Matematik 2 - Forår 2005

Reelle og Komplekse Funktioner

Monday, April 7, 2005,  8:15
Room G5-112

Schedule

8:15-8:45

Review in G5-112.  We will review the theorem giving necessary and sufficient conditions for a function to be differentiable in the complex sense, and give more examples.

8:45-10:45

Problem session. Work in groups.

10:45-12:00

Lecture in G5-112. We will prove that a power series is differentiable and that its derivative is given by termwise differentiation. We will introduce exp(z), sin(z), cos(z) as power series.

Problems

From AJ: 2.1.4, 2.1.6, 2.1.8, 2.1.7.

• Possible hint for 2.1.7:  Define S={z \in G | f(z) = f(a) }, for some chosen a \in G. Show that S is closed and open (for this you could use the mean value theorem, 11.34, p.354 in Wade) in G.
• Do the problems you didn't have time to solve last time.