Prerequisites: undergraduate differential equations, functional analysis and numerics
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Content and learning outcomes
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.
Intended learning outcomes
After the course the students are expected to understand basic mathematical and numerical methods to solve inverse problems related to partial differential equations.
Lectures and seminars
Literature and preparations
A Master degree including at least 30 university credits (hp) in Mathematics (including differential equations, functional analysis and numerical analysis).
- (Main course book) Heinz W. Engl, Martin Hanke, Andreas Neubauer, Regulation of Invers Problems, Kluwer Academic Publishers, 2000, ISBN 0-7923-6140-7 (paperback ~$40), 0-7923-4157-0 ( cloth ~$200);
- Curtis R. Vogel, Computational Methods for Inverse Problems, the Society for Industrial and Applied Mathematics, 2002.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
- INL1 - Assignment, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Other requirements for final grade
Home assignments completed
Written exam completed
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.Course web FSF3582