School of Science and Technology

Course Syllabus

General aims for second cycle education

Second-cycle courses and study programmes shall involve the acquisition of specialist knowledge, competence and skills in relation to first-cycle courses and study programmes, and in addition to the requirements for first-cycle courses and study programmes shall
- further develop the ability of students to integrate and make autonomous use of their knowledge
- develop the students' ability to deal with complex phenomena, issues and situations, and
- develop the students' potential for professional activities that demand considerable autonomy, or for research and development work.

(Higher Education Act, Chapter 1, Section 9)

Knowledge and Understanding
After completed studies, the student shall have
- gained insight into the most common problem settings for inverse problems, and
- got acquainted with the most common methods for solving inverse problems.

Competence and Skills
After completed studies, the student shall be able to
- formulate simple inverse problems from relevant applications, and
- analytically identify if an inverse problem is ill posed and suggest a regularization method together with a numerical solution approach.

Judgement and Approach
After completed studies, the student shall be able to
- evaluate the relevance of a numerical solution to an ill posed inverse problem regarding stability, accuracy, efficiency, and applicability.

- Definition and examples of ill posed inverse problems,
- general regularization theory and optimization theory,
- Tikhonov regularization,
- statistical methods for estimation,
- applications to image analysis,
- parameter estimation,
- choice of regularization parameters, and
- regularization through projection.

The teaching will be in the form of lectures and exercises in computer lab.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

For further information, see the university's local examination regulations (in Swedish).

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may prescribe which grading system shall apply. The grade is to be determined by a teacher specifically appointed by the university (an examiner).

According to regulations on grading systems for first- and second-cycle education (vice-chancellor's decision 2010-10-19, reg. no. CF 12-540/2010), one of the following grades is to be used: fail, pass, or pass with distinction. The vice-chancellor or a person appointed by the vice-chancellor may decide on exceptions from this provision for a specific course, if there are special reasons.

Grades used on course are Fail (U), Pass (G) or Pass with Distinction (VG).

For further information, see the university's local examination regulations (in Swedish).

Computational Mathematics, 9 credits, Optimization, 7,5 credits, Differential Equations, 7,5 credits

For further information, see the university's admission regulations (in Swedish).

Students who have previously completed higher education or other activities are, in accordance with the Higher Education Ordinance, entitled to have these credited towards the current programme, providing that the previous studies or activities meet certain criteria.

For further information, see the university's local credit transfer regulations (in Swedish).

Required Reading

Material som tillhandahålls av enheten för matematik.

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