(Created 2009-08-11.)

Higher education credits: 6. Grading scale: TH. Level: A (Second level). Language of instruction: The course might be given in English. Optional for: D4, E3, F4, Pi3. Course coordinator: Director of Studies, Lars-Christer Böiers, Lars_Christer.Boiers@math.lth.se, Matematik. Recommended prerequisits: FMAF01 Analytic functions or FMA037 Complex Analysis. Assessment: Written and/or oral test, to be decided by the examiner. Further information: The course might be given in English. The course is given every second year, next time in the spring of 2010. Home page: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html.

Aim
The course is designed to be a deepening and continuation of the courses Function Theory/Complex analysis (FMAF01/FMA 037). It aims to exhibit a theory which is useful both within and outside Mathematics. For example is this the case in two-dimensional potential theory, Laplace- and other integral transforms and stability theory in control theory.

Knowledge and understanding
For a passing grade the student must

in his/her own words be able to describe the concepts in the course and their properties.

in his/her own words be able to explain the logical connections between the concepts (definitions, theorems and proofs).

Skills and abilities
For a passing grade the student must

be able to show capability to identify problems which can be modelled with the concepts introduced in the course.

be able to use the concepts in the course in problem solving.

with proper terminology, in a well structured way and with clear logic be able to explain the solution to a problem.

be able to show capability, in the context of problem solving, to develop the theory somewhat further.

have developed his or her ability independently to read and judge mathematical text.

Contents
Analytic continuation. Complex integration. The argument principle. Conformal mappings. Polynomials and their zeroes. Partial fractions, meromorphic functions. Infinite products. Ordinary differential equations. Integral transforms. Asymptotic methods. Potential theory.

Literature
Lecture notes.