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Chapter 1 Introduction
1£®1 Numerical Computational Methods and Main Contents
1£®2 Error
1£®3 Stability Analysis of Numerical Methods
1£®4 How to Avoid Error
Excises 1

Chapter 2 Interpolation and Polynomial Approximation
2£®1 Introduction
2£®2 Lagrange Interpolation Polynomial
2£®3 Neville' s Interpolating Formula
2£®4 Newton Interpolation
2£®5 Hermite Interpolation
2£®6 Piecewise Polynomial Approximation
2£®7 Cubic Spline Interpolation
Excises 2

Chapter 3 Approximation Theory
3£®1 Optimal Approximation
3£®2 Optimal Approximation of Normed Linear Space
3£®3 Optimal Uniform Approximation Polynomial
3£®4 Minimum Error to Zero-Chebyshev Polynomial
3£®5 Optimal Approximation of the Inner Product Space
3£®6 Optimal Square Approximation and Orthogonal Polynomials
3£®7 Discrete Optimal Square Approximation and Least Square Method £¨L-S£©
Excises 3

Chapter 4 Numerical Integration and Differentiation
4£®1 Introduction
4£®2 Newton-Cotes Quadrature Formula
4£®3 Composite Numerical Integration
4£®4 Richardson Extrapolation and Romberg Integration
4£®5 Gaussian Quadrature
4£®6 Numerical Differentiation
Excises 4

Chapter 5 Solving Linear System of Equations
5£®1 Elementary Notions and Results of Linear Algebra
5£®2 Direct Methods for Solving Linear System of Equations
5£®3 Error of Gaussian Elimination
5£®4 Iterative Methods for Solving Linear Systems
5£®5 Conjugate Gradient Method
Excises 5

Chapter 6 Approximating Eigenvalues
6£®1 Linear Algebra and Eigenvalues
6£®2 The Power Method and the Inverse Power Method
6£®3 Householder' s Method
6£®4 QR Algorithm
6£®5 Improved Power Method
Excises 6

Chapter 7 Numerical Solutions of Nonlinear Systems
7£®1 The Bisection Method
7£®2 Fixed Point Iterative Method
7£®3 Newton' s Iteration Method
7£®4 Numerical Solutive for Nonlinear Systems of Equations
Excises 7

Chapter 8 Numerical Solutions of Ordinary Differential Equations
8£®1 Introduction
8£®2 Euler's Method
8£®3 Multistep Methods £¨¢ñ£©
8£®4 Muhistep Methods £¨¢ò£©
8£®5 Runge-Kutta Method
8£®6 Stiff Problem
8£®7 Numerical Solution for Boundary-value Problem
Excises 8
References