An introduction puter simulation methods_ applications to physical systems - Harvey Gould.pdf

Chapter 1
Introduction
∞ c 2002 by Harvey Gould, Jan Tobochnik, and Wolfgang Christian
14 January 2002
The importance puters in physics and the nature puter simulation is discussed. The
nature of object-oriented programming and puter languages is also considered.
Importance puters in Physics
Computers are ing increasingly important in how our society anized. Like any new
technology they are affecting how we learn and how we think. Physicists are in the vanguard of the
development of puter hardware and software, putation has e an integral
part of contemporary science. For the purposes of discussion, we divide the use puters in
physics into the following categories:
• numerical analysis
• symbolic manipulation
• simulation
• collection and analysis of data
• visualization
In the numerical analysis mode, the simplifying physical principles are discovered prior to the
computation. For example, we know that the solution of many problems in physics can be reduced
to the solution of a set of simultaneous linear equations. Consider the equations
2x +3y =18
x − y =4.
It is easy to find the analytical solution x =6,y =2using the method of substitution and pencil
and paper. Suppose we have to solve a set of four simultaneous equations. We again can find
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CHAPTER 1. INTRODUCTION 3
an analytical solution, perhaps using a more sophisticated method. However, if the number of
simultaneous equations es much larger, we would have to use numerical methods and a
computer to find a numerical solution. In this mode, puter is a tool of numerical analysis,
and the essential physical principles, for example, the reduction of the problem to the inversion
of a matrix, are included in puter program. Because it is often necessary pute a
multidimensional integral, manipulate large matrices, or solve plex differential equation, this
use of puter is important in physics.
An increasingly important mode putation is symbolic manipulation. As an example,
s