This book offers the first comprehensive introduction to wave scattering in nonstationary materials. G. F. Roach’s aim is to provide an accessible, self-contained resource for newcomers to this important field of research that has applications across a broad range of areas, including radar, sonar, diagnostics in engineering and manufacturing, geophysical prospecting, and ultrasonic medicine such as sonograms.
New methods in recent years have been developed to assess the structure and properties of materials and surfaces. When light, sound, or some other wave energy is directed at the material in question, “imperfections” in the resulting echo can reveal a tremendous amount of valuable diagnostic information. The mathematics behind such analysis is sophisticated and complex. However, while problems involving stationary materials are quite well understood, there is still much to learn about those in which the material is moving or changes over time. These so-called non-autonomous problems are the subject of this fascinating book. Roach develops practical strategies, techniques, and solutions for mathematicians and applied scientists working in or seeking entry into the field of modern scattering theory and its applications.
Wave Scattering by Time-Dependent Perturbations is destined to become a classic in this rapidly evolving area of inquiry.
G. F. Roach is professor emeritus of mathematics at the University of Strathclyde. His books include An Introduction to Linear and Nonlinear Scattering Theory and Green's Functions.
"This book by Roach is clearly written and covers a vast amount of material in a formal manner. As such, the book nicely complements the author's earlier book in the area and can be recommended to anyone interested in an introduction to this important area of applied mathematics."—David L. Colton, SIAM Review
"The book offers a comprehensive introductory text in acoustic wave propagation and scattering by time—dependent perturbations which occur in a broad range of applications, including radar, sonar, engineering diagnostics, geophysical prospecting, ultrasonic medicine, etc. Even though the focus is placed more on the concepts and development of constructive methods rather than on the detailed proofs, the monograph is presented in a way that should appeal to both the theoretical and applied scientist working in the field of modern scattering theory and its applications."—Leon S. Farhy, Mathematical Reviews
"Professor Roach is an acknowledged expert in applied analysis. Wave Scattering by Time-Dependent Perturbations is a significant contribution to the mathematical literature—there are no similar books. There is a need to bring some of this analysis to the attention of those people who actually want to know how best to solve time-dependent scattering problems."—Paul Martin, executive editor of The Quarterly Journal of Mechanics and Applied Mathematics
"This book is an excellent rigorous treatise of modern scattering theory. The main new characteristic is that it places the correct emphasis on non-autonomous problems. I strongly believe that it comes at the appropriate time, as it includes the latest developments in the field. This book is an important and highly instructive piece of work, and an invaluable source of information."—George Makrakis, University of Crete
