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The implicit function theorem : history, theory, and applications /

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The implicit function theorem is part of the bedrock of mathematics 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 differen...

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Bibliographic Details
Main Author: Krantz, Steven G. (Steven George), 1951-
Corporate Author: SpringerLink (Online service)
Other Authors: Parks, Harold R., 1949-
Format: eBook
Language:English
Published: Boston : Birkhäuser, [2002]
Subjects:
Implicit functions.
Fonctions implicites.
Implizite Funktion.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Implicit functions
  • An informal version of the implicit function theorem
  • The implicit function theorem paradigm
  • Historical introduction
  • Newton
  • Lagrange
  • Cauchy
  • The inductive proof of the implicit function theorem
  • The classical approach to the implicit function theorem
  • The contraction mapping fixed point principle
  • The rank theorem and the decomposition theorem
  • A counterexample
  • Ordinary differential equations
  • Numerical homotopy methods
  • Equivalent definitions of a smooth surface
  • Smoothness of the distance function
  • The Weierstrass preparation theorem
  • Implicit function theorems without differentiability
  • An inverse function theorem for continuous mappings
  • Some singular cases of the implicit function theorem
  • Analytic implicit function theorems
  • Hadamard's global inverse function theorem
  • The implicit function theorem via the Newton-Raphson method
  • the Nash-Moser implicit function theorem.