18.325 | Fall 2015 | Graduate

Topics in Applied Mathematics: Waves and Imaging


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” 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.

Course Info

As Taught In
Fall 2015
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Problem Sets
Lecture Notes