Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2001
|
| Schriftenreihe: | Applied Mathematical Sciences
144 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is devoted to the study of the acoustic wave equation and of the Maxwell system, the two most common wave equations encountered in physics or in engineering. The main goal is to present a detailed analysis of their mathematical and physical properties. Wave equations are time dependent. However, use of the Fourier transform reduces their study to that of harmonic systems: the harmonic Helmholtz equation, in the case of the acoustic equation, or the harmonic Maxwell system. This book concentrates on the study of these harmonic problems, which are a first step toward the study of more general time-dependent problems. In each case, we give a mathematical setting that allows us to prove existence and uniqueness theorems. We have systematically chosen the use of variational formulations related to considerations of physical energy. We study the integral representations of the solutions. These representations yield several integral equations. We analyze their essential properties. We introduce variational formulations for these integral equations, which are the basis of most numerical approximations. Different parts of this book were taught for at least ten years by the author at the post-graduate level at Ecole Poly technique and the University of Paris 6, to students in applied mathematics. The actual presentation has been tested on them. I wish to thank them for their active and constructive participation, which has been extremely useful, and I apologize for forcing them to learn some geometry of surfaces |
| Beschreibung: | 1 Online-Ressource (X, 318 p) |
| ISBN: | 9781475743937 9781441928894 |
| DOI: | 10.1007/978-1-4757-4393-7 |
Internformat
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Datensatz im Suchindex
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| author | Nédélec, Jean-Claude |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-4393-7 |
| format | Electronic eBook |
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| isbn | 9781475743937 9781441928894 |
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| spelling | Nédélec, Jean-Claude Verfasser aut Acoustic and Electromagnetic Equations Integral Representations for Harmonic Problems by Jean-Claude Nédélec New York, NY Springer New York 2001 1 Online-Ressource (X, 318 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 144 This book is devoted to the study of the acoustic wave equation and of the Maxwell system, the two most common wave equations encountered in physics or in engineering. The main goal is to present a detailed analysis of their mathematical and physical properties. Wave equations are time dependent. However, use of the Fourier transform reduces their study to that of harmonic systems: the harmonic Helmholtz equation, in the case of the acoustic equation, or the harmonic Maxwell system. This book concentrates on the study of these harmonic problems, which are a first step toward the study of more general time-dependent problems. In each case, we give a mathematical setting that allows us to prove existence and uniqueness theorems. We have systematically chosen the use of variational formulations related to considerations of physical energy. We study the integral representations of the solutions. These representations yield several integral equations. We analyze their essential properties. We introduce variational formulations for these integral equations, which are the basis of most numerical approximations. Different parts of this book were taught for at least ten years by the author at the post-graduate level at Ecole Poly technique and the University of Paris 6, to students in applied mathematics. The actual presentation has been tested on them. I wish to thank them for their active and constructive participation, which has been extremely useful, and I apologize for forcing them to learn some geometry of surfaces Mathematics Global analysis (Mathematics) Engineering Computer engineering Analysis Computational Intelligence Electrical Engineering Ingenieurwissenschaften Mathematik Wellengleichung (DE-588)4065315-8 gnd rswk-swf Integraldarstellung (DE-588)4127585-8 gnd rswk-swf Wellengleichung (DE-588)4065315-8 s Integraldarstellung (DE-588)4127585-8 s 1\p DE-604 Applied Mathematical Sciences 144 (DE-604)BV040244599 144 https://doi.org/10.1007/978-1-4757-4393-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nédélec, Jean-Claude Acoustic and Electromagnetic Equations Integral Representations for Harmonic Problems Applied Mathematical Sciences Mathematics Global analysis (Mathematics) Engineering Computer engineering Analysis Computational Intelligence Electrical Engineering Ingenieurwissenschaften Mathematik Wellengleichung (DE-588)4065315-8 gnd Integraldarstellung (DE-588)4127585-8 gnd |
| subject_GND | (DE-588)4065315-8 (DE-588)4127585-8 |
| title | Acoustic and Electromagnetic Equations Integral Representations for Harmonic Problems |
| title_auth | Acoustic and Electromagnetic Equations Integral Representations for Harmonic Problems |
| title_exact_search | Acoustic and Electromagnetic Equations Integral Representations for Harmonic Problems |
| title_full | Acoustic and Electromagnetic Equations Integral Representations for Harmonic Problems by Jean-Claude Nédélec |
| title_fullStr | Acoustic and Electromagnetic Equations Integral Representations for Harmonic Problems by Jean-Claude Nédélec |
| title_full_unstemmed | Acoustic and Electromagnetic Equations Integral Representations for Harmonic Problems by Jean-Claude Nédélec |
| title_short | Acoustic and Electromagnetic Equations |
| title_sort | acoustic and electromagnetic equations integral representations for harmonic problems |
| title_sub | Integral Representations for Harmonic Problems |
| topic | Mathematics Global analysis (Mathematics) Engineering Computer engineering Analysis Computational Intelligence Electrical Engineering Ingenieurwissenschaften Mathematik Wellengleichung (DE-588)4065315-8 gnd Integraldarstellung (DE-588)4127585-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Engineering Computer engineering Analysis Computational Intelligence Electrical Engineering Ingenieurwissenschaften Mathematik Wellengleichung Integraldarstellung |
| url | https://doi.org/10.1007/978-1-4757-4393-7 |
| volume_link | (DE-604)BV040244599 |
| work_keys_str_mv | AT nedelecjeanclaude acousticandelectromagneticequationsintegralrepresentationsforharmonicproblems |