(Created 2009-08-11.)

ANALYTIC FUNCTIONS, ADVANCED COURSE | FMA130 |

**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 explain the logical connections between the concepts (definitions, theorems and proofs).

*Skills and abilities*

For a passing grade the student must

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.