Preface

Summary

A wave

builds up

perhaps it says its name, I don't understand,

mutters, humps its load

of movement and foam

and withdraws. Who

can I ask what it said to me?

Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study linear wave propagation. This is a book describing such propagation.

I use the equations of linear elasticity to form a context for my description of wave propagation. However, the reader's knowledge of elasticity need not be very great, and experience with a related field theory, such as fluid mechanics or electromagnetic theory, is sufficient to understand what is written here. In many places I treat only the antiplane shear problem because I do not believe that the extra work needed to do the analogous inplane problem adds anything of significance to understanding the underlying wave processes. Nevertheless, where an inplane elastic problem introduces a unique feature, such as the presence of a nondispersive surface wave, that problem is treated.

This is also a book describing the parts of applied mathematics that describe the propagation and scattering of linear elastic waves. It assumes that the reader has a good background in calculus, differential equations, and complex analysis. By this I mean that the reader should have studied most of the topics in Courant and John, Introduction to Calculus and Analysis, Vols. 1 and 2 (1989) and in Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (1992).