Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Programming overview
- 2 Ordinary differential equations
- 3 Root-finding
- 4 Partial differential equations
- 5 Time-dependent problems
- 6 Integration
- 7 Fourier transform
- 8 Harmonic oscillators
- 9 Matrix inversion
- 10 The eigenvalue problem
- 11 Iterative methods
- 12 Minimization
- 13 Chaos
- 14 Neural networks
- 15 Galerkin methods
- References
- Index
1 - Programming overview
Published online by Cambridge University Press: 05 July 2013
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Programming overview
- 2 Ordinary differential equations
- 3 Root-finding
- 4 Partial differential equations
- 5 Time-dependent problems
- 6 Integration
- 7 Fourier transform
- 8 Harmonic oscillators
- 9 Matrix inversion
- 10 The eigenvalue problem
- 11 Iterative methods
- 12 Minimization
- 13 Chaos
- 14 Neural networks
- 15 Galerkin methods
- References
- Index
Summary
A programming language useful to this book must provide a minimal set of components that can be used to combine numbers, compare quantities and act on the result of that comparison, repeat operations until a condition is met, and contain functions that we can use to input data, and output results. Almost any language will suffice, but I have chosen to use Mathematica's programming environment as the vehicle. The reasoning is that 1. The input/output functions of Mathematica are easy to use, and require little additional preparation 2. We will be focused on the ideas, numerical and otherwise, associated with the methods we study, and I want to draw a clear distinction between those ideas and issues of implementation. This book is not meant to teach you everything you need to know about programming – we will discuss only the bare essentials needed to implement the methods. Instead, we will focus on the physical motivation and tools of analysis for a variety of techniques. My hope is that the use of Mathematica allows us to discuss implementation in a homogeneous way, and our restriction to the basic programming structure of Mathematica (as opposed to the higher-level functionality) allows for easy porting to the language of your choice.
- Type
- Chapter
- Information
- Computational Methods for Physics , pp. 1 - 20Publisher: Cambridge University PressPrint publication year: 2013