Main web page for this course: http://www.math.kth.se/~laptev/KA03/ka03.html
Literature: A. David Wunsch, "Complex Variables
with Applications", Addison-Wesley Publishing Company, Second
Edition, 1994.
You can find information about projects here or here.
|
Date |
Time |
Place |
Topics |
| 01/09 |
10:15 - 12:00 |
D41 |
Complex numbers, domains, limits, and continuity. |
|
02/09 |
08:15 - 10:00 |
D41 |
Analytic functions, Cauchy-Riemann equations. Cauchu-Riemann equations in the polar form. |
|
03/09 |
08:15 - 10:00 |
D41 |
Harmonic functions. Elementary complex functions. |
|
04/09 |
13:15 - 15:00 |
B25 |
Exercises. |
|
05/09 |
08:15 - 10:00 |
D41 |
Argument principle for polynomials. Complex integration.Contour integrals and antiderivatives. |
|
08/09 |
08:15 - 10:00 |
D41 |
Contour integrals and antiderivatives. Cauchy-Goursat theorem. |
|
09/09 |
08:15 - 10:00 |
D41 |
Existence of harmonic conjugate. Cauchy's formula. Fundamental theorem of algebra |
|
10/09 |
08:15 - 10:00 |
D41 |
Problem session |
|
11/09 |
13:15 - 15:00 |
B25 |
Exercises. |
|
12/09 |
10:15 - 12:00 |
D41 |
Generalized Cauchy's formula. Morera theorem. Poisson's formula. Sinularities, zeroes, and poles. |
|
15/09 |
08:15 - 10:00 |
D41 |
Power series. |
|
16/09 |
08:15 - 10:00 |
D41 |
Problem session. |
|
17/09 |
08:15 - 10:00 |
D41 |
Riemann zeta-function, Taylor series. |
|
18/09 |
13:15 - 15:00 |
B25 |
Exercises. |
|
19/09 |
08:15 - 10:00 |
D41 |
Laurent series. Wierstrass-Sohockii theorem. |
|
22/09 |
08:15 - 10:00 |
D41 |
Cauchy's residue theorem. Argument principle. |
|
23/09 |
08:15 - 10:00 |
D41 |
Rouche theorem. Conformal mappings. |
|
24/09 |
08:15 - 10:00 |
D41 |
Problem session. |
|
25/09 |
13:15 - 15:00 |
B25 |
Exercises. |
|
26/09 |
10:15 - 12:00 |
D41 |
Complex sphere, Möbius transformations. |
|
29/09 |
08:15 - 10:00 |
D41 |
Möbius transformations.Classification of conformal automorphisms. |
|
01/10 |
08:15 - 10:00 |
D41 |
Hyperbolic geometry. Riemann mapping theorem. |
|
02/10 |
13:15 - 15:00 |
B25 |
Exercises. |
|
03/10 |
10:15 - 12:00 |
D41 |
Riemann surfaces. Analytic continuation. Schwarz reflection principle. |
|
06/10 |
08:15 - 10:00 |
D41 |
Applications to electrostatics and fluid mechanics. |
|
08/10 |
08:15 - 10:00 |
D41 |
Problem session. |
|
09/10 |
13:15 - 15:00 |
B25 | Exercises. |
|
10/10 |
10:15 - 12:00 |
D41 |
Connections to the probabilities theory,
complex dynamics, statistical physics. |
|
13/10 |
08:15 - 10:00 |
D41 |
Course overview. |
| 15/10 |
08:15 - 10:00 |
D41 |
Project presentation. |
|
23/10 |
Tentamen (questions for oral exam) |