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Mathematical methods for wave phenomena. (English) Zbl 0554.35002
Computer Science and Applied Mathematics. Orlando etc.: Academic Press, Inc. (Harcourt Brace Jovanovich, Publishers). XV, 341 p. $ 55.00; £38.50 (1984).
The main difference of this book with respect to others in the same area, consists in the particular attention that the author dedicates to the asymptotic technique for direct scattering problem, that reflects the results of his research.
The topics are written in a very clear and simple style and particularly the last three chapters are very useful for applied mathematicians working in the field of wave phenomena.
In the first 6 chapters some standard problems are presented such eiconal equation, caustics, distribution theory, method of stationary phase, wave equation, Helmholtz and other elliptic equations. Chapter 7, 8 and 9 discuss the most original part of the book and concern: the method of steepest descents (useful for high frequences), the asymptotic techniques for direct scattering and finally the inverse method for reflector imaging with applications on physical optics and seismic problems.
Reviewer: T.Ruggeri

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35P25 Scattering theory for PDEs
78A45 Diffraction, scattering
35Q99 Partial differential equations of mathematical physics and other areas of application
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35L05 Wave equation