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Introduction to Computational Physics

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ISBN-10: 0521825695

ISBN-13: 9780521825696

Edition: 2nd 2005 (Revised)

Authors: Tao Pang

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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.
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Book details

Edition: 2nd
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 1/19/2006
Binding: Hardcover
Pages: 402
Size: 7.75" wide x 9.75" long x 1.00" tall
Weight: 2.288
Language: English

Preface to first edition
Computation and science
The emergence of modern computers
Computer algorithms and languages
Approximation of a function
Least-squares approximation
The Millikan experiment
Spline approximation
Random-number generators
Numerical calculus
Numerical differentiation
Numerical integration
Roots of an equation
Extremes of a function
Classical scattering
Ordinary differential equations
Initial-value problems
The Euler and Picard methods
Predictor-corrector methods
The Runge-Kutta method
Chaotic dynamics of a driven pendulum
Boundary-value and eigenvalue problems
The shooting method
Linear equations and the Sturm-Liouville problem
The one-dimensional Schrodinger equation
Numerical methods for matrices
Matrices in physics
Basic matrix operations
Linear equation systems
Zeros and extremes of multivariable functions
Eigenvalue problems
The Faddeev-Leverrier method
Complex zeros of a polynomial
Electronic structures of atoms
The Lanczos algorithm and the many-body problem
Random matrices
Spectral analysis
Fourier analysis and orthogonal functions
Discrete Fourier transform
Fast Fourier transform
Power spectrum of a driven pendulum
Fourier transform in higher dimensions
Wavelet analysis
Discrete wavelet transform
Special functions
Gaussian quadratures
Partial differential equations
Partial differential equations in physics
Separation of variables
Discretization of the equation
The matrix method for difference equations
The relaxation method
Groundwater dynamics
Initial-value problems
Temperature field of a nuclear waste rod
Molecular dynamics simulations
General behavior of a classical system
Basic methods for many-body systems
The Verlet algorithm
Structure of atomic clusters
The Gear predictor-corrector method
Constant pressure, temperature, and bond length
Structure and dynamics of real materials
Ab initio molecular dynamics
Modeling continuous systems
Hydrodynamic equations
The basic finite element method
The Ritz variational method
Higher-dimensional systems
The finite element method for nonlinear equations
The particle-in-cell method
Hydrodynamics and magnetohydrodynamics
The lattice Boltzmann method
Monte Carlo simulations
Sampling and integration
The Metropolis algorithm
Applications in statistical physics
Critical slowing down and block algorithms
Variational quantum Monte Carlo simulations
Green's function Monte Carlo simulations
Two-dimensional electron gas
Path-integral Monte Carlo simulations
Quantum lattice models
Genetic algorithm and programming
Basic elements of a genetic algorithm
The Thomson problem
Continuous genetic algorithm
Other applications
Genetic programming
Numerical renormalization
The scaling concept
Renormalization transform
Critical phenomena: the Ising model
Renormalization with Monte Carlo simulation
Crossover: the Kondo problem
Quantum lattice renormalization
Density matrix renormalization