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Macmillan Higher Education Palgrave Higher Education

Basic Concepts in Computational Physics

Edition 2nd Edition
ISBN 9783319272634
Publication Date March 2016
Formats Hardcover Ebook 
Publisher Springer

This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes.

The book is divided into two main parts: Deterministic methods and stochastic methods in computational physics. Based on concrete problems, the first part discusses numerical differentiation and integration, as well as the treatment of ordinary differential equations. This is extended by a brief introduction to the numerics of partial differential equations. The second part deals with the generation of random numbers, summarizes the basics of stochastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and stochastic optimization. All this is again motivated and augmented by applications from physics. In addition, the book offers a number of appendices to provide the reader with information on topics not discussed in the main text.

Numerous problems with worked-out solutions, chapter introductions and summaries, together with a clear and application-oriented style support the reader. Ready to use C++ codes are provided online.

Ewald Schachinger is a Professor in the Institute for Theoretical and Computational Physics in Graz University of Technology, Austria. 

Benjamin A. Stickler is a Professor in the Institute of Theoretical Physics at the University of Duisburg-Essen, Germany. 

Some Basic Remarks
Part I Deterministic Methods
Numerical Differentiation
Numerical Integration
The KEPLER Problem
Ordinary Differential Equations – Initial Value Problems
The Double Pendulum
Molecular Dynamics
Numerics of Ordinary Differential Equations - Boundary Value Problems
The One-Dimensional Stationary Heat Equation
The One-Dimensional Stationary SCHRÖDINGER Equation
Partial Differential Equations
Part II Stochastic Methods
Pseudo Random Number Generators
Random Sampling Methods
A Brief Introduction to Monte-Carlo Methods
The ISING Model
Some Basics of Stochastic Processes
The Random Walk and Diffusion Theory
MARKOV-Chain Monte Carlo and the POTTS Model
Data Analysis
Stochastic Optimization
Appendix: The Two-Body Problem
Solving Non-Linear Equations. The NEWTON Method
Numerical Solution of Systems of Equations
Fast Fourier Transform
Basics of Probability Theory
Phase Transitions
Fractional Integrals and Derivatives in 1D
Least Squares Fit
Deterministic Optimization.


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