  Book: Computational Physics The materials on this page are taken from the book Computational Physics by M. Newman, an introduction to the field of computational physics using the Python programming language. If you're interested you can find information about the book here. The book itself is available from the usual booksellers or online here.

The Python programming language is an excellent choice for learning, teaching, or doing computational physics. It is a well-designed, modern programming language that is simultaneously easy to learn and very powerful. It includes a range of features tailored for scientific computing, including features for handling vectors, inverting and diagonalizing matrices, performing Fourier transforms, making graphs, and creating 3D graphics.

This page contains a selection of resources I've developed for teachers and students interested in computational physics and Python.

Here are several complete book chapters on Python computational physics. You're welcome to download these chapters, print them out, use them in class, or just read them for yourself. Comments or questions are welcome.

• Chapter 2: Python programming for physicists – This chapter gives an introduction to the Python language at a level suitable for readers with no previous programming experience. It introduces the basic elements of programming with variables and arrays, assignments, arithmetic and functions, inputs, outputs, conditionals, and loops, all in the Python language. The ideas are illustrated with examples drawn from various branches of physics, including classical mechanics, special relativity, and quantum physics.
• Chapter 3: Graphics and visualization – This chapter gives an introduction to some of Python's features for making scientific graphics, including graphs, density plots, and 3D visualizations of physical systems.
• Chapter 4: Accuracy and speed – Very important for good scientific programming is an understanding of the limitations of the computer. Computers are neither infinitely fast nor infinitely accurate. This chapter explains how we estimate the accuracy of our calculations and how long they will take, and some of the pitfalls that can be encountered if we don't take care with such things.
• Chapter 5: Integrals and derivatives – Having mastered the fundamentals of Python programming, we move on to the main business of computational physics. This chapter introduces methods for performing integrals and derivatives on the computer, including basic techniques like the trapezoidal rule and Simpson's rule, and more advanced techniques like adaptive methods, Romberg integration, and Gaussian quadrature. Example applications include the heat capacity of solids, thermal radiation, electrostatics calculations, and image processing.

Subsequent chapters cover a range of further topics in computational physics, including the solution of linear and nonlinear systems of equations, the solution of ordinary and partial differential equations, Fourier transforms, stochastic processes, and Monte Carlo methods. For a full table of contents, see here.

### Appendices

Here are three useful appendices that go with the chapters above:

• Appendix A: Installing Python – How to install Python on your computer, plus some additional packages that you'll need to do the examples and exercises in the chapters above
• Appendix B: Differences between Python versions – A summary of the differences between versions 2 and 3 of Python
• Appendix C: Gaussian quadrature – A derivation of the integration points for Gaussian quadrature, based on the mathematics of Legendre polynomials. Also contains a discussion of the Stieltjes polynomials and their use in Gauss-Kronrod quadrature.

### Example programs

The following files contain copies of the example programs from the chapters above. All programs are in Python version 3, but they will work fine in version 2 also (technically version 2.6 or later) if you add this line to the beginning of the program:

```from __future__ import print_function,division
```
The file names below correspond to the names printed in the margins of the chapter pages next to each program.

Chapter 2:

Chapter 3:

Chapter 4:

• `qsho.py` – Calculate the internal energy of a quantum simple harmonic oscillator at temperature T

Chapter 5:

### Data sets

Here are some data sets that accompany the examples and exercises in the chapters above:

### Miscellaneous useful code

Here are a few other pieces of Python code that are useful for some of the exercises.