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 $\geq 4$ and
the endmark:= $\frac{midtoets}{3}+\frac{homework}{6}+\frac{tentamen}{2}$ 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 $x+iy$ with $x,y\in {\bf R}$. Are the following functions holomorphic?
(a) $f(x+iy)=x^2+iy^2$, (b) $f(x+iy)=x^2+2ixy-y^2$, (c) $f(x+iy)=x^2+y^2$.
II §1:$1^{a,b,c}$,6, II §2:$4^{a,b,c,h}$. 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.