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."
General
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