The implicit function theorem is part ofthe 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
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 classicmonograph.
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 placein context a substantial body of mathematical
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