These notes give a fairly elementary introduction to the local
theory of differentiable mappings. Sard's Theorem and the
Preparation Theorem of Malgrange and Mather are the basic tools and
these are proved first. There follows a number of illustrations
including: the local part of Whitney's Theorem on mappings of the
plane into the plane, quadratic differentials, the Instability
Theorem of Thom, one of Mather's theorems on finite determinacy and
a glimpse of the theory of Toujeron. The later part of the book
develops Mather's theory of unfoldings of singularities. Its
application to Catastrophe theory is explained and the Elementary
Catastrophes are illustrated by many pictures. The book is suitable
as a text for courses to graduates and advanced undergraduates but
may also be of interest to mathematical biologists and economists.
General
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