** Wiskunde 5, complex function theory**

* Generalities and contents*

Book: S. Lang - Complex Analysis; a course of 9/10 weeks with
approximately the following contents:

Ch 1, Complex numbers and holomorphic functions, 4 hours.

Ch 2, Power series, 4 hours.

Ch 3, Cauchy, integration over paths, homotopy, 4 hours.

Ch 4, Cauchy's theorem, second part, 2 hours.

Ch 5, Application of Cauchy's formula, 4 hours.

Ch 6, Calculus of residues, 4 hours.

Ch 7, §5, Fractional linear transformations, 4 hours.

Ch 13, §1,2, Infinite products and Weierstrass products , 4 hours.

Ch 15, §2, Gamma function, i.h.b. zijn Weierstrass product, 4 hours.

Ch 14, §1,2 Elliptic functions.

* Courses*: Tuesday 11.15-13.00 ZG 8 and
Wednesday 11.15-13.00 ZG 8.

* Exercise classes Tuesday 13.15-16.00 *

M.K. Çamlibel, group 1, ZG 107

G.E. Loots group 2, WSN 39

H. Winkler, group 3, WSN 35

* Homework*.
On the Tuesday course the homework exercise will be given. One is
supposed to hand in the homework next Tuesday morning. The homework
will be corrected and graded by the student-assistent A.C. de Niet. He will
return this homework a week later. There will 8 homeworks. The ``mark for
homework'' will be the average of the 6 best ones.

There will also be a ``midtoets'' and of course a ``tentamen''.
The conditions for passing this course are: tentamen and

the endmark:=
should be
sufficient.

** Week 1, December 4 and 5, 2001**

Approximately Ch 1. in the course. The exercise classes start next week.
The homework exercise is I §3:3 (pag 17).

** Week 2, December 11 and 12**

Approximately Ch 2. in the course. Exercises for Tuesday:

I §2:8,9, I §4:3, Exercise not in the book:

Every complex number is written as with . Are the
following functions holomorphic?

(a) , (b) , (c) .

II §1:,6, II §2:. Homework exercise: II §2:12.

** Week 3, December 18 and 19**

In the course the end of Ch 2. and beginnig Ch 3. Exercises for Tuesday:

II §3:1,2, II §4:1,2, II §5:1,2,3. Homework exercise II §6:6.