Rays, Waves, and Scattering : : Topics in Classical Mathematical Physics / / John A. Adam.

• Superior document: Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package
• VerfasserIn: Adam, John A.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2017]; ©2017
• Year of Publication: 2017
• Language: English
• Series: Princeton Series in Applied Mathematics ; 56
• Physical Description: 1 online resource (616 p.) :; 126 line illus.

This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas.Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes.Provides a panoramic look at wave motion in many different contextsFeatures problems and exercises throughoutIncludes numerous appendixes, some on topics not often coveredAn ideal reference book for practitionersCan also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineeringAccessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable

Table of Contents

Frontmatter -- Contents -- Preface -- Acknowledgments -- Chapter 1. Introduction -- Part I. Rays -- Chapter 2. Introduction to the "Physics" of Rays -- Chapter 3. Introduction to the Mathematics of Rays -- Chapter 4. Ray Optics: The Classical Rainbow -- Chapter 5. An Improvement over Ray Optics: Airy's Rainbow -- Chapter 6. Diffraction Catastrophes -- Chapter 7. Introduction to the WKB(J) Approximation: All Things Airy -- Chapter 8. Island Rays -- Chapter 9. Seismic Rays -- Part II. Waves -- Chapter 10. Elastic Waves -- Chapter 11. Surface Gravity Waves -- Chapter 12. Ocean Acoustics -- Chapter 13. Tsunamis -- Chapter 14. Atmospheric Waves -- Part III. Classical Scattering -- Chapter 15. The Classical Connection -- Chapter 16. Gravitational Scattering -- Chapter 17. Scattering of Surface Gravity Waves by Islands, Reefs, and Barriers -- Chapter 18. Acoustic Scattering -- Chapter 19. Electromagnetic Scattering: The Mie Solution -- Chapter 20. Diffraction of Plane Electromagnetic Waves by a Cylinder -- Part IV. Semiclassical Scattering -- Chapter 21. The Classical-to-Semiclassical Connection -- Chapter 22. The WKB(J) Approximation Revisited -- Chapter 23. A Sturm-Liouville Equation: The Time-Independent One-Dimensional Schrödinger Equation -- Part V. Special Topics in Scattering Theory -- Chapter 24. The S-Matrix and Its Analysis -- Chapter 25. The Jost Solutions: Technical Details -- Chapter 26. One-Dimensional Jost Solutions: The S-Matrix Revisited -- Chapter 27. Morphology-Dependent Resonances: The Effective Potential -- Chapter 28. Back Where We Started -- Appendices -- Bibliography -- Index