Manifolds, tensor analysis and applications:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
New York ; Heidelberg <<[u.a.]>>
Springer
1988
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Applied mathematical sciences
75 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 654 S. graph. Darst. |
| ISBN: | 3540967907 0387967907 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804140076349784064 |
|---|---|
| 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
|
| any_adam_object | 1 |
| 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 |
| building | Verbundindex |
| 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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| id | DE-604.BV024663315 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:54:13Z |
| institution | BVB |
| isbn | 3540967907 0387967907 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018074365 |
| oclc_num | 230938186 |
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| owner | DE-83 |
| owner_facet | DE-83 |
| physical | 654 S. graph. Darst. |
| psigel | TUB-nve |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| series2 | Applied mathematical sciences |
| 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 |