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This class covers the mathematics of inverse problems involving waves, with examples taken from reflection seismology, synthetic aperture radar, and computerized tomography. There will be occasional problem sets and an oral presentation of a good (landmark, foundational) paper from the literature. Presentations will take place during the class sessions. Topics will be covered such as Scattering Series, inversion, Computerized Tomography and Radon Transform.


This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer need to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.


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Course Credit: MIT

Course Curriculum

Full set of lecture notes in one file 02:15:00
Front Matter, including Table of Contents 00:10:00
Chapter 1 Wave Equations 00:35:00
Chapter 2 Geometrical Optics 00:15:00
Chapter 3 Scattering Series 00:20:00
Chapter 4 Adjoint-state Methods 00:15:00
Chapter 5 Synthetic-aperture Radar 00:30:00
Chapter 6 Computerized Tomography 00:05:00
Chapter 7 Seismic Imaging 00:05:00
Chapter 8 Microlocal Analysis of Imaging 00:20:00
Chapter 9 Optimization 00:05:00
Appendix A Calculus of Variations, Functional Derivatives 00:05:00
Appendix B Finite Difference Methods for Wave Equations 00:05:00
Appendix C Stationary Phase 00:05:00
Submit Your Assignment 00:00:00
Certification 00:00:00

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