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An Introduction to Computational Physics (Second Edition) by Tao Pang



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An Introduction to Computational Physics (Second Edition) written by Tao Pang , University of Nevada, Las Vegas Thoroughly updated and revised for its second edition, this advanced textbook provides an introduction to the basic methods of computational physics, and an overview of recent progress in several areas of scientific computing. Tao Pang presents many step-by-step examples, including program listings in JavaTM, of practical numerical methods from modern physics and related areas. Now including many more exercises, the volume can be used as a textbook for either undergraduate or first-year graduate courses on computational physics or scientific computation. It will also be a useful reference for anyone involved in computational research.

An Introduction to Computational Physics (Second Edition) written by Tao Pang cover the following topics.



  • Preface to first edition
    Preface
    Acknowledgments

  • 1. Introduction
    1.1 Computation and science
    1.2 The emergence of modern computers
    1.3 Computer algorithms and languages
    Exercises

  • 2. Approximation of a function
    2.1 Interpolation
    2.2 Least-squares approximation
    2.3 The Millikan experiment
    2.4 Spline approximation
    2.5 Random-number generators
    Exercises

  • 3. Numerical calculus
    3.1 Numerical differentiation
    3.2 Numerical integration
    3.3 Roots of an equation
    3.4 Extremes of a function
    3.5 Classical scattering
    Exercises

  • 4. Ordinary differential equations
    4.1 Initial-value problems
    4.2 The Euler and Picard methods
    4.3 Predictor–corrector methods
    4.4 The Runge–Kutta method
    4.5 Chaotic dynamics of a driven pendulum
    4.6 Boundary-value and eigenvalue problems
    4.7 The shooting method
    4.8 Linear equations and the Sturm–Liouville problem
    4.9 The one-dimensional Schr¨odinger equation
    Exercises

  • 5. Numerical methods for matrices
    5.1 Matrices in physics
    5.2 Basic matrix operations
    5.3 Linear equation systems
    5.4 Zeros and extremes of multivariable functions
    5.5 Eigenvalue problems
    5.6 The Faddeev–Leverrier method
    5.7 Complex zeros of a polynomial
    5.8 Electronic structures of atoms
    5.9 The Lanczos algorithm and the many-body problem
    5.10 Random matrices
    Exercises

  • 6. Spectral analysis
    6.1 Fourier analysis and orthogonal functions
    6.2 Discrete Fourier transform
    6.3 Fast Fourier transform
    6.4 Power spectrum of a driven pendulum
    6.5 Fourier transform in higher dimensions
    6.6 Wavelet analysis
    6.7 Discrete wavelet transform
    6.8 Special functions
    6.9 Gaussian quadratures
    Exercises

  • 7. Partial differential equations
    7.1 Partial differential equations in physics
    7.2 Separation of variables
    7.3 Discretization of the equation
    7.4 The matrix method for difference equations
    7.5 The relaxation method
    7.6 Groundwater dynamics
    7.7 Initial-value problems
    7.8 Temperature field of a nuclear waste rod
    Exercises

  • 8. Molecular dynamics simulations
    8.1 General behavior of a classical system
    8.2 Basic methods for many-body systems
    8.3 The Verlet algorithm
    8.4 Structure of atomic clusters
    8.5 The Gear predictor–corrector method
    8.6 Constant pressure, temperature, and bond length
    8.7 Structure and dynamics of real materials
    8.8 Ab initio molecular dynamics
    Exercises 254

  • 9. Modeling continuous systems
    9.1 Hydrodynamic equations
    9.2 The basic finite element method
    9.3 The Ritz variational method
    9.4 Higher-dimensional systems
    9.5 The finite element method for nonlinear equations
    9.6 The particle-in-cell method
    9.7 Hydrodynamics and magnetohydrodynamics
    9.8 The lattice Boltzmann method
    Exercises

  • 10. Monte Carlo simulations
    10.1 Sampling and integration
    10.2 The Metropolis algorithm
    10.3 Applications in statistical physics
    10.4 Critical slowing down and block algorithms
    10.5 Variational quantum Monte Carlo simulations
    10.6 Green’s function Monte Carlo simulations
    10.7 Two-dimensional electron gas
    10.8 Path-integral Monte Carlo simulations
    10.9 Quantum lattice models
    Exercises

  • 11. Genetic algorithm And programming
    11.1 Basic elements of a genetic algorithm
    11.2 The Thomson problem
    11.3 Continuous genetic algorithm
    11.4 Other applications
    11.5 Genetic programming
    Exercises

  • 12. Numerical renormalization
    12.1 The scaling concept
    12.2 Renormalization transform
    12.3 Critical phenomena: the Ising model
    12.4 Renormalization with Monte Carlo simulation
    12.5 Crossover: the Kondo problem
    12.6 Quantum lattice renormalization
    12.7 Density matrix renormalization
    Exercises


  • References
    Index

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