There is not one textbook. The material will be inspired from various sources. Here is a list of references that sometimes go way beyond what we'll do in class.
For Continuum Mechanics, a decent book is:
Spencer, A. J. M. Continuum Mechanics. Dover Publications, 2004. ISBN: 9780486435947. [Preview with Google Books]
For Optics, the best book is:
Born, Max, and Emil Wolf. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Cambridge University Press, 1999. ISBN: 9780521642224. [Preview with Google Books]
For Radar Imaging, see the review article "A Mathematical Tutorial on Synthetic Aperture Radar" by Margaret Cheney as well as her book:
Cheney, Margaret, and Brett Borden. Fundamentals of Radar Imaging. Society for Industrial and Applied Mathematics, 2009. ISBN: 9780898716771. [Preview with Google Books]
For Computerized Tomography, see the book:
Natterer, F., and Frank Wübbeling. Mathematical Methods in Image Reconstruction. Society for Industrial and Applied Mathematics, 2001. ISBN: 9780898714722. [Preview with Google Books]
For Seismology, see the review notes "Mathematics of Reflection Seismology (1995)" by William W. Symes.
For the introductory treatment of Wave Equations, I've used:
Evans, Lawrence C. Partial Differential Equations. American Mathematical Society, 2010. ISBN: 9780821849743. [Preview with Google Books]
"Notes on the Algebraic Structure of Wave Equations" (PDF) by Steven Johnson.
For Geometrical Optics, I like "Lectures on Geometrical Optics" by Professor Jeffrey Rauch.
We gave a Summer School on Waves and Imaging in 2011 in Vancouver, Canada. Some of the material listed there will be useful as well.