Computational Physics

A Practical Introduction to Computational Physics and Scientific Computing



to the Fortran edition

This book is the culmination of my ten years' experience in teaching three introductory, undergraduate level, scientific computing/computational physics classes at the National Technical University of Athens. It is suitable mostly for junior or senior level science courses, but I am currently teaching its first chapters to sophomores without a problem. A two semester course can easily cover all the material in the book, including lab sessions for practicing.

Why another book in computational physics? Well, when I started teaching those classes there was no bibliography available in Greek, so I was compelled to write lecture notes for my students. Soon, I realized that my students, majoring in physics or applied mathematics, were having a hard time with the technical details of programming and computing, rather than with the physics concepts. I had to take them slowly by the hand through the "howto" of computing, something that is reflected in the philosophy of this book. Hoping that this could be useful to a wider audience, I decided to translate these notes in English and put them in an order and structure that would turn them into "a book".

I also decided to make the book freely available on the web. I was partly motivated by my anger caused by the increase of academic (e)book prices to ridiculous levels during times of plummeting publishing costs. Publishers play a diminishing role in academic publishing. They get an almost ready-made manuscript in electronic form by the author. They need to take no serious investment risk on an edition, thanks to print-on-demand capabilities. They have virtually zero cost ebook publishing. Moreover, online bookstores have decreased costs quite a lot. Academic books need no advertisement budget, their success is due to their academic reputation. I don't see all of these reflected on reduced book prices, quite the contrary, I'm afraid.

My main motivation, however, is the freedom that independent publishing would give me in improving, expanding and changing the book in the future. It is great to have no length restrictions for the presentation of the material, as well as not having to report to a publisher. The reader/instructor that finds the book long, can read/print the portion of the book that she finds useful for her.

This is not a reference book. It uses some interesting, I hope, physics problems in order to introduce the student to the fundamentals of solving a scientific problem numerically. At the same time, it keeps an eye in the direction of advanced and high performance scientific computing. The reader should follow the instructions given in each chapter, since the book teaches by example. Several skills are taught through the solution of a particular problem. My lectures take place in a (large) computer lab, where the students are simultaneously doing what I am doing (and more). The program that I am editing and the commands that I am executing are shown on a large screen, displaying my computer monitor and actions live. The book provides no systematic teaching of a programming language or a particular tool. A very basic introduction is given in the first chapter and then the reader learns whatever is necessary for the solution of her problem. There is more than one way to do it and the problems can be solved by following a basic or a fancy way, depending on the student's computational literacy. The book provides the necessary tools for both. A bibliography is provided at the end of the book, so that the missing pieces of a puzzle can be sought in the literature.

This is also not a computational physics playground. Of course I hope that the reader will have fun doing what is in the book, but my goal is to provide an experience that will set the solid foundation for her becoming a high performance computing, number crunching, heavy duty data analysis expert in the future. This is why the programming language of the core numerical algorithms has been chosen to be Fortran, a highly optimized, scientifically oriented, programming language. The computer environment is set in a Unix family operating system, enriched by all the powerful GNU tools provided by the Free Software Foundation. These tools are indispensable in the complicated data manipulation needed in scientific research, which requires flexibility and imagination. Of course, Fortran is not the best choice for heavy duty object oriented programming, and is not optimal for interacting with the operating system. The philosophy is to let Fortran do what is best for, number crunching, and leave data manipulation and file administration to external, powerful tools. Tools, like awk, shell scripting, gnuplot, Perl and others, are quite powerful and complement all the weaknesses of Fortran mentioned before. The plotting program is chosen to be gnuplot, which provides very powerful tools to manipulate the data and create massive and complicated plots. It can also create publication quality plots and contribute to the "fun part" of the learning experience by creating animations, interactive 3d plots etc. All the tools used in the book are open source software and they are accessible to everyone for free. They can be used in a Linux environment, but they can also be installed and used in Microsoft Windows and Mac OS X.

The other hard part in teaching computational physics to scientists and engineers is to explain that the approach of solving a problem numerically is quite different from solving it analytically. Usually, students of this level are coming with a background in analysis and fundamental physics. It is hard to put them into the mode of thinking about solving a problem using only additions, multiplications and some logical operations. The hardest part is to explain the discretization of a model defined analytically, which can be done in many ways, depending on the accuracy of the approximation. Then, one has to extrapolate the numerical solution, in order to obtain a good approximation of the analytic one. This is done step by step in the book, starting with problems in simple motion and ending with discussing finite size scaling in statistical physics models in the vicinity of a continuous phase transition.

The book comes together with additional material which can be found at the web page of the book. The accompanying software contains all the computer programs presented in the book, together with useful tools and programs solving some of the exercises of each chapter. Each chapter has problems complementing the material covered in the text. The student needs to solve them in order to obtain hands on experience in scientific computing. I hope that I have already stressed enough that, in order for this book to be useful, it is not enough to be read in a cafe or in a living room, but one needs to do what it says.

Hoping that this book will be useful to you as a student or as an instructor, I would like to ask you to take some time to send me feedback for improving and/or correcting it. I would also appreciate fan mail or, if you are an expert, a review of the book. If you use the book in a class, as a main textbook or as supplementary material, I would also be thrilled to know about it. Send me email at and let me know if I can publish, anonymously or not, (part of) what you say on the web page (otherwise I will only use it privately for my personal ego-boost). Well, nothing is given for free: As one of my friends says, some people are payed in dollars and some others in ego-dollars!

Have fun computing scientifically!

Athens, 2014.

. Read also the foreword to the 2nd (C++) Edition