Preface to the First Edition
Preface to the Second Edition
1 Computational Methods
1-1 Numerical calculations and beyond
1-2 Integers and floating numbers
1-3 Programming language and program library
1-4 Examples of algebraic, integer and floating number calculations
1-5 Examples of unconventional techniques
Problems
2 Integration and Differentiation
2-1 Numerical integration
2-2 Rectangular and trapezoidal rules
2-3 Simpson's rule
2-4 Gaussian quadrature
2-5 Monte Carlo integration
2-6 Multidimensional integrals and improper integrals
2-7 Numerical differentiation
Problems
3 Interpolation and Extrapolation
3-1 Polynomial interpolation
.3-2 Interpolation using rational functions
3-3 Continued fraction
3-4 Fourier transform
3-5 Extrapolation
3-6 Inverse interpolation
3-7 Cubic spline
Problems
4 Special Functions
4-1 Hermite polynomials and harmonic oscillator
4-2 Legendre polynomials and spherical harmonics
4-3 Spherical Bessel functions
4-4 Laguerre polynomials
4-5 Error integrals and gamma functions
Problems
5 Matrices
5-1 System of linear equations
5-2 Matrix inversion and LU-decomposition
5-3 Matrix approach to the eigenvalue problem
5-4 Tridiagonalization method
5-5 Eigenvalues and eigenvectors of a tridiagonal matrix
5-6 Lanczos method of constructing matrices
5-7 Nonsymmetric matrices and complex matrices
Problems
6 Methods of Least Squares
6-1 Statistical description of data
6-2 Uncertainties and their propagation
6-3 The method of maximum likelihood
6-4 The method of least squares
6-5 Statistical tests of the results
6-6 Linear least-squares fit
6-7 Nonlinear least-squares fit to data
Problems
7 Monte Carlo Calculations
7-1 Generation of random numbers
7-2 Molecular diffusion and Brownian motion
7-3 Data simulation and hypothesis testing
7-4 Percolation and critical phenomena
7-5 The Ising model
7-6 Path integrals in quantum mechanics
7-7 Fractals
Problems
8 Finite Difference Solution of Differential Equations
8-1 Types of differential equations
8-2 Runge-Kutta methods
8-3 Solution of initial value problems by extrapolation
8-4 Boundary value problems by shooting methods
8-5 Relaxation methods
8-6 Boundary value problems in partial differential equations
8-7 Parabolic partial differential equations
8-8 Hyperbolic partial differential equations
8-9 Nonlinear differential equations
8-10 Stiffness problems
Problems
9 Finite Element Solution to PDE
9-1 Background
9-2 Shape functions and finite element approximation
9-3 Assembling contributions from elements
9-4 Variational approach
9-5 Application to a two-dimensional Poisson equation
Problems
Appendix A
A-1 Decomposition into prime numbers
A-2 Bit-reversed order
A-3 Gaussian elimination of a tridiagonal matrix
A-4 Random bit generator
A-5 Reduction of higher-order ODE to first-order
Appendix B List of Fortran Program Examples
Bibliography
Index
· · · · · · (收起)