An introduction to the mathematical theory of waves
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc. [u.a.]
2000
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| Schriftenreihe: | Student mathematical library
3 : IAS, Park City mathematical subseries |
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| 100 | 1 | |a Knobel, Roger |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to the mathematical theory of waves |c Roger Knobel |
| 264 | 1 | |a Providence, RI |b American Math. Soc. [u.a.] |c 2000 | |
| 300 | |a XIV, 196 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
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| adam_text | Contents
Foreword xi
Preface xiii
Part 1. Introduction
Chapter 1. Introduction to Waves 3
§1.1. Wave phenomena 4
§1.2. Examples of waves 4
Chapter 2. A Mathematical Representation of Waves 7
§2.1. Representation of one dimensional waves 7
§2.2. Methods for visualizing functions of two variables 9
Chapter 3. Partial Differential Equations 13
§3.1. Introduction and examples 13
§3.2. An intuitive view 15
§3.3. Terminology 17
Part 2. Traveling and Standing Waves
Chapter 4. Traveling Waves 23
§4.1. Traveling waves 23
vii
viii Contents
§4.2. Wave fronts and pulses 26
§4.3. Wave trains and dispersion 27
Chapter 5. The Korteweg deVries Equation 31
§5.1. The KdV equation 32
§5.2. Solitary wave solutions 32
Chapter 6. The Sine Gordon Equation 37
§6.1. A mechanical transmission line 37
§6.2. The Sine Gordon equation 38
§6.3. Traveling wave solutions 42
Chapter 7. The Wave Equation 45
§7.1. Vibrating strings 45
§7.2. A derivation of the wave equation 46
§7.3. Solutions of the wave equation 50
Chapter 8. D Alembert s Solution of the Wave Equation 53
§8.1. General solution of the wave equation 53
§8.2. The d Alembert form of a solution 55
Chapter 9. Vibrations of a Semi infinite String 59
§9.1. A semi infinite string with fixed end 59
§9.2. A semi infinite string with free end 64
Chapter 10. Characteristic Lines of the Wave Equation 67
§10.1. Domain of dependence and range of influence 67
§10.2. Characteristics and solutions of the wave equation 69
§10.3. Solutions of the semi infinite problem 73
Chapter 11. Standing Wave Solutions of the Wave Equation 77
§11.1. Standing waves 77
§11.2. Standing wave solutions of the wave equation 78
§11.3. Standing waves of a finite string 80
§11.4. Modes of vibration 83
Contents ix
Chapter 12. Standing Waves of a Nonhomogeneous String 87
§12.1. The wave equation for a nonhomogeneous string 87
§12.2. Standing waves of a finite string 88
§12.3. Modes of vibration 90
§12.4. Numerical calculation of natural frequencies 91
Chapter 13. Superposition of Standing Waves 95
§13.1. Finite superposition 95
§13.2. Infinite superposition 98
Chapter 14. Fourier Series and the Wave Equation 101
§14.1. Fourier sine series 101
§14.2. Fourier series solution of the wave equation 106
Part 3. Waves in Conservation Laws
Chapter 15. Conservation Laws 113
§15.1. Derivation of a general scalar conservation law 113
§15.2. Constitutive equations 116
Chapter 16. Examples of Conservation Laws 119
§16.1. Plug flow chemical reactor 119
§16.2. Diffusion 121
§16.3. Traffic flow 123
Chapter 17. The Method of Characteristics 127
§17.1. Advection equation 127
§17.2. Nonhomogeneous advection equation 131
§17.3. General linear conservation laws 133
§17.4. Nonlinear conservation laws 134
Chapter 18. Gradient Catastrophes and Breaking Times 137
§18.1. Gradient catastrophe 138
§18.2. Breaking time 141
x Contents
Chapter 19. Shock Waves 145
§19.1. Piecewise smooth solutions of a conservation law 145
§19.2. Shock wave solutions of a conservation law 147
Chapter 20. Shock Wave Example: Traffic at a Red Light 153
§20.1. An initial value problem 153
§20.2. Shock wave solution 154
Chapter 21. Shock Waves and the Viscosity Method 159
§21.1. Another model of traffic flow 159
§21.2. Traveling wave solutions of the new model 161
§21.3. Viscosity 163
Chapter 22. Rarefaction Waves 165
§22.1. An example of a rarefaction wave 165
§22.2. Stopped traffic at a green light 169
Chapter 23. An Example with Rarefaction and Shock Waves 173
Chapter 24. Nonunique Solutions and the Entropy Condition 181
§24.1. Nonuniqueness of piecewise smooth solutions 181
§24.2. The entropy condition 183
Chapter 25. Weak Solutions of Conservation Laws 187
§25.1. Classical solutions 187
§25.2. The weak form of a conservation law 188
Bibliography 193
Index 195
|
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| illustrated | Illustrated |
| indexdate | 2024-12-23T15:17:12Z |
| institution | BVB |
| isbn | 0821820397 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008848408 |
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| physical | XIV, 196 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | American Math. Soc. [u.a.] |
| record_format | marc |
| series | Student mathematical library |
| series2 | Student mathematical library |
| spellingShingle | Knobel, Roger An introduction to the mathematical theory of waves Student mathematical library Golven (algemeen, natuurkunde) gtt Mouvement ondulatoire, Théorie du Mouvement ondulatoire, Théorie du ram Partiële differentiaalvergelijkingen gtt Wave-motion, Theory of Wellengleichung (DE-588)4065315-8 gnd Schwingung (DE-588)4053999-4 gnd Schwingungsgleichung (DE-588)4180567-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Wellenbewegung (DE-588)4467376-0 gnd Welle (DE-588)4065310-9 gnd |
| subject_GND | (DE-588)4065315-8 (DE-588)4053999-4 (DE-588)4180567-7 (DE-588)4037952-8 (DE-588)4467376-0 (DE-588)4065310-9 |
| title | An introduction to the mathematical theory of waves |
| title_auth | An introduction to the mathematical theory of waves |
| title_exact_search | An introduction to the mathematical theory of waves |
| title_full | An introduction to the mathematical theory of waves Roger Knobel |
| title_fullStr | An introduction to the mathematical theory of waves Roger Knobel |
| title_full_unstemmed | An introduction to the mathematical theory of waves Roger Knobel |
| title_short | An introduction to the mathematical theory of waves |
| title_sort | an introduction to the mathematical theory of waves |
| topic | Golven (algemeen, natuurkunde) gtt Mouvement ondulatoire, Théorie du Mouvement ondulatoire, Théorie du ram Partiële differentiaalvergelijkingen gtt Wave-motion, Theory of Wellengleichung (DE-588)4065315-8 gnd Schwingung (DE-588)4053999-4 gnd Schwingungsgleichung (DE-588)4180567-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Wellenbewegung (DE-588)4467376-0 gnd Welle (DE-588)4065310-9 gnd |
| topic_facet | Golven (algemeen, natuurkunde) Mouvement ondulatoire, Théorie du Partiële differentiaalvergelijkingen Wave-motion, Theory of Wellengleichung Schwingung Schwingungsgleichung Mathematische Physik Wellenbewegung Welle |
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