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The implicit function theorem: history, theory, and applications/ Steven G. Krantz, Harold R. Parks.

By: Contributor(s): Publication details: Boston: Birkhäuser, c2002.Description: xi, 163 p.; 24 cmISBN:
  • 0817642854 (alk. paper)
  • 3764342854 (alk. paper)
Subject(s): DDC classification:
  • 515.8 K91i
Online resources:
Partial 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 theor .
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Includes bibliographical references (p. [151]-159) and index.

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 theor .

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