Matematik 2 - Forår 2005

Reelle og Komplekse Funktioner

Monday, April 25, 2005,  8:15
Room G5-112

Schedule

8:15-8:45

Review in G5-112.  We will review the following result: any holomorphic function is analytic, and give examples. We will also review Cauchy's formula for higher order derivatives.

8:45-10:30

Problem session. Work in groups.

10:30-12:00

Lecture in G5-112. We will discuss types of singularities (removable, pole, essential) and define meromorphic functions.

Problems

From AJ: 5.1.1, 5.1.3 (you can use real analysis methods), 5.1.4 (consider a sequence z_n in C\G with | z_n -a|→ ρ and follow the hint to show that z_n lie in a compact set), 5.1.5

• Find the Taylor expansions and their radii of convergence for f(z)=1/[(z-2)(z-5)] and g(z)=1/(z-2)² at z=1.
• Redo #2.1.9 (reflection principle) using the fact that f is analytic.