Entry requirements

60 credit points within the natural sciences or

technology

including Linear algebra MN1, Analysis MN1 and

Analysis MN2.

Particularly important prerequisites are

convergence of number series and number sequences, the geometry of the complex plane,

polar representation of complex numbers,

elementary functions, the Taylor expansion, derivatives and integrals, line integrals in the plane and Green's formula.

Aims

The goal of the course is to give an introduction to

analytic and harmonic functions.

Content

Complex numbers. Topology in C, limits

and continuity. Analytic and harmonic

functions. Conformal mappings: Möbius

transformations and other elementary functions,

applications to harmonic

functions. Complex integration. Cauchy's

integral formula and its consequences.

Sequences of functions and series of

functions, in particular power series.

Uniform convergence and analyticity.

Laurent series with applications. Zeros and

isolated singularities. Residues and

applications. The argument principle and

Rouches theorem. Power series solutions

of ordinary differential equations.

Julia and Mandelbrot sets.

Instruction

Lectures and the Internet.

Assessment

Written exam and hand-in exercises.