Global analysis: differential forms in analysis, geometry and physics
Saved in:
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English German |
| Published: |
Providence, Rhode Island
American Mathematical Society
2002
|
| Series: | Graduate studies in mathematics
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 343 Seiten Diagramme |
| ISBN: | 0821829513 9780821829516 |
Staff View
MARC
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| 100 | 1 | |a Agricola, Ilka |d 1973- |0 (DE-588)122374029 |4 aut | |
| 240 | 1 | 0 | |a Globale Analysis |
| 245 | 1 | 0 | |a Global analysis |b differential forms in analysis, geometry and physics |c Ilka Agricola, Thomas Friedrich ; translated by Andreas Nestke |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c 2002 | |
| 300 | |a xiii, 343 Seiten |b Diagramme | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 52 | |
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| 650 | 7 | |a Variedades diferenciáveis |2 larpcal | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Differential forms | |
| 650 | 4 | |a Mathematical physics | |
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Record in the Search Index
| _version_ | 1804129337783353344 |
|---|---|
| adam_text | Contents
Preface
v
Chapter
1.
Elements of Multilinear Algebra
1
Exercises
8
Chapter
2.
Differential Forms in Kn
11
§2.1.
Vector Fields and Differential Forms
11
§2.2.
Closed and Exact Differential Forms
18
§2.3.
Gradient, Divergence and Curl
23
§2.4.
Singular Cubes and Chains
26
§2.5.
Integration of Differential Forms and Stokes Theorem
30
§2.6.
The Classical Formulas of Green and Stokes
35
§2.7.
Complex Differential Forms and Holomorphic Functions
36
§2.8.
Brouwer s Fixed Point Theorem
38
Exercises
43
Chapter
3.
Vector Analysis on Manifolds
47
§3.1.
Submanifolds of R
47
§3.2.
Differential Calculus on Manifolds
54
§3.3.
Differential Forms on Manifolds
67
§3.4.
Orientable
Manifolds
69
§3.5.
Integration of Differential Forms over Manifolds
76
§3.6.
Stokes Theorem for Manifolds
79
§3.7.
The Hedgehog Theorem (Hairy Sphere Theorem)
81
xi
-JJ.JJ
Contents
§3.8.
The Classical Integral Formulas
82
§3.9.
The Lie Derivative and the Interpretation of the Divergence
87
§3.10.
Harmonic Functions
94
§3.11.
The Laplacian on Differential Forms
100
Exercises
105
Chapter
4.
Pfaffian Systems
П1
§4.1.
Geometric Distributions HI
§4.2.
The Proof of Frobenius Theorem
116
§4.3.
Some Applications of Frobenius Theorem
120
Exercises
126
Chapter
5.
Curves and Surfaces in Euclidean 3-Space
129
§5.1.
Curves in Euclidean 3-Space
129
§5.2.
The Structural Equations of a Surface
141
§5.3.
The First and Second Fundamental Forms of a Surface
147
§5.4.
Gaussian and Mean Curvature
155
§5.5.
Curves on Surfaces and Geodesic Lines
172
§5.6.
Maps between Surfaces
180
§5.7.
Higher-Dimensional Riemannian Manifolds
183
Exercises
198
Chapter
6.
Lie Groups and Homogeneous Spaces
207
§6.1.
Lie Groups and Lie Algebras
207
§6.2.
Closed Subgroups and Homogeneous Spaces
215
§6.3.
The Adjoint Representation
221
Exercises
226
Chapter
7.
Symplectic Geometry and Mechanics
229
§7.1.
Symplectic Manifolds
229
§7.2.
The Darboux Theorem
236
§7.3.
First Integrals and the Moment Map
238
§7.4.
Completely
Integrable Hamiltonian
Systems
241
§7.5.
Formulations of Mechanics
252
Exercises
264
Chapter
8.
Elements of Statistical Mechanics and Thermodynamics
271
§8.1.
Statistical States of a Hamiltonian System
271
Contents xiii
§8.2. Thermodynamical Systems in
Equilibrium
283
Exercises
292
Chapter
9. Elements
of Electrodynamics
295
§9.1.
The Maxwell Equations
295
§9.2.
The Static Electromagnetic Field
299
§9.3.
Electromagnetic Waves
304
§9.4.
The Relativistic Formulation of the Maxwell Equations
311
§9.5.
The
Lorentz
Force
317
Exercises
325
Bibliography
333
Symbols
337
Index
339
|
| any_adam_object | 1 |
| author | Agricola, Ilka 1973- Friedrich, Thomas 1949-2018 |
| author2 | Nestke, Andreas |
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| author_facet | Agricola, Ilka 1973- Friedrich, Thomas 1949-2018 Nestke, Andreas |
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| author_sort | Agricola, Ilka 1973- |
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| dewey-ones | 514 - Topology |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014560681 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:03:32Z |
| institution | BVB |
| isbn | 0821829513 9780821829516 |
| language | English German |
| lccn | 2002027681 |
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| physical | xiii, 343 Seiten Diagramme |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
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| spelling | Agricola, Ilka 1973- (DE-588)122374029 aut Globale Analysis Global analysis differential forms in analysis, geometry and physics Ilka Agricola, Thomas Friedrich ; translated by Andreas Nestke Providence, Rhode Island American Mathematical Society 2002 xiii, 343 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 52 Formas diferenciais larpcal Formes différentielles Física matemática larpcal Physique mathématique Variedades diferenciáveis larpcal Mathematische Physik Differential forms Mathematical physics Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf Differentialform (DE-588)4149772-7 gnd rswk-swf Globale Analysis (DE-588)4021285-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Globale Analysis (DE-588)4021285-3 s DE-604 Differentialform (DE-588)4149772-7 s Symplektische Geometrie (DE-588)4194232-2 s 1\p DE-604 Friedrich, Thomas 1949-2018 (DE-588)14097413X aut Nestke, Andreas trl Erscheint auch als Online-Ausgabe 978-1-4704-2101-4 Graduate studies in mathematics 52 (DE-604)BV009739289 52 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009899267&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Agricola, Ilka 1973- Friedrich, Thomas 1949-2018 Global analysis differential forms in analysis, geometry and physics Graduate studies in mathematics Formas diferenciais larpcal Formes différentielles Física matemática larpcal Physique mathématique Variedades diferenciáveis larpcal Mathematische Physik Differential forms Mathematical physics Symplektische Geometrie (DE-588)4194232-2 gnd Differentialform (DE-588)4149772-7 gnd Globale Analysis (DE-588)4021285-3 gnd |
| subject_GND | (DE-588)4194232-2 (DE-588)4149772-7 (DE-588)4021285-3 (DE-588)4123623-3 |
| title | Global analysis differential forms in analysis, geometry and physics |
| title_alt | Globale Analysis |
| title_auth | Global analysis differential forms in analysis, geometry and physics |
| title_exact_search | Global analysis differential forms in analysis, geometry and physics |
| title_full | Global analysis differential forms in analysis, geometry and physics Ilka Agricola, Thomas Friedrich ; translated by Andreas Nestke |
| title_fullStr | Global analysis differential forms in analysis, geometry and physics Ilka Agricola, Thomas Friedrich ; translated by Andreas Nestke |
| title_full_unstemmed | Global analysis differential forms in analysis, geometry and physics Ilka Agricola, Thomas Friedrich ; translated by Andreas Nestke |
| title_short | Global analysis |
| title_sort | global analysis differential forms in analysis geometry and physics |
| title_sub | differential forms in analysis, geometry and physics |
| topic | Formas diferenciais larpcal Formes différentielles Física matemática larpcal Physique mathématique Variedades diferenciáveis larpcal Mathematische Physik Differential forms Mathematical physics Symplektische Geometrie (DE-588)4194232-2 gnd Differentialform (DE-588)4149772-7 gnd Globale Analysis (DE-588)4021285-3 gnd |
| topic_facet | Formas diferenciais Formes différentielles Física matemática Physique mathématique Variedades diferenciáveis Mathematische Physik Differential forms Mathematical physics Symplektische Geometrie Differentialform Globale Analysis Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009899267&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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