Differential Geometry and Mathematical Physics: Part I. Manifolds, Lie Groups and Hamiltonian Systems
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2013
|
| Schriftenreihe: | Theoretical and Mathematical Physics
|
| Schlagworte: | |
| Online-Zugang: | TUM01 UBT01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Differentiable manifolds -- 2 Vector bundles -- 3 Vector fields -- 4 Differential forms -- 5 Lie groups -- 6 Lie group actions -- 7 Linear symplectic algebra -- 8 Symplectic geometry -- 9 Hamiltonian systems -- 10 Symmetries -- 11 Integrability -- 12 Hamilton-Jacobi theory -- References Starting from an undergraduate level, this book systematically develops the basics of• Calculus on manifolds, vector bundles, vector fields and differential forms,• Lie groups and Lie group actions,• Linear symplectic algebra and symplectic geometry,• Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory.The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics.The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.• Calculus on manifolds, vector bundles, vector fields and differential forms,• Lie groups and Lie group actions,• Linear symplectic algebra and symplectic geometry,• Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory.The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics.The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact. |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9789400753457 |
| DOI: | 10.1007/978-94-007-5345-7 |
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| 500 | |a Starting from an undergraduate level, this book systematically develops the basics of• Calculus on manifolds, vector bundles, vector fields and differential forms,• Lie groups and Lie group actions,• Linear symplectic algebra and symplectic geometry,• Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory.The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics.The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. | ||
| 500 | |a The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.• Calculus on manifolds, vector bundles, vector fields and differential forms,• Lie groups and Lie group actions,• Linear symplectic algebra and symplectic geometry,• Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory.The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. | ||
| 500 | |a The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics.The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact. | ||
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Physics | |
| 650 | 4 | |a Topological Groups | |
| 650 | 4 | |a Global analysis | |
| 650 | 4 | |a Global differential geometry | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Mechanics | |
| 650 | 4 | |a Mathematical Methods in Physics | |
| 650 | 4 | |a Global Analysis and Analysis on Manifolds | |
| 650 | 4 | |a Topological Groups, Lie Groups | |
| 650 | 4 | |a Differential Geometry | |
| 700 | 1 | |a Rudolph, Gerd |e Sonstige |4 oth | |
| 700 | 1 | |a Schmidt, Matthias |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804150075000094720 |
|---|---|
| adam_text | DIFFERENTIAL GEOMETRY AND MATHEMATICAL PHYSICS
/ RUDOLPH, GERD
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
1 DIFFERENTIABLE MANIFOLDS
2 VECTOR BUNDLES
3 VECTOR FIELDS
4 DIFFERENTIAL FORMS
5 LIE GROUPS
6 LIE GROUP ACTIONS
7 LINEAR SYMPLECTIC ALGEBRA
8 SYMPLECTIC GEOMETRY
9 HAMILTONIAN SYSTEMS
10 SYMMETRIES
11 INTEGRABILITY
12 HAMILTON-JACOBI THEORY
REFERENCES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
DIFFERENTIAL GEOMETRY AND MATHEMATICAL PHYSICS
/ RUDOLPH, GERD
: 2013
ABSTRACT / INHALTSTEXT
STARTING FROM AN UNDERGRADUATE LEVEL, THIS BOOK SYSTEMATICALLY DEVELOPS
THE BASICS OF • CALCULUS ON MANIFOLDS, VECTOR BUNDLES, VECTOR FIELDS
AND DIFFERENTIAL FORMS, • LIE GROUPS AND LIE GROUP ACTIONS, • LINEAR
SYMPLECTIC ALGEBRA AND SYMPLECTIC GEOMETRY, • HAMILTONIAN SYSTEMS,
SYMMETRIES AND REDUCTION, INTEGRABLE SYSTEMS AND HAMILTON-JACOBI THEORY.
THE TOPICS LISTED UNDER THE FIRST ITEM ARE RELEVANT FOR VIRTUALLY ALL
AREAS OF MATHEMATICAL PHYSICS. THE SECOND AND THIRD ITEMS CONSTITUTE THE
LINK BETWEEN ABSTRACT CALCULUS AND THE THEORY OF HAMILTONIAN SYSTEMS.
THE LAST ITEM PROVIDES AN INTRODUCTION TO VARIOUS ASPECTS OF THIS
THEORY, INCLUDING MORSE FAMILIES, THE MASLOV CLASS AND CAUSTICS. THE
BOOK GUIDES THE READER FROM ELEMENTARY DIFFERENTIAL GEOMETRY TO ADVANCED
TOPICS IN THE THEORY OF HAMILTONIAN SYSTEMS WITH THE AIM OF MAKING
CURRENT RESEARCH LITERATURE ACCESSIBLE. THE STYLE IS THAT OF A
MATHEMATICAL TEXTBOOK,WITH FULL PROOFS GIVEN IN THE TEXT OR AS
EXERCISES. THE MATERIAL IS ILLUSTRATED BY NUMEROUS DETAILED EXAMPLES,
SOME OF WHICH ARE TAKEN UP SEVERAL TIMES FOR DEMONSTRATING HOW THE
METHODS EVOLVE AND INTERACT
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| isbn | 9789400753457 |
| language | English |
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| spelling | Differential Geometry and Mathematical Physics Part I. Manifolds, Lie Groups and Hamiltonian Systems by Gerd Rudolph, Matthias Schmidt Dordrecht Springer Netherlands 2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Theoretical and Mathematical Physics 1 Differentiable manifolds -- 2 Vector bundles -- 3 Vector fields -- 4 Differential forms -- 5 Lie groups -- 6 Lie group actions -- 7 Linear symplectic algebra -- 8 Symplectic geometry -- 9 Hamiltonian systems -- 10 Symmetries -- 11 Integrability -- 12 Hamilton-Jacobi theory -- References Starting from an undergraduate level, this book systematically develops the basics of• Calculus on manifolds, vector bundles, vector fields and differential forms,• Lie groups and Lie group actions,• Linear symplectic algebra and symplectic geometry,• Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory.The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics.The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.• Calculus on manifolds, vector bundles, vector fields and differential forms,• Lie groups and Lie group actions,• Linear symplectic algebra and symplectic geometry,• Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory.The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics.The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact. Mathematische Physik Physics Topological Groups Global analysis Global differential geometry Mathematical physics Mechanics Mathematical Methods in Physics Global Analysis and Analysis on Manifolds Topological Groups, Lie Groups Differential Geometry Rudolph, Gerd Sonstige oth Schmidt, Matthias Sonstige oth https://doi.org/10.1007/978-94-007-5345-7 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025731221&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025731221&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Differential Geometry and Mathematical Physics Part I. Manifolds, Lie Groups and Hamiltonian Systems Mathematische Physik Physics Topological Groups Global analysis Global differential geometry Mathematical physics Mechanics Mathematical Methods in Physics Global Analysis and Analysis on Manifolds Topological Groups, Lie Groups Differential Geometry |
| title | Differential Geometry and Mathematical Physics Part I. Manifolds, Lie Groups and Hamiltonian Systems |
| title_auth | Differential Geometry and Mathematical Physics Part I. Manifolds, Lie Groups and Hamiltonian Systems |
| title_exact_search | Differential Geometry and Mathematical Physics Part I. Manifolds, Lie Groups and Hamiltonian Systems |
| title_full | Differential Geometry and Mathematical Physics Part I. Manifolds, Lie Groups and Hamiltonian Systems by Gerd Rudolph, Matthias Schmidt |
| title_fullStr | Differential Geometry and Mathematical Physics Part I. Manifolds, Lie Groups and Hamiltonian Systems by Gerd Rudolph, Matthias Schmidt |
| title_full_unstemmed | Differential Geometry and Mathematical Physics Part I. Manifolds, Lie Groups and Hamiltonian Systems by Gerd Rudolph, Matthias Schmidt |
| title_short | Differential Geometry and Mathematical Physics |
| title_sort | differential geometry and mathematical physics part i manifolds lie groups and hamiltonian systems |
| title_sub | Part I. Manifolds, Lie Groups and Hamiltonian Systems |
| topic | Mathematische Physik Physics Topological Groups Global analysis Global differential geometry Mathematical physics Mechanics Mathematical Methods in Physics Global Analysis and Analysis on Manifolds Topological Groups, Lie Groups Differential Geometry |
| topic_facet | Mathematische Physik Physics Topological Groups Global analysis Global differential geometry Mathematical physics Mechanics Mathematical Methods in Physics Global Analysis and Analysis on Manifolds Topological Groups, Lie Groups Differential Geometry |
| url | https://doi.org/10.1007/978-94-007-5345-7 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025731221&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025731221&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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