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I'm really interested on how to simulate physical systems that I'm currently studying as a first year student at University. For example, how to replicate a Pendulum using different algorithms (Euler's formula, RK4, ...), how to draw a vectorial field, how to recreate the N-Body problem and what are the bests current technics, ... The problem is that I didn't find a lot of books on that particular subject, but only "random" articles on them.
Does anybody knows good books about this subject?

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There is a free book online titled Computational Physics and the author is Konstantinos Anagnostopoulos. The book is available for download in PDF format. There are 2 versions of the book. One where the computer codes in the book are in Fortran and another copy for C++. I've only used the Fortran version but I assume the only differences are in the codes.

The approach used in this book is to introduce a topic in physics and to describe problems under the topics. An approach to solving these problems is presented and the author starts introducing computer codes to help. The explanations are not always the best but it does introduce many topics in each chapter and would supplement courses you've had or are taking In many cases the author presents a topic and works through it building up his computer codes in subsequent sections, introducing issues one may encounter on a given topic. The codes are listed line by line in the book. The book covers topics in

  1. Kinematics
  2. Motion of a particle
  3. Planar motion
  4. Motion in space
  5. Electrostatics
  6. Diffusion Equation
  7. Anharmonic oscillator
  8. Schrodinger Equation
  9. Random Walker
  10. Monte Carlo Simulations

and other topics. There is also a chapter in Fortran programming explaining the basics. The C++ version of the book probably covers the same thing in C++.

The prerequisites vary as one gets further into the book. The book starts with topics in kinematics and goes to quantum mechanics. Calculus and differential equations are a must and these are encountered in the early chapters.

In addition to the free book, the site offers free source files for the computer codes the author uses to solve the problems. The codes are written in C++ and Fortran and are described in the book.

In chapter one there are sections on GNUPlot and shell scripting to help the user in plotting and analyzing the simulation data.

The Table of Contents in the book lists the sections in each chapter with names relative to the topics encountered. Downloading and perusing the TOC can help to determine if the book covers topics of interest.

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