Holdings: Manifolds, tensor analysis and applications

Manifolds, tensor analysis and applications:

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Bibliographic Details
Main Authors:	Abraham, Ralph (Author), Marsden, Jerrold E. 1942-2010 (Author), Ratiu, Tudor S. (Author)
Format:	Book
Language:	Undetermined
Published:	New York ; Heidelberg <<[u.a.]>> Springer 1988
Edition:	2. ed.
Series:	Applied mathematical sciences 75
Subjects:	Differentialform Mannigfaltigkeit Globale Analysis Tensorrechnung Nichtlineare Analysis Tensoranalysis Dynamisches System
Online Access:	Inhaltsverzeichnis
Physical Description:	654 S. graph. Darst.
ISBN:	3540967907 0387967907

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MARC


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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 Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S.
author_GND	(DE-588)124171141
author_facet	Abraham, Ralph Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S.
author_role	aut aut aut
author_sort	Abraham, Ralph
author_variant	r a ra j e m je jem t s r ts tsr
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bvnumber	BV024663315
classification_rvk	SK 350 SK 370 SK 490
ctrlnum	(OCoLC)230938186 (DE-599)BVBBV024663315
discipline	Mathematik
edition	2. ed.
format	Book
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indexdate	2024-07-09T21:54:13Z
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physical	654 S. graph. Darst.
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spelling	Abraham, Ralph Verfasser aut Manifolds, tensor analysis and applications R. Abraham ; J. E. Marsden ; T. Ratiu 2. ed. New York ; Heidelberg <<[u.a.]>> Springer 1988 654 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 75 Differentialform (DE-588)4149772-7 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Globale Analysis (DE-588)4021285-3 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 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 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 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018074365&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 Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. Manifolds, tensor analysis and applications Differentialform (DE-588)4149772-7 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Globale Analysis (DE-588)4021285-3 gnd Tensorrechnung (DE-588)4192487-3 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Tensoranalysis (DE-588)4204323-2 gnd Dynamisches System (DE-588)4013396-5 gnd
subject_GND	(DE-588)4149772-7 (DE-588)4037379-4 (DE-588)4021285-3 (DE-588)4192487-3 (DE-588)4177490-5 (DE-588)4204323-2 (DE-588)4013396-5
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	Differentialform (DE-588)4149772-7 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Globale Analysis (DE-588)4021285-3 gnd Tensorrechnung (DE-588)4192487-3 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Tensoranalysis (DE-588)4204323-2 gnd Dynamisches System (DE-588)4013396-5 gnd
topic_facet	Differentialform Mannigfaltigkeit Globale Analysis Tensorrechnung Nichtlineare Analysis Tensoranalysis Dynamisches System
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018074365&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT abrahamralph manifoldstensoranalysisandapplications AT marsdenjerrolde manifoldstensoranalysisandapplications AT ratiutudors manifoldstensoranalysisandapplications

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