计算物理学(第2版)(英文版)

P.O.J谢勒著的《计算物理学》（第2版）（英文 版）是一部非常规范的高等计算物理教科书。内容包 括用于计算物理学中的重要算法的简洁描述。本书第 1部分介绍数值方法的基本理论，其中包含大量的习 题和仿真实验。本书第2部分主要聚焦经典和量子系 统的仿真等内容。 本书读者对象：计算物理等相关专业的研究生。

Part I Numerical Methods 1 Error Analysis 1.1 Machine Numbers and Rounding Errors 1.2 Numerical Errors of Elementary Floating Point Operations 1.2.1 Numerical Extinction 1.2.2 Addition 1.2.3 Multiplication 1.3 Error Propagation 1.4 Stability of lterative Algorithms 1.5 Example: Rotation 1.6 Truncation Error 1.7 Problems 2 Interpolation 2.1 Interpolating Functions 2.2 Polynomial Interpolation 2.2.1 lagrange Polynomials 2.2.2 Barycentric Lagrange Interpolation 2.2.3 Newton's Divided Differences 2.2.4 Neville Method 2.2.5 Error of Polynomial Interpolation 2.3 Splice Interpolation 2.4 Rational Interpolation 2.4.1 Pad6 Approximant 2.4.2 Barycentric Rational Interpolation 2.5 Multivariate Interpolation 2.6 Problems 3 Numerical Differentiation 3.1 One-Sided Difference Quotient 3.2 Central Difference Quotient 3.3 Extrapolation Methods 3.4 Higher Derivatives 3.5 Partial Derivatives of Multivariate Functions 3.6 Problems 4 Numerical Integration 4.1 Equidistant Sample Points 4.1.1 Closed Newton-Cotes Formulae 4.1.2 Open Newton-Cotes Formulae 4.1.3 Composite Newton-Cotes Rules 4.1.4 Extrapolation Method (Romberg Integration) 4.2 Optimized Sample Points 4.2.1 Clenshaw-Curtis Expressions 4.2.2 Gaussian Integration. 4.3 Problems 5 Systems of Inhomogeneous Linear Equations 5.1 Gaussian Elimination Method 5.1.1 Pivoting 5.1.2 Direct LU Decomposition 5.2 QR Decomposition 5.2.1 QR Decomposition by Orthogonalization 5.2.2 QR Decomposition by Householder Reflections 5.3 Linear Equations with Tridiagonal Matrix 5.4 Cyclic Tridiagonal Systems 5.5 Iterative Solution of Inhomogeneous Linear Equations 5.5.1 General Relaxation Method 5.5.2 Jacobi Method 5.5.3 Gauss-Seidel Method 5.5.4 Damping and Successive Over-Relaxation 5.6 Conjugate Gradients 5.7 Matrix Inversion 5.8 Problems 6 Roots and Extremai Points 6.1 Root Finding 6.1.1 Bisection 6.1.2 Regula Falsi (False Position) Method 6.1.3 Newton-Raphson Method 6.1.4 Secant Method 6.1.5 Interpolation 6.1.6 Inverse Interpolation 6.1.7 Combined Methods 6.1.8 Multidimensional Root Finding 6.1.9 Quasi-Newton Methods 6.2 Function Minimization 6.2.1 The Ternary Search MetlTod 6.2.2 The Golden Section Search Method (Brent's Method) 6.2.3 Minimization in Multidimensions 6.2.4 Steepest Descent Method 6.2.5 Conjugate Gradient Method 6.2.6 Newton-R~phson Method 6.2.7 Quasi-Newton Methods 6.3 Problems 7 Fourier Transformation 8 Random Numbers and Monte Carlo Methods 9 Eigenvalue Problems 10 Data Fitting 11 Discretization of Differential Equations 12 Equations of Motion Part II Simulation of Classical and Quantum Systems 13 Rotational Motion 14 Molecular Mechanics 15 Thermodynamic Systems 16 Random Walk and Brownian Motion 17 Electrostatics 18 Waves 19 Diffusion 20 Nonlinear Systems 21 Simple Quantum Systems Appendix I Performing the Computer Experiments Appendix II Methods and Algorithms References Index