Holdings: Manifolds, tensor analysis, and applications

Manifolds, tensor analysis, and applications:

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Bibliographic Details
Main Authors:	Abraham, Ralph 1936- (Author), Marsden, Jerrold E. 1942-2010 (Author), Ratiu, Tudor S. (Author)
Format:	Book
Language:	English
Published:	New York Springer [1988]
Edition:	Second edition
Series:	Applied mathematical sciences 75
Subjects:	Analyse globale (Mathématiques) Calcul tensoriel Variétés (Mathématiques) Calculus of tensors Global analysis (Mathematics) Manifolds (Mathematics) Differentialform Globale Analysis Mannigfaltigkeit Nichtlineare Analysis Tensoranalysis Dynamisches System Tensorrechnung
Online Access:	Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	vii, 654 Seiten Diagramme
ISBN:	0387967907 3540967907 9781461269908

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Record in the Search Index

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adam_text	R. ABRAHAM J.E. MARSDEN T. RATIU MANIFOLDS, TENSOR ANALYSIS, AND APPLICATIONS SECOND EDITION SPRINGER CONTENTS PREFACE V BACKGROUND NOTATION VII CHAPTER I TOPOLOGY I 1.1 TOPOLOGICAL SPACES 2 1.2 METRIC SPACES 9 1.3 CONTINUITY 14 1.4 SUBSPACES, PRODUCTS, AND QUOTIENTS 18 1.5 COMPACTNESS 24 1.6 CONNECTEDNESS 31 1.7 BAIRE SPACES 37 CHAPTER 2 BANACH SPACES AND DIFFERENTIAL CALCULUS 40 2.1 BANACH SPACES 40 2.2 LINEAR AND MULTILINEAR MAPPINGS 56 2.3 THE DERIVATIVE 75 2.4 PROPERTIES OF THE DERIVATIVE 83 2.5 THE INVERSE AND IMPLICIT FUNCTION THEOREMS 116 CHAPTER 3 MANIFOLDS AND VECTOR BUNDLES 141 3.1 MANIFOLDS 141 3.2 SUBMANIFOLDS, PRODUCTS, AND MAPPINGS . 150 3.3 THE TANGENT BUNDLE * . .. 157 3.4 VECTOR BUNDLES . 167 3.5 SUBMERSIONS. IMMERSIONS AND TRANSVERSALITY 196 CHAPTER 4 VECTOR FIELDS AND DYNAMICAL SYSTEMS 238 4.1 VECTOR FIELDS AND FLOWS . 238 4.2 VECTOR FIELDS AS DIFFERENTIAL OPERATORS 265 4.3 AN INTRODUCTION TO DYNAMICAL SYSTEMS 298 4.4 FROBENIUS THEOREM AND FOLIATIONS 326 CHAPTER 5 TENSORS 338 5.1 TENSORS IN LINEAR SPACES 338 5.2 TENSOR BUNDLES AND TENSOR FIELDS 349 5.3 THE LIE DERIVATIVE: ALGEBRAIC APPROACH 359 5.4 THE LIE DERIVATIVE: DYNAMIC APPROACH 370 5.5 PARTITIONS OF UNITY 377 CHAPTER 6 DIFFERENTIAL FORMS 392 6.1 EXTERIOR ALGEBRA . 392 6.2 DETERMINANTS. VOLUMES, AND THE HODGE STAR OPERATOR 402 6.3 DIFFERENTIAL FORMS 417 6.4 THE EXTERIOR DERIVATIVE. INTERIOR PRODUCT, AND LIE DERIVATIVE 423 6.5 ORIENTATION, VOLUME ELEMENTS, AND THE CODIFFERENTIAL 450 CHAPTER 7 INTEGRATION ON MANIFOLDS 464 7.1 THE DEFINITION OF THE INTEGRAL 464 7.2 STOKES THEOREM 476 7.3 THE CLASSICAL THEOREMS OF GREEN, GAUSS, AND STOKES 504 7.4 INDUCED FLOWS ON FUNCTION SPACES AND ERGODICITY 513 7.5 INTRODUCTION TO HODGE-DERHAM THEORY AND TOPOLOGICAL APPLICATIONS OF DIFFERENTIAL FORMS 538 CHAPTER 8 APPLICATIONS 560 8.1 HAMILTONIAN MECHANICS 560 8.2 FLUID MECHANICS 584 8.3 ELECTROMAGNETISM 599 8.3 THE LIE-POISSON BRACKET IN CONTINUUM MECHANICS AND PLASMA PHYSICS 609 8.4 CONSTRAINTS AND CONTROL 624 REFERENCES 631 INDEX 643 SUPPLEMENTARY CHAPTERS *AVAILABLE FROM THE AUTHORS AS THEY ARE PRODUCED S-L LIE GROUPS S-2 INTRODUCTION TO DIFFERENTIAL TOPOLOGY S-3 TOPICS IN RIEMANNIAN GEOMETRY
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author	Abraham, Ralph 1936- Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S.
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series	Applied mathematical sciences
series2	Applied mathematical sciences
spelling	Abraham, Ralph 1936- Verfasser (DE-588)115444254 aut Manifolds, tensor analysis, and applications R. Abraham, J.E. Marsden, T. Ratiu Second edition New York Springer [1988] vii, 654 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences Volume 75 Hier auch später erschienene, unveränderte Nachdrucke Analyse globale (Mathématiques) Analyse globale (Mathématiques) ram Calcul tensoriel Calcul tensoriel ram Variétés (Mathématiques) Variétés (Mathématiques) ram Calculus of tensors Global analysis (Mathematics) Manifolds (Mathematics) Differentialform (DE-588)4149772-7 gnd rswk-swf Globale Analysis (DE-588)4021285-3 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 s DE-604 Globale Analysis (DE-588)4021285-3 s Tensorrechnung (DE-588)4192487-3 s Mannigfaltigkeit (DE-588)4037379-4 s Differentialform (DE-588)4149772-7 s 1\p DE-604 Tensoranalysis (DE-588)4204323-2 s 2\p DE-604 Dynamisches System (DE-588)4013396-5 s 3\p DE-604 Marsden, Jerrold E. 1942-2010 Verfasser (DE-588)124171141 aut Ratiu, Tudor S. Verfasser aut Erscheint auch als Online-Ausgabe, eBook 978-1-4612-1029-0 Applied mathematical sciences 75 (DE-604)BV000005274 75 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000544111&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Abraham, Ralph 1936- Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. Manifolds, tensor analysis, and applications Applied mathematical sciences Analyse globale (Mathématiques) Analyse globale (Mathématiques) ram Calcul tensoriel Calcul tensoriel ram Variétés (Mathématiques) Variétés (Mathématiques) ram Calculus of tensors Global analysis (Mathematics) Manifolds (Mathematics) Differentialform (DE-588)4149772-7 gnd Globale Analysis (DE-588)4021285-3 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Tensoranalysis (DE-588)4204323-2 gnd Dynamisches System (DE-588)4013396-5 gnd Tensorrechnung (DE-588)4192487-3 gnd
subject_GND	(DE-588)4149772-7 (DE-588)4021285-3 (DE-588)4037379-4 (DE-588)4177490-5 (DE-588)4204323-2 (DE-588)4013396-5 (DE-588)4192487-3
title	Manifolds, tensor analysis, and applications
title_auth	Manifolds, tensor analysis, and applications
title_exact_search	Manifolds, tensor analysis, and applications
title_full	Manifolds, tensor analysis, and applications R. Abraham, J.E. Marsden, T. Ratiu
title_fullStr	Manifolds, tensor analysis, and applications R. Abraham, J.E. Marsden, T. Ratiu
title_full_unstemmed	Manifolds, tensor analysis, and applications R. Abraham, J.E. Marsden, T. Ratiu
title_short	Manifolds, tensor analysis, and applications
title_sort	manifolds tensor analysis and applications
topic	Analyse globale (Mathématiques) Analyse globale (Mathématiques) ram Calcul tensoriel Calcul tensoriel ram Variétés (Mathématiques) Variétés (Mathématiques) ram Calculus of tensors Global analysis (Mathematics) Manifolds (Mathematics) Differentialform (DE-588)4149772-7 gnd Globale Analysis (DE-588)4021285-3 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Tensoranalysis (DE-588)4204323-2 gnd Dynamisches System (DE-588)4013396-5 gnd Tensorrechnung (DE-588)4192487-3 gnd
topic_facet	Analyse globale (Mathématiques) Calcul tensoriel Variétés (Mathématiques) Calculus of tensors Global analysis (Mathematics) Manifolds (Mathematics) Differentialform Globale Analysis Mannigfaltigkeit Nichtlineare Analysis Tensoranalysis Dynamisches System Tensorrechnung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000544111&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000005274
work_keys_str_mv	AT abrahamralph manifoldstensoranalysisandapplications AT marsdenjerrolde manifoldstensoranalysisandapplications AT ratiutudors manifoldstensoranalysisandapplications

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