Differential forms:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2019]
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030688152&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xvi, 256 Seiten Diagramme, Porträts |
| ISBN: | 9789813272774 9789811213779 |
Internformat
MARC
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| 245 | 1 | 0 | |a Differential forms |c Victor Guillemin, Peter Haine, Massachusetts Institute of Technology, USA |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a xvi, 256 Seiten |b Diagramme, Porträts | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Differentialform |0 (DE-588)4149772-7 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Haine, Peter |e Verfasser |0 (DE-588)119755873X |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-030688152 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 535 2020 A 3941 |
|---|---|
| DE-BY-TUM_katkey | 2504831 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040008743251 |
| _version_ | 1821934339931242498 |
| adam_text | Contents Preface Introduction Organization Notational Conventions Acknowledgments v v vii xi xii About the Authors xiii Chapter 1.1. 1.2. 1-3· 1.4. 1.5. 1.6. 1.7. 1.8. 1.9. 1. Multilinear Algebra Background Quotient and dual spaces Tensors Alternating k-tensors The space Лк(Ѵ*) The wedge product The interior product The pullback operation on Лк(Ѵ*) Orientations 1 1 4 9 13 19 23 26 29 33 Chapter 2. The Concept of a Differential Form 2.1. Vector fields and 1-forms 2.2. Integral curves for vector fields 2.3. Differential /c-forms 2.4. Exterior differentiation 2.5. The interior product operation 2.6. The pullback operation on forms 2.7. Divergence, curl, and gradient 2.8. Symplectic geometry and classical mechanics 37 37 42 50 53 58 61 68 72 Chapter 3. Integration of Forms 3.1. Introduction 3.2· The Poincaré lemma for compactly supported forms on rectangles The Poincaré lemma for compactly supported forms on open Յ.Յ· subsets of R 81 81 XV 81 86
xvi Contents 3.4. 3.5. 3.6. 3.7. Тће degree of a differentiable mapping The change of variables formula Techniques for computing the degree of a mapping Appendix: Sard’s theorem 88 92 98 106 Chapter 4. Manifolds and Forms on Manifolds 4.1. Manifolds 4.2. Tangentspaces 4.3. Vector fields and differential forms on manifolds 4.4. Orientations 4.5. Integration of forms on manifolds 4.6. Stokes’ theorem and the divergence theorem 4.7. Degree theory on manifolds 4.8. Applications of degree theory 4.9. The index of a vector field 111 111 119 125 133 142 147 153 158 165 Chapters. Cohomology via Forms 5.1. The de Rham cohomology groups of a manifold 5.2. The Mayer-Vietoris sequence 5.3. Cohomology of good covers 5.4. Poincaré duality 5.5. Thom classes and intersection theory 5.6. The Lefschetz theorem 5.7. The Kiinneth theorem 5.8. Čech cohomology 171 171 182 190 197 203 212 221 225 Appendix a. 233 Bump Functions and Partitions of Unity Appendix в. The Implicit Function Theorem 237 Appendix c. Good Covers and Convexity Theorems 245 Bibliography 249 Index of Notation 251 Glossary of Terminology 253
|
| any_adam_object | 1 |
| author | Guillemin, Victor 1937- Haine, Peter |
| author_GND | (DE-588)12110172X (DE-588)119755873X |
| author_facet | Guillemin, Victor 1937- Haine, Peter |
| author_role | aut aut |
| author_sort | Guillemin, Victor 1937- |
| author_variant | v g vg p h ph |
| building | Verbundindex |
| bvnumber | BV045301011 |
| classification_rvk | SK 370 |
| classification_tum | MAT 535 |
| ctrlnum | (OCoLC)1091667816 (DE-599)BVBBV045301011 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV045301011 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T18:23:25Z |
| institution | BVB |
| isbn | 9789813272774 9789811213779 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030688152 |
| oclc_num | 1091667816 |
| open_access_boolean | |
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| owner_facet | DE-703 DE-83 DE-19 DE-BY-UBM DE-739 DE-20 DE-188 DE-384 DE-91G DE-BY-TUM |
| physical | xvi, 256 Seiten Diagramme, Porträts |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | World Scientific |
| record_format | marc |
| spellingShingle | Guillemin, Victor 1937- Haine, Peter Differential forms Differentialform (DE-588)4149772-7 gnd |
| subject_GND | (DE-588)4149772-7 |
| title | Differential forms |
| title_auth | Differential forms |
| title_exact_search | Differential forms |
| title_full | Differential forms Victor Guillemin, Peter Haine, Massachusetts Institute of Technology, USA |
| title_fullStr | Differential forms Victor Guillemin, Peter Haine, Massachusetts Institute of Technology, USA |
| title_full_unstemmed | Differential forms Victor Guillemin, Peter Haine, Massachusetts Institute of Technology, USA |
| title_short | Differential forms |
| title_sort | differential forms |
| topic | Differentialform (DE-588)4149772-7 gnd |
| topic_facet | Differentialform |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030688152&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT guilleminvictor differentialforms AT hainepeter differentialforms |
Inhaltsverzeichnis
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 535 2020 A 3941 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |