Computational Physics: Problem Solving with Python, 3rd Edition

The use of computation and simulation has become an essential part of the scientific process. Being able to transform a theory into an algorithm requires significant theoretical insight, detailed physical and mathematical understanding, and a working level of competency in programming.

This upper-division text provides an unusually broad survey of the topics of modern computational physics from a multidisciplinary, computational science point of view. Its philosophy is rooted in learning by doing (assisted by many model programs), with new scientific materials as well as with the Python programming language. Python has become very popular, particularly for physics education and large scientific projects. It is probably the easiest programming language to learn for beginners, yet is also used for mainstream scientific computing, and has packages for excellent graphics and even symbolic manipulations.

The text is designed for an upper-level undergraduate or beginning graduate course and provides the reader with the essential knowledge to understand computational tools and mathematical methods well enough to be successful. As part of the teaching of using computers to solve scientific problems, the reader is encouraged to work through a sample problem stated at the beginning of each chapter or unit, which involves studying the text, writing, debugging and running programs, visualizing the results, and the expressing in words what has been done and what can be concluded. Then there are exercises and problems at the end of each chapter for the reader to work on their own (with model programs given for that purpose).

Table of Contents

Chapter 1 Introduction
Chapter 2 Computing Software Basics
Chapter 3 Errors and Uncertainties in Computations
Chapter 4 Monte Carlo: Randomness,Walks, and Decays
Chapter 5 Differentiation and Integration
Chapter 6 Matrix Computing
Chapter 7 Trial-and-Error Searching and Data Fitting
Chapter 8 Solving Differential Equations: Nonlinear Oscillations
Chapter 9 ODE Applications: Eigenvalues, Scattering, and Projectiles
Chapter 10 High-Performance Hardware and Parallel Computers
Chapter 11 Applied HPC: Optimization, Tuning, and GPU Programming
Chapter 12 Fourier Analysis: Signals and Filters
Chapter 13 Wavelet and Principal Components Analyses: Nonstationary Signals and
Chapter 14 Nonlinear Population Dynamics
Chapter 15 Continuous Nonlinear Dynamics
Chapter 16 Fractals and Statistical Growth Models
Chapter 17 Thermodynamic Simulations and Feynman Path Integrals
Chapter 18 Molecular Dynamics Simulations
Chapter 19 PDE Review and Electrostatics via Finite Differences and Electrostatics via Finite Differences
Chapter 20 Heat Flow via Time Stepping
Chapter 21 Wave Equations I: Strings and Membranes
Chapter 22 Wave Equations II: Quantum Packets and Electromagnetic
Chapter 23 Electrostatics via Finite Elements
Chapter 24 Shocks Waves and Solitons
Chapter 25 Fluid Dynamics
Chapter 26 Integral Equations of Quantum Mechanics