Manifolds, tensor analysis, and applications:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
[1988]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Applied mathematical sciences
75 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | vii, 654 Seiten Diagramme |
| ISBN: | 0387967907 3540967907 9781461269908 |
Internformat
MARC
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| 245 | 1 | 0 | |a Manifolds, tensor analysis, and applications |c R. Abraham, J.E. Marsden, T. Ratiu |
| 250 | |a Second edition | ||
| 264 | 1 | |a New York |b Springer |c [1988] | |
| 300 | |a vii, 654 Seiten |b Diagramme | ||
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Datensatz im Suchindex
| _version_ | 1804115320692015104 |
|---|---|
| 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 1936- Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. |
| author_GND | (DE-588)115444254 (DE-588)124171141 |
| author_facet | Abraham, Ralph 1936- Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. |
| author_role | aut aut aut |
| author_sort | Abraham, Ralph 1936- |
| author_variant | r a ra j e m je jem t s r ts tsr |
| building | Verbundindex |
| bvnumber | BV000866358 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 |
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| callnumber-search | QA1 |
| callnumber-sort | QA 11 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 350 SK 370 SK 490 |
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| ctrlnum | (OCoLC)18562688 (DE-599)BVBBV000866358 |
| dewey-full | 514/.74 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology 510 - Mathematics |
| dewey-raw | 514/.74 510 |
| dewey-search | 514/.74 510 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV000866358 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:20:44Z |
| institution | BVB |
| isbn | 0387967907 3540967907 9781461269908 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000544111 |
| oclc_num | 18562688 |
| open_access_boolean | |
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| physical | vii, 654 Seiten Diagramme |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| 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 |