Matematik 2 - Forår 2005

Reelle og Komplekse Funktioner

Monday, May 2, 2005,  8:15
Room G5-112

Schedule

8:15-8:45

Review in G5-112.  We will review the residue theorem and give examples.

8:45-10:45

Problem session. Work in groups.

10:45-12:00

Lecture in G5-112. I will give two applications of the residue theorem. The first one is the so-called 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.