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An Introduction to Numerical Methods for the Physical Sciences
Beschreibung:
There is only a very limited number of physical systems that can be exactly described in terms of simple analytic functions. There are, however, a vast range of problems which are amenable to a computational approach. This book provides a concise, self-contained introduction to the basic numerical and analytic techniques, which form the foundations of the algorithms commonly employed to give a quantitative description of systems of genuine physical interest. The methods developed are applied to representative problems from classical and quantum physics.
There is only a very limited number of physical systems that can be exactly described in terms of simple analytic functions. There are, however, a vast range of problems which are amenable to a computational approach. This book provides a concise, self-contained introduction to the basic numerical and analytic techniques, which form the foundations of the algorithms commonly employed to give a quantitative description of systems of genuine physical interest. The methods developed are applied to representative problems from classical and quantum physics.
- Preface
- Preliminaries
- Some Elementary Results
- The Numerical Solution of Ordinary Differential Equations
- Case Study: Damped and Driven Oscillations
- Numerical Linear Algebra
- Polynomial Approximations
- Sturm--Liouville Theory
- Case Study: The Quantum Oscillator
- Variational Principles
- Case Study: The Ground State of Atoms
- Bibliography
- Author's Biography
- Index