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 .

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.