《計算物理學（第2版）》是2017年世界圖書出版公司出版的著作，作者是POJ謝勒。
基本介紹
- 書名：計算物理學（第2版）
- 作者：POJ謝勒
- ISBN：9787519219635
- 出版社：世界圖書出版公司
- 出版時間：2017年
內容提要,作品目錄,
內容提要
P.O.J謝勒著的《計算物理學》（第2版）（英文 版）是一部 規範的高等計算物理教科書。內容包 括用於計算物理學中的重要算法的簡潔描述。本書第 1部分介紹數值方法的基本理論，其中包含大量的習 題和仿真實驗。本書第2部分主要聚焦經典和量子系 統的仿真等內容。
本書讀者對象：計算物理等相關專業的研究生。
本書讀者對象：計算物理等相關專業的研究生。
作品目錄
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
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
