Matematik 2  Forår 2005
Reelle og Komplekse Funktioner
11. kursusgang
Monday, April 7, 2005, 8:15
Room G5112
Schedule

8:158:45

Review in G5112. We will review the theorem giving necessary and
sufficient conditions for a function to be differentiable in the complex
sense, and give more examples.

8:4510:45

Problem session. Work in groups.

10:4512:00

Lecture in G5112. 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.
Updated April 4, CD.