Matematik 2  Forår 2005
Reelle og Komplekse Funktioner
16. kursusgang
Monday, April 25, 2005, 8:15
Room G5112
Schedule

8:158:45

Review in G5112. 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.

8:4510:30

Problem session. Work in groups.

10:3012:00

Lecture in G5112. 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/[(z2)(z5)] and g(z)=1/(z2)^{2} at z=1.

Redo #2.1.9 (reflection principle) using the fact that f is analytic.
Updated April 21, CD.