The implicit function theorem: history, theory, and applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2003
|
| Edition: | 2. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XI, 163 S. graph. Darst. |
| ISBN: | 0817642854 3764342854 |
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Record in the Search Index
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| adam_text | STEVEN G. KRANTZ HAROLD R. PARKS THE IMPLICIT FUNCTION THEOREM HISTORY,
THEORY, AND APPLICATIONS BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS
PREFACE IX 1 INTRODUCTION TO THE IMPLICIT FUNCTION THEOREM 1 1.1
IMPLICIT FUNCTIONS 1 1.2 AN INFORMAL VERSION OF THE IMPLICIT FUNCTION
THEOREM 3 1.3 THE IMPLICIT FUNCTION THEOREM PARADIGM 7 2 HISTORY 13 2.1
HISTORICAL INTRODUCTION 13 2.2 NEWTON 15 2.3 LAGRANGE 20 2.4 CAUCHY 27 3
BASIC IDEAS 35 3.1 INTRODUCTION 35 3.2 THE INDUCTIVE PROOF OF THE
IMPLICIT FUNCTION THEOREM 36 3.3 THE CLASSICAL APPROACH TO THE IMPLICIT
FUNCTION THEOREM 41 3.4 THE CONTRACTION MAPPING FIXED POINT PRINCIPLE 48
3.5 THE RANK THEOREM AND THE DECOMPOSITION THEOREM 52 3.6 A
COUNTEREXAMPLE 58 4 APPLICATIONS 61 4.1 ORDINARY DIFFERENTIAL EQUATIONS
61 4.2 NUMERICAL HOMOTOPY METHODS 65 VIII CONTENTS 4.3 EQUIVALENT
DEFINITIONS OF A SMOOTH SURFACE 73 4.4 SMOOTHNESS OF THE DISTANCE
FUNCTION 78 5 VARIATIONS AND GENERALIZATIONS 93 5.1 THE WEIERSTRASS
PREPARATION THEOREM 93 5.2 IMPLICIT FUNCTION THEOREMS WITHOUT
DIFFERENTIABILITY 99 5.3 AN INVERSE FUNCTION THEOREM FOR CONTINUOUS
MAPPINGS 101 5.4 SOME SINGULAR CASES OF THE IMPLICIT FUNCTION THEOREM
107 6 ADVANCED IMPLICIT FUNCTION THEOREMS 117 6.1 ANALYTIC IMPLICIT
FUNCTION THEOREMS 117 6.2 HADAMARD S GLOBAL INVERSE FUNCTION THEOREM 121
6.3 THE IMPLICIT FUNCTION THEOREM VIA THE NEWTON-RAPHSON METHOD . 129
6.4 THE NASH-MOSER IMPLICIT FUNCTION THEOREM 134 6.4.1 INTRODUCTORY
REMARKS 134 6.4.2 ENUNCIATION OF THE NASH-MOSER THEOREM 135 6.4.3 FIRST
STEP OF THE PROOF OF NASH-MOSER 136 6.4.4 THE CRUX OF THE MATTER 138
6.4.5 CONSTRUCTION OF THE SMOOTHING OPERATORS 141 6.4.6 A USEFUL
COROLLARY 144 GLOSSARY 145 BIBLIOGRAPHY 151 INDEX 161
|
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| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| indexdate | 2024-07-09T19:57:40Z |
| institution | BVB |
| isbn | 0817642854 3764342854 |
| language | English |
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| spelling | Krantz, Steven G. 1951- Verfasser (DE-588)130535907 aut The implicit function theorem history, theory, and applications Steven G. Krantz ; Harold R. Parks 2. print. Boston [u.a.] Birkhäuser 2003 XI, 163 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Implizite Funktion Implizite Funktion (DE-588)4570203-2 gnd rswk-swf Implizite Funktion (DE-588)4570203-2 s DE-604 Parks, Harold R. Verfasser aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012791333&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krantz, Steven G. 1951- Parks, Harold R. The implicit function theorem history, theory, and applications Implizite Funktion Implizite Funktion (DE-588)4570203-2 gnd |
| subject_GND | (DE-588)4570203-2 |
| title | The implicit function theorem history, theory, and applications |
| title_auth | The implicit function theorem history, theory, and applications |
| title_exact_search | The implicit function theorem history, theory, and applications |
| title_full | The implicit function theorem history, theory, and applications Steven G. Krantz ; Harold R. Parks |
| title_fullStr | The implicit function theorem history, theory, and applications Steven G. Krantz ; Harold R. Parks |
| title_full_unstemmed | The implicit function theorem history, theory, and applications Steven G. Krantz ; Harold R. Parks |
| title_short | The implicit function theorem |
| title_sort | the implicit function theorem history theory and applications |
| title_sub | history, theory, and applications |
| topic | Implizite Funktion Implizite Funktion (DE-588)4570203-2 gnd |
| topic_facet | Implizite Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012791333&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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