This textbook provides a compendium of numerical methods to assist physics students and researchers in their daily work. It carefully considers error estimates, stability and convergence issues, the choice of optimal methods, and techniques to increase program execution speeds. The book supplies numerous examples throughout the chapters that are concluded by more comprehensive problems with a strong physics background. Instead of uncritically employing modern black-box tools, the readers a...

This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds.Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a wee...

This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to th...

This book is designed as a practical and intuitive introduction to probability, statistics and random quantities for physicists. The book aims at getting to the main points by a clear, hands-on exposition supported by well-illustrated and worked-out examples. A strong focus on applications in physics and other natural sciences is maintained throughout. In addition to basic concepts of random variables, distributions, expected values and statistics, the book discusses the notions of entropy...

Our book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series partitioning. The source codes of the computer programs implementing these original automatic algorithms...

This book guides undergraduate students in the use of Maxima—a computer algebra system—in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook.When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly attractive in that it is open-source, multiple-platform software that st...

Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear engineering, which are illustrative of uses in other fields. Five appendices are included, which provide useful information on probability distributions, general...

Nuclear engineering has undergone extensive progress over the years. In the past century, colossal developments have been made and with specific reference to the mathematical theory and computational science underlying this discipline, advances in areas such as high-order discretization methods, Krylov Methods and Iteration Acceleration have steadily grown.Nuclear Computational Science: A Century in Review addresses these topics and many more; topics which hold special ties to the ...

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 d...

The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics. It is also a simple model of polymer entropy which is useful in modelling phase behaviour in polymers. This monograph provides an authoritative examination of interacting self-avoiding walks, presenting aspects of the thermodynamic limit, phase behaviour, scaling and critical exponents for lattice polygons, lattice animals and surfaces. It also includes a comprehensive account...

This work provides a short "getting started" guide to Fortran 90/95. The main target audience consists of newcomers to the field of numerical computation within Earth system sciences (students, researchers or scientific programmers). Furthermore, readers accustomed to other programming languages may also benefit from this work, by discovering how some programming techniques they are familiar with map to Fortran 95.The main goal is to enable readers to quickly start using Fortran 95...

This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are...