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An Introduction to the Mathematical Theory of Waves


About this Title

Roger Knobel, University of Texas-Pan American, Edinburg, TX

Publication: The Student Mathematical Library
Publication Year 2000: Volume 3
ISBNs: 978-0-8218-2039-1 (print); 978-1-4704-2231-8 (online)
DOI: http://dx.doi.org/10.1090/stml/003
MathSciNet review: MR1711746
MSC: Primary 35-01; Secondary 35Lxx, 74Jxx, 76B15, 76D33

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Table of Contents


Part 1. Introduction

  • Chapter 1. Introduction to waves
  • Chapter 2. A mathematical representation of waves
  • Chapter 3. Partial differential equation

Part 2. Traveling and standing waves

  • Chapter 4. Traveling waves
  • Chapter 5. The Korteweg-de Vries equation
  • Chapter 6. The Sine-Gordon equation
  • Chapter 7. The wave equation
  • Chapter 8. D’Alembert’s solution of the wave equation
  • Chapter 9. Vibrations of a semi-infinite string
  • Chapter 10. Characteristic lines of the wave equation
  • Chapter 11. Standing wave solutions of the wave equation
  • Chapter 12. Standing waves of a nonhomogeneous string
  • Chapter 13. Superposition of standing waves
  • Chapter 14. Fourier series and the wave equation

Part 3. Waves in conservation laws

  • Chapter 15. Conservation laws
  • Chapter 16. Examples of conservation laws
  • Chapter 17. The method of characteristics
  • Chapter 18. Gradient catastrophes and breaking times
  • Chapter 19. Shock waves
  • Chapter 20. Shock wave example: Traffic at a red light
  • Chapter 21. Shock waves and the viscosity method
  • Chapter 22. Rarefaction waves
  • Chapter 23. An example with rarefaction and shock waves
  • Chapter 24. Nonunique solutions and the entropy condition
  • Chapter 25. Weak solutions of conservation laws