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Rays, Waves, and Scattering

Topics in Classical Mathematical Physics
  • John A. Adam and John Adam
Language: English
Published/Copyright: 2017
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About this book

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 contexts
  • Features problems and exercises throughout
  • Includes numerous appendixes, some on topics not often covered
  • An ideal reference book for practitioners
  • Can also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineering
  • Accessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable

Author / Editor information

John A. Adam is professor of mathematics at Old Dominion University. His books include X and the City: Modeling Aspects of Urban Life, Mathematics in Nature: Modeling Patterns in the Natural World, and Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin (all Princeton).

Reviews

"A tour de force of the mathematical description of waves. . . . I sincerely wish I had encountered such a book early in my teaching career. The material presented in it would have provided a very useful enhancement to a number of courses I have taught to undergraduate physics majors over the years."---James A. Lock, American Journal of Physics

Topics

  • Publicly Available

    Frontmatter

    i
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  • Publicly Available

    Contents

    vii
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    Preface

    xvii
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    Acknowledgments

    xxiii
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    Chapter 1. Introduction

    1
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  • Part I. Rays
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    Chapter 2. Introduction to the “Physics” of Rays

    17
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    Chapter 3. Introduction to the Mathematics of Rays

    33
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    Chapter 4. Ray Optics: The Classical Rainbow

    76
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    Chapter 5. An Improvement over Ray Optics: Airy’s Rainbow

    95
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    Chapter 6. Diffraction Catastrophes

    113
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    Chapter 7. Introduction to the WKB(J) Approximation: All Things Airy

    137
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    Chapter 8. Island Rays

    162
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    Chapter 9. Seismic Rays

    173
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  • Part II. Waves
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    Chapter 10. Elastic Waves

    189
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    Chapter 11. Surface Gravity Waves

    200
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    Chapter 12. Ocean Acoustics

    237
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    Chapter 13. Tsunamis

    255
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    Chapter 14. Atmospheric Waves

    273
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  • Part III. Classical Scattering
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    Chapter 15. The Classical Connection

    301
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    Chapter 16. Gravitational Scattering

    316
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    Chapter 17. Scattering of Surface Gravity Waves by Islands, Reefs, and Barriers

    332
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    Chapter 18. Acoustic Scattering

    348
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    Chapter 19. Electromagnetic Scattering: The Mie Solution

    371
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    Chapter 20. Diffraction of Plane Electromagnetic Waves by a Cylinder

    397
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  • Part IV. Semiclassical Scattering
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    Chapter 21. The Classical-to-Semiclassical Connection

    415
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    Chapter 22. The WKB(J) Approximation Revisited

    434
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    Chapter 23. A Sturm-Liouville Equation: The Time-Independent One-Dimensional Schrödinger Equation

    459
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  • Part V. Special Topics in Scattering Theory
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    Chapter 24. The S-Matrix and Its Analysis

    477
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    Chapter 25. The Jost Solutions: Technical Details

    491
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    Chapter 26. One-Dimensional Jost Solutions: The S-Matrix Revisited

    504
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    Chapter 27. Morphology-Dependent Resonances: The Effective Potential

    512
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    Chapter 28. Back Where We Started

    523
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    Appendices

    537
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    Bibliography

    567
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    Index

    585
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
May 22, 2017
eBook ISBN:
9781400885404
Pages and Images/Illustrations in book
https://doi.org/10.1515/9781400885404
eBook ISBN: 9781400885404
Keywords for this book
Scattering; Wavelength; Diffraction; Amplitude; Geometrical optics; Wavefront; Refraction; Wave vector; Ray (optics); Wavenumber; Wave packet; Tsunami; S-wave; Scattering amplitude; Surface wave; Rayleigh scattering; Capillary wave; Approximation; Wave equation; Wavelet; Refractive index; Rayleigh wave; Mie scattering; Wave function; Plane wave; Waveguide; Wave propagation; Gravity wave; Lee wave; Phase (waves); Transverse wave; Wave; Electromagnetic radiation; Polarization (waves); Wave–particle duality; Breaking wave; Atmospheric wave; Rossby wave; Wave power; Equation; Drop (liquid); Multipole expansion; Airy disk; Equatorial waves; Rossby-gravity waves; Acoustic wave; Total internal reflection; Bessel function; Momentum transfer; Scattering theory; Photon; Standing wave; Inviscid flow; Angle of incidence (optics); Airy function; Dimension; Phase velocity; Dispersion relation; Angular momentum; Resonance; Evanescent field; Shock wave; Angular frequency; Hyperbolic function; Radiant energy; Doppler effect; Continuous spectrum; Leaky mode; Penetration depth; Quantum mechanics
Audience(s) for this book
For an expert adult audience, including professional development and academic research
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