Inverse Problems



Graduate course 2D5245, 7.5 credits, starting Tuesday September 11th (2012) at 13.15-15 in room 3733, KTH (math).

Preliminary Schedule: Thuesdays 13.15 - 15.00, until December, in room 3733, Lindstedtsvagen 25, KTH.


Goal: to understand basic mathematical and numerical methods to solve inverse problems related to partial differential equations.

Some topics: ill-posed problems and their numerical solution by regularization methods, regularization of linear problems, Tikhonov regularization, regularization of non linear problems.

Some applications: differentation as an invers problem, X-ray tomography, data-assimilation for weather and climate prediction, inverse scattering, optimal design, image processing, parameter identification.

Prerequisites: undergraduate differential equations, functional analysis and numerics.

Literature:

Plan:

Homework: Here is a preliminary list of questions to prepare for the exam. The exam consists of five questions related to the list.

Presentations:
To pass the course requires atleast 15 credits. A good answer on a question in the exam gives 2 credits. A good solution of a homework problem gives 2 credits. A good presentation gives 5 credits. Therefore one obtains 25 = 5x2 + 5x2 + 5 credits if everything is good.

Welcome!
Anders Szepessy,
szepessy@kth.se, 790 7494