MARC Record from Library of Congress

LEADER: 02514cam a22002774a 4500
001 2002018234
003 DLC
005 20080306082333.0
008 020117s2002 mau b 001 0 eng
010 $a 2002018234
020 $a0817642854 (alk. paper)
020 $a3764342854 (alk. paper)
040 $aDLC$cDLC$dDLC
042 $apcc
050 00 $aQA331.5$b.K712 2002
082 00 $a515/.8$221
100 1 $aKrantz, Steven G.$q(Steven George),$d1951-
245 14 $aThe implicit function theorem :$bhistory, theory, and applications /$cSteven G. Krantz, Harold R. Parks.
260 $aBoston :$bBirkhäuser,$cc2002.
300 $axi, 163 p. ;$c24 cm.
504 $aIncludes bibliographical references (p. [151]-159) and index.
505 8 $aMachine generated contents note: 1 Introduction to the Implicit Function Theorem -- 1.1 Implicit Functions -- 1.2 An Informal Version of the Implicit Function Theorem -- 1.3 The Implicit Function Theorem Paradigm -- 2 History -- 2.1 Historical Introduction -- 2.2 Newton -- 2.3 Lagrange -- 2.4 Cauchy -- 3 Basic Ideas -- 3.1 Introduction -- 3.2 The Inductive Proof of the Implicit Function Theorem -- 3.3 The Classical Approach to the Implicit Function Theorem -- 3.4 The Contraction Mapping Fixed Point Principle -- 3.5 The Rank Theorem and the Decomposition Theorem -- 3.6 A Counterexample -- 4 Applications -- 4.1 Ordinary Differential Equations -- 4.2 Numerical Homotopy Methods -- 4.3 Equivalent Definitions of a Smooth Surface -- 4.4 Smoothness of the Distance Function -- 5 Variations and Generalizations -- 5.1 The Weierstrass Preparation Theorem -- 5.2 Implicit Function Theorems without Differentiability -- 5.3 An Inverse Function Theorem for Continuous Mappings -- 5.4 Some Singular Cases of the Implicit Function Theorem -- 6 Advanced Implicit Function Theorems -- 6.1 Analytic Implicit Function Theorems -- 6.2 Hadamard's Global Inverse Function Theorem -- 6.3 The Implicit Function Theorem via the Newton-Raphson Method -- 6.4 The Nash-Moser Implicit Function Theorem -- 6.4.1 Introductory Remarks -- 6.4.2 Enunciation of the Nash-Moser Theorem -- 6.4.3 First Step of the Proof of Nash-Moser -- 6.4.4 The Crux of the Matter -- 6.4.5 Construction of the Smoothing Operators -- 6.4.6 A Useful Corollary.
650 0 $aImplicit functions.
700 1 $aParks, Harold R.,$d1949-
856 41 $3Table of contents$uhttp://www.loc.gov/catdir/toc/fy033/2002018234.html
856 42 $3Publisher description$uhttp://www.loc.gov/catdir/enhancements/fy0812/2002018234-d.html