نام كتاب : An Introduction to Computational Physicsنويسنده :Tao Pangانتشارات : Cambridge University-2006تعداد صفحات : 384 صفحهحجم فايل : 1.97 مگابايتيك كتاب درسي عالي جهت تدريس درس فيزيك محاسباتي - به همراه شبيه سازي ديناميك مولكولي و مونت كارلوفصول كتاب: Introduction 11.1 Computation and science 11.2 The emergence of modern computers 41.3 Computer algorithms and languages 7Exercises 142 Approximation of a function 162.1 Interpolation 162.2 Least-squares approximation 242.3 The Millikan experiment 272.4 Spline approximation 302.5 Random-number generators 37Exercises 443 Numerical calculus 493.1 Numerical differentiation 493.2 Numerical integration 563.3 Roots of an equation 623.4 Extremes of a function 663.5 Classical scattering 70Exercises 764 Ordinary differential equations 804.1 Initial-value problems 814.2 The Euler and Picard methods 814.3 Predictor–corrector methods 834.4 The Runge–Kutta method 884.5 Chaotic dynamics of a driven pendulum 904.6 Boundary-value and eigenvalue problems 944.7 The shooting method 964.8 Linear equations and the Sturm–Liouville problem 994.9 The one-dimensional Schr¨odinger equation 105Exercises 1155 Numerical methods for matrices 1195.1 Matrices in physics 1195.2 Basic matrix operations 1235.3 Linear equation systems 1255.4 Zeros and extremes of multivariable functions 1335.5 Eigenvalue problems 1385.6 The Faddeev–Leverrier method 1475.7 Complex zeros of a polynomial 1495.8 Electronic structures of atoms 1535.9 The Lanczos algorithm and the many-body problem 1565.10 Random matrices 158Exercises 1606 Spectral analysis 1646.1 Fourier analysis and orthogonal functions 1656.2 Discrete Fourier transform 1666.3 Fast Fourier transform 1696.4 Power spectrum of a driven pendulum 1736.5 Fourier transform in higher dimensions 1746.6 Wavelet analysis 1756.7 Discrete wavelet transform 1806.8 Special functions 1876.9 Gaussian quadratures 191Exercises 1937 Partial differential equations 1977.1 Partial differential equations in physics 1977.2 Separation of variables 1987.3 Discretization of the equation 2047.4 The matrix method for difference equations 2067.5 The relaxation method 2097.6 Groundwater dynamics 2137.7 Initial-value problems 2167.8 Temperature field of a nuclear waste rod 219Exercises 2228 Molecular dynamics simulations 2268.1 General behavior of a classical system 2268.2 Basic methods for many-body systems 2288.3 The Verlet algorithm 2328.4 Structure of atomic clusters 2368.5 The Gear predictor–corrector method 2398.6 Constant pressure, temperature, and bond length 2418.7 Structure and dynamics of real materials 2468.8 Ab initio molecular dynamics 250Exercises 2549 Modeling continuous systems 2569.1 Hydrodynamic equations 2569.2 The basic finite element method 2589.3 The Ritz variational method 2629.4 Higher-dimensional systems 2669.5 The finite element method for nonlinear equations 2699.6 The particle-in-cell method 2719.7 Hydrodynamics and magnetohydrodynamics 2769.8 The lattice Boltzmann method 279Exercises 28210 Monte Carlo simulations 28510.1 Sampling and integration 28510.2 The Metropolis algorithm 28710.3 Applications in statistical physics 29210.4 Critical slowing down and block algorithms 29710.5 Variational quantum Monte Carlo simulations 29910.6 Green’s function Monte Carlo simulations 30310.7 Two-dimensional electron gas 30710.8 Path-integral Monte Carlo simulations 31310.9 Quantum lattice models 315Exercises 32011 Genetic algorithm and programming 32311.1 Basic elements of a genetic algorithm 32411.2 The Thomson problem 33211.3 Continuous genetic algorithm 33511.4 Other applications 33811.5 Genetic programming 342Exercises 34512 Numerical renormalization 34712.1 The scaling concept 34712.2 Renormalization transform 35012.3 Critical phenomena: the Ising model 35212.4 Renormalization with Monte Carlo simulation 35512.5 Crossover: the Kondo problem 35712.6 Quantum lattice renormalization 36012.7 Density matrix renormalization 364Exercises 367Reference