Matematik 2  Forår 2005
Reelle og Komplekse Funktioner
18. kursusgang
Monday, May 2, 2005, 8:15
Room G5112
Schedule

8:158:45

Review in G5112. We will review the residue theorem and give examples.

8:4510:45

Problem session. Work in groups.

10:4512:00

Lecture in G5112. I will give two applications of the residue theorem. The first one is the socalled argument principle. The second application is to improper Riemann integrals of rational functions.
Problems


Fra Eksamen juni 2004: Opgave 1, Opgave 4 (1.4.)

Fra AJ: 7.1.2, 7.1.3

Show, for f, g ∈ H(B(a,r)), with f(a)=g(a)=0, g not identically zero, that lim_{z→ a}(f(z)/g(z))=lim_{z→ a}(f '(z)/g '(z)), provided that the limits exist (i.e. n≥ k, if a is a zero of order n for f and a is a zero of order k for g). This is L'Hospital's rule in the complex case.
Updated April 29, CD.