Asymptotic Solution of Some Diffraction Problems (Classic Reprint) - Hardcover

Joseph Bishop Keller

$9780331426298: Asymptotic Solution of Some Diffraction Problems (Classic Reprint)$

Hardcover

ISBN 10: 0331426293 ISBN 13: 9780331426298

Publisher: Forgotten Books, 2017

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Explore how high-frequency methods reveal the behavior of wave diffraction.

This book explains a practical asymptotic approach to solving boundary-value problems for waves, focusing on how solutions behave as frequency grows large. The leading term matches the familiar geometrical-optics picture, while the method directly builds the full asymptotic expansion without needing exact solutions.

The text presents a clear formulation of the method, then applies it to a range of diffraction problems. It shows how to derive recursive equations along ray paths and how energy conservation emerges in narrow ray tubes. Several canonical geometries are treated, highlighting when the approach gives complete results and when additional techniques are needed for diffracted rays. The work also discusses connections to Maxwell’s and Schr�dinger-type problems, and compares asymptotic results with exact solutions where available.

Learn how to set up an asymptotic expansion for u as frequency grows, and how to interpret the phase and amplitude along rays.
See step-by-step how to derive the eikonal and transport equations that underpin geometrical optics.
Review multiple classic diffraction scenarios, including plane and spherical waves, and waves near curved boundaries.
Understand when the method provides complete answers and when auxiliary methods are required for diffracted components.

Ideal for readers of applied mathematics, physics, and engineering who want a rigorous, hands-on guide to high-frequency wave analysis and diffraction.

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