Basic Concepts in Computational Physics

Abstract

This book addresses all these scenarios on a very basic level. It is addressed to lecturers who will have to teach a basic course/basic courses in Computational Physics or numerical methods and to students as a companion in their first steps into the realm of this fascinating field of modern research. Following these intentions this book was divided into two parts. Part I deals with deterministic methods in Computational Physics. We discuss, in particular, numerical differentiation and integration, the treatment of ordinary differential equations, and we present some notes on the numerics of partial differential equations. Each section within this part of the book is complemented by numerous applications. Part II of this book provides an introduction to stochastic methods in Computational Physics. In particular, we will examine how to generate random numbers following a given distribution, summarize the basics of stochastics in order to establish the necessary background to understand techniques like M ARKOV -Chain Monte Carlo. Finally, algorithms of stochastic optimization are discussed. Again, numerous examples out of physics like

diffusion processes or the P OTTS model are investigated exhaustively. Finally, this book contains an appendix that augments the main parts of the book with a detailed discussion of supplementary topics.