AN INTRODUCTION TO CATASTROPHE THEORY AND ITS APPLICATIONS

This article is divided into two parts. In the first we give a description of the basic theorems of elementary catastrophe theory, along with heuristic explanations of why these theorems are valid. In particular, the main ideas in Mather’s proof of Thorn’s classification theorem are presented. The second part contains three applications of catastrophe theory to the buckling of beams, optics, and convex conservation laws. In these sections we attempt to state the problems precisely, to show how catastrophe theory may be used in a mathematically rigorous fashion, and to state what new information can be obtained by the use of catastrophe theory.