本书包括绪论、非线性方程的解法、线性方程组的数值解法、多项式插值、函数逼近、数值积分和数值微分、常微分方程数值解法和偏微分方程数值解法等8章，主要介绍了数值分析的基本概念、算法的构造和算法的理论分析等内容。各章末还配有习题和上机编程实验题，供读者练习使用。
本书结构完整，条理清晰，内容丰富，既可作为国内开设全英文或双语数值分析课程的本科生、研究生教材或教学参考用书，也可供从事科学计算的相关人员参考。

1 Introduction
1.1 Error
1.1.1 Sources of Approximation
1.1.2 Absolute Error and Relative Error
1.1.3 Significant Digits (or Figures)
1.1.4 Error Estimation of a Function
1.2 Computer Arithmetic
1.3 Numerical Stability
1.4 Ill-Conditioned Problem
1.5 Hornor's Method
Exercise 1
2 Solutions of Equations in One Variable
2.1 Introduction
2.2 The Bisection Method
2.3 Fixed-Point Iteration
2.3.1 Fixed-Point Iteration
2.3.2 Convergence
2.3.3 Order of Convergence
2.3.4 Aitken Method
2.4 Newton's Method
2.4.1 Local Convergence of Newton's Method
2.4.2 Modified Newton's Method for on Equation with Multiple Roots
2.4.3 The Secant Method
2.5 Zeros of Polynomials
2.5.1 Distribution of Zeros of Real Coefficient Polynomials
2.5.2 Bairstov Method
Exercise 2
3 Numerical Methods for Linear System
3.1 Direct Method
3.1.1 Gaussian Elimination Method
3.1.2 Gaussian Elimination Method with Partial Pivoting
3.1.3 Thomas Algorithm for Tridiagonal System
3.2 Matrix Factorization
3.2.1 Matrix Factorization
3.2.2 Matrix Factorization for the Symmetric Matrix
3.2.3 Matrix Factorization of Gaussian Elimination Method with Partial Pivoting
3.3 Norms and Error Analysis
3.3.1 Norms of Vectors
3.3.2 Norms of Matrices
3.3.3 Error Analysis
3.4 Iterative Methods
3.4.1 Jacobi Iterative Method
3.4.2 Gauss-Seidel Iterative Method
3.4.3 Successive Over-Relaxation Method
3.4.4 Convergency of Iterative Method
3.5 Power Method
Exercise 3
4 Interpolation
4.1 Lagrange Interpolating Polynomials
4.2 Newton's Divided-Difference Formula
4.2.1 Divided Difference
4.2.2 Forward Difference and Newton's Forward-Difference Formula
4.3 Hermite InterpoJation
4.4 PieeewisePolynomial Interpolation
4.4.1 Error Analysis of High-Degree Interpolating Polynomials
4.4.2 Piecewise-Linear Interpolation
4.4.3 Piecewise Hermite Interpolation
4.5 Cubic Spline Interpolation
4.5.1 Cubic Splines
4.5.2 Construction of a Cubic Spline
4.5.3 Converqence of Cubic Spline
Exercise 4
5 Approximation Theory
5.1 Best Uniform Approximation
5.1.1 Normed Linear Space
5.1.2 Polynomial of Best Uniform Approximation
5.2 Least Squares Approximation
5.2.1 Inner Product Space
5.2.2 Least Squares Approximation
5.2.3 Least Squares Approximation to Continuous Function
5.2.4 Least Squares Solution of Overdetermined Linear Equations
5.2.5 Discrete Least Squares Approximation
Exercise 5
6 Numerical Integration and Differentiation
6.1 Elements of Numerical Integration
6.1.1 Newton-Cotes Formula
6.1.2 Measuring Precision
6.1.3 Errors of Trapezoidal Rule.Simpson's Rule and Boole's Rule
6.1.4 Stability
6.2 Composite Numerical Integration
6.2.1 Composite Trapezoidal Rule
6.2.2 Composite Simpson's Rule
6.2.3 Composite Boole's Rule
6.3 Romberg Integration
6.4 Gaussian Quadrature
6.4.1 Orthogonal Polynomials
6.4.2 Truncation Error of Gaussian Quadrature
6.4.3 Stability and Convergence
6.5 Numerical Differentiation
Exercise 6
7 Initial-Value Problems for Ordinary Differential Equations
7.1 Euler's Method
7.1.1 Euler's Explicit Method
7.1.2 Euler's Implicit Method
7.1.3 Trapezoidal Method
7.1.4 Modified Euler's Method
7.1.5 Global Truncation Error
7.2 Runge-Kutta Methods
7.2.1 Second-Order Runge-Kutta Method
7.2.2 High-Order Runge-Kutta Method
7.2.3 Implicit Runge-Kutta Method
7.3 Stability and Convergence of One-Step Method
7.4 Multistep Methods
7.4.1 Adams Methods
7.4.2 Taylor Methods
7.4.3 Convergency and Stability of Multistep Methods
Exercise 7
8 Numerical Methods for Partial Differential Equations
8.1