本教材按照“理论+算法+代码+实例”的结构方式，具有实际问题建模实例的特色，真正体现数学建模的思想，培养解决实际工程问题能力。具体讲，每一章都有应用这一章理论知识、数值算法及程序代码的解决工程问题的实例。例如，在线性方程组数值解法章节，将引入Google搜索引擎实例，阐述Google搜索引擎背后的数学建模思路与过程，并给出MATLAB程序代码，实现GooglePageRank计算。让读者切实体会和体验数值分析的精髓，培养应用数学解决实际问题的意识、素养与能力。

Chapter 1 Introduction
1.1 Numerical Analysis: What and Why?
1.2 Review of Calculus
1.3 Computer Arithmetic and Error Analysis
1.4 Algorithms and Convergence
1.5 Numerical Software
1.6 Reading: Golub and Moler
1.7 Self Assessment Exercises
Chapter 2 Solution of Nonlinear Equations
2.1 Introduction
2.2 Bisection Method
2.3 Fixed Point Iteration
2.4 Newton's Method
2.5 Secant Method
2.6 Survey of Methods and Software
2.7 Reading: Newton
2.8 Self Assessment Exercises
Chapter 3 Solution of Linear Systems
3.1 Introduction
3.2 Gaussian Elimination Method
3.2.1 Gaussian Elimination
3.2.2 Gaussian Elimination Algorithm
3.2.3 Partial Pivoting
3.2.4 Scaled Partial Pivoting
3.3 LU Factorization
3.4 Vector and Matrix Norms
3.5 Error of Calculated Solution
3.5.1 Error of Calculated Solution
3.5.2 A Practical Error Bound
3.6 Residual Correction Method
3.7 Jacobi Iterative Method
3.7.1 Jacobi Iteration
3.7.2 Convergence of the Jacobi Method
3.8 Gauss-Seidel Iterative Method
3.8.1 Gauss-Seidel Iteration
3.8.2 Termination of the Iteration
3.9 Survey of Methods and Software
3.9.1 MATLAB Functions
3.9.2 Comparison of Direct and Iterative Methods
3.9.3 Some Modern Methods and Software
3.10 Reading: Gauss, Jacobi and Seidel
3.11 Self Assessment Exercises
Chapter 4 Polynomial Interpolation and Curve Fitting
4.1 Introduction
4.2 Lagrange Form
4.3 Newton's Divided Difference Formula
4.4 Error of the Interpolating Polynomial
4.5 Runge's Phenomenon
4.6 Curve Fitting
4.6.1 Overview
4.6.2 Fitting a Straight Line
4.6.3 Fitting Linear Forms
4.6.4 Polynomial Fitting
4.6.5 Fitting Exponential Functions
4.7 Survey of Methods and Software
4.8 Reading: Lagrange and Runge
4.9 Self Assessment Exercises
Chapter 5 Numerical Differentiation and Numerical Integration
5.1 Introduction
5.2 Numerical Differentiation
5.3 Numerical Integration Based on Interpolation
5.3.1 Integration via Polynomial Interpolation
5.3.2 Trapezoid Rule
5.3.3 Simpson's Rule
5.4 Composite Trapezoid Rule
5.5 Romberg Integration
5.6 Reading: Cotes, Simpson and Romberg
5.7 Self Assessment Exercises
Chapter 6 Solution of Ordinary Differential Equations
6.1 Introduction
6.2 Euler's Method
6.3 Local and Global Truncation Errors
6.4 Taylor's Methods
6.5 Runge-Kutta Methods
6.6 Stability
6.7 First Order Systems
6.8 Reading: Euler, Kutta and Taylor
6.9 Self Assessment Exercises
Reference
Appendix A Introduction to MATLAB
A.1 A Glance of MATLAB
A.2 Starting Up
A.3 MATLAB as a Calculator
A.4 Plotting
A.5 Programming
A.6 Commonly Used Commands Summary
Appendix B Answers for Selected Exercises
Appendix C Common Mathematical Knowledge