Basic Concepts In Computational Physics
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Basic Concepts in Computational Physics
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.
Computational Physics
"Computational Physics: Basic Concepts" serves as an indispensable guide for students, researchers, and enthusiasts exploring the intersection of physics and computational methods. This book offers a comprehensive exploration of the fundamental principles of computational physics, providing a solid foundation to tackle complex problems in various branches of physics. The book begins by elucidating the foundational principles and theoretical underpinnings essential for effective computational simulations. It covers a variety of numerical techniques, including finite difference methods and Monte Carlo simulations, with practical examples and applications. Recognizing the importance of coding skills, it includes a section on programming tailored for physicists, teaching readers to implement numerical algorithms using popular programming languages. "Computational Physics: Basic Concepts" extends its coverage to diverse branches of physics such as classical mechanics, electromagnetism, quantum mechanics, and statistical physics, illustrating the versatility of computational techniques. Each chapter includes problem-solving exercises designed to reinforce understanding and enhance computational skills. Techniques for data visualization and interpretation are discussed, enabling effective communication of findings. The book also shares practical tips and best practices to optimize computational workflows and avoid common pitfalls. Whether you're a student new to computational physics or a seasoned researcher, "Computational Physics: Basic Concepts" provides a thorough and accessible resource for mastering the essential elements of this dynamic field.
An Introduction to Computational Physics
Author: Tao Pang
language: en
Publisher: Cambridge University Press
Release Date: 2006-01-19
Thoroughly revised for its second edition, this advanced textbook provides an introduction to the basic methods of computational physics, and an overview of progress in several areas of scientific computing by relying on free software available from CERN. The book begins by dealing with basic computational tools and routines, covering approximating functions, differential equations, spectral analysis, and matrix operations. Important concepts are illustrated by relevant examples at each stage. The author also discusses more advanced topics, such as molecular dynamics, modeling continuous systems, Monte Carlo methods, genetic algorithm and programming, and numerical renormalization. It includes many more exercises. This 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.