The Calculus of Variations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2004
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The calculus of variations has a long history of interaction with other branches of mathematics such as geometry and differential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations. This book is an introduction to the calculus of variations for mathematicians and scientists. The reader interested primarily in mathematics will find results of interest in geometry and differential equations. I have paused at times to develop the proofs of some of these results, and discuss briefly various topics not normally found in an introductory book on this subject such as the existence and uniqueness of solutions to boundary-value problems, the inverse problem, and Morse theory. I have made "passive use" of functional analysis (in particular normed vector spaces) to place certain results in context and reassure the mathematician that a suitable framework is available for a more rigorous study. For the reader interested mainly in techniques and applications of the calculus of variations, I leavened the book with numerous examples mostly from physics. In addition, topics such as Hamilton's Principle, eigenvalue approximations, conservation laws, and nonholonomic constraints in mechanics are discussed. More importantly, the book is written on two levels. The technical details for many of the results can be skipped on the initial reading. The student can thus learn the main results in each chapter and return as needed to the proofs for a deeper understanding |
| Beschreibung: | 1 Online-Ressource (XIV, 292 p) |
| ISBN: | 9780387216973 9780387402475 |
| DOI: | 10.1007/b97436 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/b97436 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:03Z |
| institution | BVB |
| isbn | 9780387216973 9780387402475 |
| language | English |
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| spelling | Brunt, Bruce Verfasser aut The Calculus of Variations by Bruce Brunt New York, NY Springer New York 2004 1 Online-Ressource (XIV, 292 p) txt rdacontent c rdamedia cr rdacarrier Universitext The calculus of variations has a long history of interaction with other branches of mathematics such as geometry and differential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations. This book is an introduction to the calculus of variations for mathematicians and scientists. The reader interested primarily in mathematics will find results of interest in geometry and differential equations. I have paused at times to develop the proofs of some of these results, and discuss briefly various topics not normally found in an introductory book on this subject such as the existence and uniqueness of solutions to boundary-value problems, the inverse problem, and Morse theory. I have made "passive use" of functional analysis (in particular normed vector spaces) to place certain results in context and reassure the mathematician that a suitable framework is available for a more rigorous study. For the reader interested mainly in techniques and applications of the calculus of variations, I leavened the book with numerous examples mostly from physics. In addition, topics such as Hamilton's Principle, eigenvalue approximations, conservation laws, and nonholonomic constraints in mechanics are discussed. More importantly, the book is written on two levels. The technical details for many of the results can be skipped on the initial reading. The student can thus learn the main results in each chapter and return as needed to the proofs for a deeper understanding Mathematics Mathematical optimization Calculus of Variations and Optimal Control; Optimization Mathematik Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s 1\p DE-604 https://doi.org/10.1007/b97436 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brunt, Bruce The Calculus of Variations Mathematics Mathematical optimization Calculus of Variations and Optimal Control; Optimization Mathematik Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4062355-5 |
| title | The Calculus of Variations |
| title_auth | The Calculus of Variations |
| title_exact_search | The Calculus of Variations |
| title_full | The Calculus of Variations by Bruce Brunt |
| title_fullStr | The Calculus of Variations by Bruce Brunt |
| title_full_unstemmed | The Calculus of Variations by Bruce Brunt |
| title_short | The Calculus of Variations |
| title_sort | the calculus of variations |
| topic | Mathematics Mathematical optimization Calculus of Variations and Optimal Control; Optimization Mathematik Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Mathematics Mathematical optimization Calculus of Variations and Optimal Control; Optimization Mathematik Variationsrechnung |
| url | https://doi.org/10.1007/b97436 |
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