18.325 | Fall 2015 | Graduate

Topics in Applied Mathematics: Waves and Imaging


Problem Sets

1 Solve exercises 2, 3, 7, and 8 in the exercises section at the end of Chapter 1 (PDF) in the lecture notes.
2 Solve exercises 2, 5, and 7 in the exercises section at the end of Chapter 3 (PDF) in the lecture notes.
3 Do Problem Set 3 (PDF). Download and load the dataset ct.mat (MAT) in MATLAB®
4 Solve exercise 3 in Chapter 3 (PDF), exercise 1 in Chapter 5 (PDF), and exercise 2 in Chapter 2 (PDF) in the lecture notes.


Students are required to give an oral presentation of a good (landmark, foundational) paper from the literature. The presentations will take place during the last two class sessions.

The following is a list of some advanced papers. Some may be adequate for the term paper presentation.

Lewis, R., and W. Symes. “On the Relation Between the Velocity Coefficient and Boundary Value for Solutions of the One-dimensional Wave Equation.” Inverse Problems 7, no. 4 (1991): 597–631.

Beylkin, Gregory. “Imaging of Discontinuities in the Inverse Scattering Problem by Inversion of a Causal Generalized Radon Transform.” Journal of Mathematical Physics 26, no. 1 (1985): 99.

Kroode, A. P. E. ten, D. -J. Smit, et al. “A Microlocal Analysis of Migration.” Wave Motion 28, no. 2 (1998): 149–72.

Bruckstein, Alfred M., Bernard C. Levy, et al. “Differential Methods in Inverse Scattering.” Society of Industrial and Applied Mathematics 45, no. 2 (1985): 312–35.

Gelfand, I. M., and B. M. Levitan. “On the Determination of a Differential Equation from its Spectral Function.” Izvestiya Rossiiskoi Akademii Nauk Seriya Matematicheskaya 15, no. 4 (1951): 309–60.

Course Info

As Taught In
Fall 2015
Learning Resource Types
Problem Sets
Lecture Notes