Matematik 2 - Forår 2005

Reelle og Komplekse Funktioner

Monday, April 4, 2005,  8:15
Room G5-112

Schedule

8:15-8:45

Introduction in G5-112. I will give the definition of a complex differentiable function and show that the Cauchy-Riemann equations hold. After this I will give examples, as time permits.

8:45-10:45

Problem session. Work in groups.

10:45-12:00

Lecture in G5-112. We will go over part of Section 2 from AJ¹, especially Theorem 2.4.

Problems

From AJ: 2.1.5, 2.1.1, 2.1.3, 2.1.9.

• The function f(z)=1/(z³ +8) is holomorphic everywhere except where the denominator is 0. (why?). Find the points where f is not holomorphic.
• Show that the Jacobian of a holomorphic function f is |f'(z)|² for every z=(x,y) in the domain of f.