由Richard L.Burden编写的这本《数值分析》第7版介绍了现代数值近似技术的理论及实用知识，解释了它们的工作原理。

同它的前几个版本一样，该书仍将重点放在近似技术的数值分析上，以便为读者今后的学习打下坚实的数值分析与科学计算基础。本书内容丰富、翔实，可以根据不同的学习对象和学习目的，选择、组织、串联相应的章节，形成侧重于理论或是侧重于实用的两种学习策略。书中的每个概念均以大量的例子说明，同时书中还包含2000多个习题，范围从方法、算法的基本应用到理论的归纳与扩展，涉及物理、计算机、生物、社会科学等多个不同的领域。通过这些实例，进一步说明在现实世界中，数值方法是如何被应用的。第七版新增了两个突出的部分，一是前承条件共轭梯度方法，为线性方程系统提供了更完备的解决方法；另一部分是同伦与连续方法，为非线性方程系统的近似求解提供了不同的方法。

1 Mathematical Preliminaries

　　1.1 Review of Calculus

　　1.2 Roundoff Errors and Computer Arithmetic

　　1.3 Algorithms and Convergence

　　1.4 Numerical Software

2 Solutions of Equations in One Variable

　　2.1 The Bisection Method

　　2.2 Fixed-Point Iteration

　　2.3 Newton's Method

　　2.4 Error Analysis for Iterative Methods

　　2.5 Accelerating Convergence

　　2.6 Zeros of Polynomials Müller's Method

　　2.7 Survey of Methods and Software

3 Interpolation and Polynomial Approximation

　　3.1 Interpolation and the Lagrange Polynomial

　　3.2 Divided Differences

　　3.3 Hermite Interpolation

　　3.4 Cubic Spline Interpolation

　　3.5 Parametric Curves

　　3.6 Survey of Methods and Software

4. Numerical Differentiation and Integration

　　4.1 Numerical Differentiation

　　4.2 Richardson's Extrapolation

　　4.3 Elements of Numerical Integration

　　4.4 Composite numerical Integration

　　4.5 Romberg Integration

　　4.6 Adaptive Quadrature Methods

　　4.7 Gaussian Quadrature

　　4.8 Multiple Integrals

　　4.9 Improper Integrals

　　4.10 Survey of Methods and Software

5 Initial-Value Problems for ordinary Differential Equations

　　5.1 The Elementary Theory of Initial-Value Problems

　　5.2 Euler's Method

　　5.3 Higher-Order Taylor Methods

　　5.4 Runge-Kutta Methods

　　5.5 Error Control and the Runge-Kutta-Fehlberg Method

　　5.6 Multistep methods

　　5.7 Variable Step-Size Multistep Methods

　　5.8 Extrapolation Methods

　　5.9 Higher-Order Equations and Systems of Differential Equations

　　5.10 Stability

　　5.11 Stiff Differential Equations

　　5.12 Survey of Methods and Software

6 Direct Methods for Solving Linear Systems

　　6.1 Linear Systems of Equations

　　6.2 Pivoting Strategies

　　6.3 Linear Algebra and Matrix Inversion

　　6.4 The Determinant of a Matrix

　　6.5 matrix Factorization

　　6.6 Special Types of Matrices

　　6.7 Survey of Methods and Software

7 Iterative Techniques in Matrix algebra

　　7.1 Norms of Vectors and Matrices

　　7.2 Eigenvalues and Eigenvectors

　　7.3 Iterative Techniques for Solving Linear Systems

　　7.4 Error Bounds and Iterative Refinement

　　7.5 The Conjugate Gradient Method

　　7.6 Survey of Methods and Software

8 Approximation Theory

　　8.1 Discrete Least Squares Approximation

　　8.2 Orthogonal Polynomials and Least Squares Approximation

　　8.3 Chebyshev Polynomials and Econcomization of Power Series

　　8.4 Rational Function Approximation

　　8.5 Trigonometric Polynomial approximation

　　8.6 Fast Fourier Transforms

　　8.7 Survey of Methods and software

9 Approximating Eigenvalues

　　9.1 Linear algebra and Eigenvalues

　　9.2 The Power Method

　　9.3 Householder's Method

　　9.4 The QR Algorithm

　　9.5 Survey of Methods and software

10 Numerical Solutions of Nonlinear Systems of Equations

　　10.1 Fixed Points for Functions of Several Variables

　　10.2 Newton's Method

　　10.3 Quasi-Newton Methods

　　10.4 Steepest Descent Techniques

　　10.5 Homotopy and Continuation Methods

　　10.6 Survey of Methods and Software

11 Boundary-Value Problems for Ordinary Differential Equations

　　11.1 The Linear Shooting Method

　　11.2 The Shooting Method for Nonlinear Problems

　　11.3 Finite-Difference Methods for Linear Problems

　　11.4 Finite-Difference Methods for Nonlinear Problems

　　11.5 The Rayleigh-Ritz Method

　　11.6 Survey of Methods and Software

12 Numerical solutions to Partial Differential Equations

　　12.1 Elliptic Partial Differential Equations

　　12.2 Parabolic Partial Differential Equations

　　12.3 Hyperbolic Partial Differential Equations

　　12.4 An Introduction to the Finite-Element Method

　　12.5 Survey of Methods and software

Bibliography

Answers to Selected Exercises

Index