Singularity theory is a far-reaching extension of maxima and minima
investigations of differentiable functions, with implications for many
different areas of mathematics, engineering (catastrophe theory and the
theory of bifurcations), and science. The three parts of this first
volume of a two-volume set deal with the stability problem for smooth
mappings, critical points of smooth functions, and caustics and wave
front singularities. The second volume describes the topological and
algebro-geometrical aspects of the theory: monodromy, intersection
forms, oscillatory integrals, asymptotics, and mixed Hodge structures of
singularities.
The first volume has been adapted for the needs of non-mathematicians,
presupposing a limited mathematical background and beginning at an
elementary level. With this foundation, the book's sophisticated
development permits readers to explore more applications than previous
books on singularities.