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 Acoustics, see the book:

Kinsler, Lawrence E. *Fundamentals of Acoustics*. Wiley, 1999. ISBN: 9780471847892.

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" (PDF) 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]

Folland, Gerald B. *Introduction to Partial Differential Equations*. Princeton University Press, 1975. ISBN: 9788120318854.

John, Fritz. *Partial Differential Equations*. Springer, 2013. ISBN: 9781468493351.

Whitham, Gerald Beresford. *Linear and Nonlinear Waves*. Wiley-Interscience, 1999. ISBN: 9780471359425.

"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.