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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

This volume is not part of this online collection, but can be purchased through our online bookstore.

### 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