Course
Outline - Mat 70400 - Spring 2014
Course meetings, Tues
-Thurs 2:30 PM - 4:00 PM pm Room 6417
Texts: Complex Analysis by L. Ahlfors, McGraw Hill.
Conformal Invariants by L. Ahlfors, AMS Chelsea.
Hyperbolic Geometry from a
local viewpoint, L. Keen, N. Lakic, Cambridge Other
texts
Instructor:
Prof. Keen. Office Room 4208.01 Phone 212
817 8531 or email lkeen@gc.cuny.edu Office hours: By
appointment
Outline
This is the second semester and will be a continuation of the course in Fall 2013. Assignments will be from the above texts or as indicated below.
Contents of the course will include:
Normal Families, Equicontinuity, Arzela's Theorem, The Riemann Mapping Theorem, Dirichlet's Problem Explicit
Conformal Maps
Elliptic Functions, General Theory of Periodic functions, Weierstrass Theory Linear
An introduction to hyperbolic geometry, Uniformization
Distortion Theorems
If there is time we will talk about quasi-conformal mappings and the basics of complex dynamics
Homework assignments will appear on this page
approximately every week. Students are strongly advised to work on all the
homework problems to make sure they are keeping pace with the class.
The final grade will be based only on the homework grades.
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Date |
Class
Topic |
Reading
and Assignment |
Jan 28 | Equicontinuity and Normal Families,Ahlfors, Chap 5, sec 4 | |
Jan 30 | Class Cancelled | Chap 5, sec 4, 4.5/1,2 due 2/1 1 |
Feb 4 | Normal Families Cont'd. Riemann Mapping Theorem | Chap 5, sec 4, 4.5/1,2 due 2/1 1 |
Feb 6 | Riemann Mapping Theorem, Reflection Principle | no assignment |
Feb 11 | Mappings of Polygons | Chap 6, sec 2, 2.2/1,3 due 2/18 |
Feb 13 | Rectangles and Triangles, Harmonic functions | Chap 6, sec 2, 2.3/1,3 due 2/20 |
Feb 18 | Harnack's principle, Dirichlet Problem | Chap 6, sec 2, 3 2.3/1,3 due 2/20 |
Feb 20 | Rectangles and Triangles, Harmonic functions | Chap 6, sec 3, 4 sec 4.1/1,2 due 3/4 |
Feb 22 | No Class Monday classes | |
Feb 25 | Dirichet Problem, Canonical Domains | Chap. 6, sec 5.1/1,2 Due Mar 11 |
Feb 27 | Green's Functions, Periodic Functions | Chap 6, Sec 5.2/1,2 Due Mar 13 |
Mar 4 | Elliptic Functions | |
Mar 6 | Elliptic Functions, cont'd. | Mar 11 | Elliptic Functions, cont'd. | Mar 13 | Elliptic Functions, cont'd. | Chap 7, sec 3.21,2 Due Mar 18 | Mar 18 | Elliptic Functions, cont'd. | Chap 7, sec 3.3/1,2,3,4,5,6,7 Due Mar 25 | Mar 20 | Elliptic Functions, cont'd. | Mar 25 | Analytic continuation. | Mar 27 | Riemann surfaces, flows | Apr 1 | Riemann surfaces. | Apr 3 | Riemann surfaces, cont'd. | Exercise Sheet due Apr 24 | Apr 8 | Univalent functions | Apr 10 | Univalent functions, cont'd. | Apr 15,17,22 | Spring Break |