Computational Physics

The classic in the field for more than 25 years, now with increased emphasis on data science and new chapters on quantum computing, machine learning (AI), and general relativity

Computational physics combines physics, applied mathematics, and computer science in a cutting-edge multidisciplinary approach to solving realistic physical problems. It has become integral to modern physics research because of its capacity to bridge the gap between mathematical theory and real-world system behavior.

Computational Physics provides the reader with the essential knowledge to understand computational tools and mathematical methods well enough to be successful. Its philosophy is rooted in “learning by doing”, assisted by many sample programs in the popular Python programming language. The first third of the book lays the fundamentals of scientific computing, including programming basics, stable algorithms for differentiation and integration, and matrix computing. The latter two-thirds of the textbook cover more advanced topics such linear and nonlinear differential equations, chaos and fractals, Fourier analysis, nonlinear dynamics, and finite difference and finite elements methods. A particular focus in on the applications of these methods for solving realistic physical problems.

Readers of the fourth edition of Computational Physics will also find:

• An exceptionally broad range of topics, from simple matrix manipulations to intricate computations in nonlinear dynamics
• A whole suite of supplementary material: Python programs, Jupyter notebooks and videos

Computational Physics is ideal for students in physics, engineering, materials science, and any subjects drawing on applied physics.

Table of Contents

Part I Basics

Chapter 1 Introduction

Chapter 2 Software Basics

Chapter 3 Errors and Uncertainties

Chapter 4 Monte Carlo Simulations

Chapter 5 Differentiation and Integration

Chapter 6 Trial-and-Error Searching and Data Fitting

Chapter 7 Matrix Computing and N-D Searching

Chapter 8 Differential Equations and Nonlinear Oscillations

Part ll Data Science

Chapter 9 Fourier Analyses

Chapter 10 Wavelet and Principal Components Analysis

Chapter 11 Neural Networks and Machine Learning

Chapter 12 Quantum Computing (G. He, Coauthor)

Part lll Applications

Chapter 13 ODE Applications; Eigenvalues, Scattering, Trajectories

Chapter 14 Fractals and Statistical Growth Models

Chapter 15 Nonlinear Population Dynamics

Chapter 16 Nonlinear Dynamics of Continuous Systems

Chapter 17 Thermodynamics Simulations and Feynman Path Integrals

Chapter 18 Molecular Dynamics Simulations

Chapter 19 General Relativity

Chapter 20 Integral Equations

Part IV PDE Applications

Chapter 21 PDE Review, Electrostatics and Relaxation

Chapter 22 Heat Flow and Leapfrogging

Chapter 23 String and Membrane Waves

Chapter 24 Quantum Wave Packets and EM Waves

Chapter 25 Shock and Soliton Waves

Chapter 26 Fluid Hydrodynamics

Chapter 27 Finite Element Electrostatics 0

About the Authors

Rubin H. Landau, PhD, is Professor Emeritus in the Department of Physics at Oregon State University, Corvallis, Oregon, USA. In his long and distinguished research career he has been instrumental in the development of computational physics as a defined subject, and founded both the Computational Physics Degree Program and the Northwest Alliance for Computational Science and Engineering.

Manuel J. Páez, PhD, is a Professor in the Department of Physics at the University of Antioquia in Medellin, Colombia. He teaches courses in both physics and programming, and he and Professor Landau have collaborated on pathbreaking computational physics investigations.

Cristian C. Bordeianu, PhD, taught Physics and Computer Science at the Military College “Stefan cel Mare,” Campulung Moldovenesc, Romania.