2 Introduction to Interpolation
插值简介
3.3 Lagrange Approximation
拉格朗日逼近
3.4 Newton Polynomials
牛顿多项式
3.5 Chebyshev Polynomials (Optional)
切比雪夫多项式(选读)
3.6 Padé Approximations
帕德逼近
Chapter 4 Curve Fitting
曲线拟合
4.1 Least-Squares Line
最小二乘拟合曲线
4.2 Methods of Curve Fitting
曲线拟合
4.3 Interpolation by Spline Functions
样条函数插值
4.4 Bézier Curves
贝塞尔曲线
Chapter 5 Numerical Integration
数值积分
5.1 Introduction to Quadrature
积分简介
5.2 Composite Trapezoidal and Simpson’s Rule
组合梯形公式和辛普森公式
5.3 Recursive Rules and Romberg Integration
递归公式与龙贝格积分
5.4 Gauss-Legendre Integration (Optional)
高斯-勒让德积分(选读)
Chapter 6 Solution of Differential Equations
微分方程求解
6.1 Introduction to Differential Equations
微分方程简介
6.2 Euler’s Method
欧拉方法
6.3 Heun’s Method
休恩方法
Appendix A Introduction to MATLAB
MATLAB简介
Appendix B Some Math Expressions and Pronunciations
一些数学表达式及其读法
Appendix C 1000 English-Chinese Math Key Words
1000英汉数学词汇