Complexe Functies WISB311 Spring 2012

Schedule (rooster)
The class in BLOCK 3 and 4 is held on Mondays, from 9:00 to 10:45, in the room BBL165 of the Buys Ballot Laboratorium. The exercise classes are on Wednesdays, from 11:00 to 12:45, in BBL 061.

Teacher  The teacher of this class is Yuri Kuznetsov, and the teaching assistent is Leslie Molag (l.d.molag@students.uu.nl).
The book  We shall be following the book by Serge Lang Complex analysis, 4th edition. Graduate Texts in Mathematics 103. Springer, 1999.
The exercises  This class has mandatory exercises that count for 10% of the final grade.
The exam   There will be written exams at the end of the BLOCK 3 and 4. Each exam counts for 45% of the final grade.

Results Midterm Exam 18-04-2012

The material
week Material to cover Exercises (Solutions written by Leslie)
Hand in exercise.
(To hand in on week n+1)
BLOK 3
6 Complex numbers. Complex valued functions. Holomorphic functions.
The Cauchy-Riemann equations. Angles under holomorphic maps.		 I§1: 4, 5, 7, 8. I§2: 2, 8, 10, 13.
Exam 2010 Problem 1
I§2: 11,12 (p. 12)
7
 Power series. Convergence radius. Analytic functions.
Differentiation of power series. Analytic ⇒ Holomorphic.		 I§2: 3, 4. I§3: 1, 2, 3, 4. I§4: 5.
 II§2: 8 (p. 59)
8
 Formulas for the convergence radius.
The set of zeroes of an analytic function is discrete. Analytic continuation.		 I§4: 6, 7. II§1: 1, 3, 4. II§2: 1, 3, 4, 5, 10. II§2: 6 (p. 59)
9
 Sums, products, and compositions of convergent power series.
Inverse function of an analytic function.
 II§4: 1, 2. II§2: 7, 11. II§3: 5.
Prove the cases 0 and ∞ of Thm 2.6 (p. 55).
 Hand in
10
 Open mapping theorem. Maximum modulus principle. II§5: 1-6 II§6: 1-6 II§3: 1 (p. 67)
11
 Hertentamen week
12
 Connected topological spaces.
Integrals along piecewise-differentiable paths. Local primitive of a holomorphic function.
 III§2: 1, 3, 4, 8, 9, 10. III§2: 7 (p. 103)
13
 Integrals along continuous paths.
Invariance of the integral under homotopies of paths and of loops.
Global primitives of holomorphic functions.
 III§2: 2, 6.  III§5: 1-4. III§6: 1-4
  III§2: 11
14
 Local Cauchy Integral Formula. Holomorphic ⇒ Analytic. III§6: 5, 6, 7, 8. III§7: 1, 3.
Hand in
15
 Geen hoorcollege (2de Paasdag), wel werkcolege

16
 Deeltentamen I:  Woensdag 18-04-2012, RUPPERT zaal BLAUW, 9.00-12.00
BLOK 4
17
 Laurent series. Isolated singularities: Removable singularities, poles, essential singularities.
 V§2: 4,5,8,9,11,13 V§2: 14 (p. 165)
18
 Geen hoorcollege, wel werkcolege Study V§1 (pp.156-158). V§1: 1-5. V§1: 9 (p. 159)
19
 Winding number. Homologous paths. Chains. Global Cauchy Theorem.
 V§3: 1-5 V§3: 6 (p. 171)
20
 Cauchy Integral Formula. Residues.
 VI§1: 15,16,18,19,26,28 VI §1: 33 (p.189)
21
 Computation of improper definite integrals. VI §2: 1,5,9,10,14,15 Hand in
22
 Hertentamen week
23
 Fractional linear transformations.
 VII §5: 1-5,11 VII §4: 7 (p.230)
24
 Ananlytic automorphisms of the unit disc and the upper half-plane.
Statement of the Riemann Mapping Theorem.		 VI§1: 37, 38. VI §2: 11, 18, 21
25
 Geen hoorcollege, wel werkcolege

26
 Deeltentamen II: Woensdag 27-06-2012, EDUC zaal BETA, 9.00-12.00
34
 Hertentamen: TBA



Last updated: 26 April 2012
 
kuznet@math.uu.nl