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Bibliographic Details
Main Authors:	Guillemin, Victor 1937- (Author), Haine, Peter (Author)
Format:	Book
Language:	English
Published:	New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2019]
Subjects:	Differentialform
Online Access:	Inhaltsverzeichnis
Physical Description:	xvi, 256 Seiten Diagramme, Porträts
ISBN:	9789813272774 9789811213779

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MARC


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Record in the Search Index

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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
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id	DE-604.BV045301011
illustrated	Illustrated
indexdate	2024-07-10T08:14:16Z
institution	BVB
isbn	9789813272774 9789811213779
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-030688152
oclc_num	1091667816
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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
spelling	Guillemin, Victor 1937- Verfasser (DE-588)12110172X aut Differential forms Victor Guillemin, Peter Haine, Massachusetts Institute of Technology, USA New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2019] © 2019 xvi, 256 Seiten Diagramme, Porträts txt rdacontent n rdamedia nc rdacarrier Differentialform (DE-588)4149772-7 gnd rswk-swf Differentialform (DE-588)4149772-7 s DE-604 Haine, Peter Verfasser (DE-588)119755873X aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf 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 Inhaltsverzeichnis
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

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