The implicit function theorem is part of the bedrock of mathematical
analysis and geometry. Finding its genesis in eighteenth century studies
of real analytic functions and mechanics, the implicit and inverse
function theorems have now blossomed into powerful tools in the theories
of partial differential equations, differential geometry, and geometric
analysis.
There are many different forms of the implicit function theorem,
including (i) the classical formulation for Ck functions,
(ii) formulations in other function spaces, (iii) formulations for
non-smooth function, and (iv) formulations for functions with degenerate
Jacobian. Particularly powerful implicit function theorems, such as the
Nash-Moser theorem, have been developed for specific applications (e.g.,
the imbedding of Riemannian manifolds). All of these topics, and many
more, are treated in the present uncorrected reprint of this classic
monograph.
Originally published in 2002, The Implicit Function Theorem is an
accessible and thorough treatment of implicit and inverse function
theorems and their applications. It will be of interest to
mathematicians, graduate/advanced undergraduate students, and to those
who apply mathematics. The book unifies disparate ideas that have played
an important role in modern mathematics. It serves to document and place
in context a substantial body of mathematical ideas.