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[转载] <<数值方法/分析 (作者:伯登 & 费尔斯)>>科普书 --> 可以自由免费下载其第9版

已有 910 次阅读 2019-6-5 19:09 |系统分类:科普集锦|文章来源:转载

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今天从旧书摊捡了一本旧版费尔斯&伯登的<<数值方法/分析>>科普书,目前出版的应该是第10版 (网上可以自由下载其第9版) (记得本书早版的特色是带有编好的FORTRAN,Pascal计算机程序)其目录为:

1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS.
Review of Calculus.
Round-off Errors and Computer Arithmetic.
Algorithms and Convergence.
Numerical Software and Chapter Summary.


2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE.
The Bisection Method.
Fixed-Point Iteration.
Newton's Method and Its Extensions.
Error Analysis for Iterative Methods.
Accelerating Convergence.
Zeros of Polynomials and Müller's Method.
Numerical Software and Chapter Summary.


3. INTERPOLATION AND POLYNOMIAL APPROXIMATION.
Interpolation and the Lagrange Polynomial.
Data Approximation and Neville's Method.
Divided Differences.
Hermite Interpolation.
Cubic Spline Interpolation.
Parametric Curves.
Numerical Software and Chapter Summary.


4. NUMERICAL DIFFERENTIATION AND INTEGRATION.
Numerical Differentiation.
Richardson's Extrapolation.
Elements of Numerical Integration.
Composite Numerical Integration.
Romberg Integration.
Adaptive Quadrature Methods.
Gaussian Quadrature.
Multiple Integrals.
Improper Integrals.
Numerical Software and Chapter Summary.


5. INITIAL-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS.
The Elementary Theory of Initial-Value Problems.
Euler's Method.
Higher-Order Taylor Methods.
Runge-Kutta Methods.
Error Control and the Runge-Kutta-Fehlberg Method.
Multistep Methods.
Variable Step-Size Multistep Methods.
Extrapolation Methods.
Higher-Order Equations and Systems of Differential Equations.
Stability.
Stiff Differential Equations.
Numerical Software and Chapter Summary.


6. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS.
Linear Systems of Equations.
Pivoting Strategies.
Linear Algebra and Matrix Inversion.
The Determinant of a Matrix.
Matrix Factorization.
Special Types of Matrices.
Numerical Software and Chapter Summary.


7. ITERATIVE TECHNIQUES IN MATRIX ALGEBRA.
Norms of Vectors and Matrices.
Eigenvalues and Eigenvectors.
The Jacobi and Gauss-Siedel Iterative Techniques.
Relaxation Techniques for Solving Linear Systems.
Error Bounds and Iterative Refinement.
The Conjugate Gradient Method.
Numerical Software and Chapter Summary.


8. APPROXIMATION THEORY.
Discrete Least Squares Approximation.
Orthogonal Polynomials and Least Squares Approximation.
Chebyshev Polynomials and Economization of Power Series.
Rational Function Approximation.
Trigonometric Polynomial Approximation.
Fast Fourier Transforms.
Numerical Software and Chapter Summary.


9. APPROXIMATING EIGENVALUES.
Linear Algebra and Eigenvalues.
Orthogonal Matrices and Similarity Transformations.
The Power Method.
Householder's Method.
The QR Algorithm.
Singular Value Decomposition.
Numerical Software and Chapter Summary.


10. NUMERICAL SOLUTIONS OF NONLINEAR SYSTEMS OF EQUATIONS.
Fixed Points for Functions of Several Variables.
Newton's Method.
Quasi-Newton Methods.
Steepest Descent Techniques.
Homotopy and Continuation Methods.
Numerical Software and Chapter Summary.


11. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS.
The Linear Shooting Method.
The Shooting Method for Nonlinear Problems.
Finite-Difference Methods for Linear Problems.
Finite-Difference Methods for Nonlinear Problems.
The Rayleigh-Ritz Method.
Numerical Software and Chapter Summary.


12. NUMERICAL SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS.
Elliptic Partial Differential Equations.
Parabolic Partial Differential Equations.
Hyperbolic Partial Differential Equations.
An Introduction to the Finite-Element Method.
Numerical Software and Chapter Summary.


Bibliography.

Answers to Selected Exercises.

Index

Computer Programs



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