MATH 411  Honors Complex Variables (Fall 2016)
Time and Location
Time: MWF 3:00  3:50 pm Room:
CAB
377
Instructor
Dr. Arno Berger (CAB 683,
berger@ualberta.ca)
Office hours
W 4:15  6:00 pm, R 3:00  6:00 pm or by appointment.
General information
Please see this PDF
document for all relevant details concerning MATH
411. (An abbreviated version of this document will be
distributed in class.)
Course notes
Be prepared to take careful notes in class, as
no set textbook will be used.
The course will loosely follow the fine notes by
Drs. Runde and Bowman (PDF, 4.7MB) which you are very welcome to
use. Be aware, however, that notation and terminology
may differ from those used in class.
Material covered in class (Course Diary)
I plan to keep an uptodate list of the topics, examples etc. covered in class.
Lecture #

Date

Material covered / special events

Remarks/ additional material



WELCOME TO MATH 411 !!


1

Fri 2 Sep

The complex numbers: Algebraic foundations.



Mon 5 Sep

No class  Labour Day.


2

Wed 7 Sep

Geometric properties.


3

Fri 9 Sep

Sequences and series of complex numbers.


4

Mon 12 Sep

A brief review of topological concepts. The extended
complex plane.


5

Wed 14 Sep

Limits and continuity.


6

Fri 16 Sep

Linear functions. Complex differentiability.

Handout  Lemma II.6

7

Mon 19 Sep

The CauchyRiemann equations.


8

Wed 21 Sep

Power series: Examples.


9

Fri 23 Sep

More on power series. Path integrals.


10

Mon 26 Sep

The Cauchy Integral Theorem.


11

Wed 28 Sep

Goursat's Lemma. More general paths.

Handout  arbitrary paths

12

Fri 30 Sep

The Cauchy Integral formula.

Thursday office hours extended to 3:00 
6:00 pm.

13

Mon 3 Oct

Sequences of analytic functions. Weierstrass' Theorem.


14

Wed 5 Oct

Morera's Theorem.


15

Fri 7 Oct

Liouville's Theorem. Fundamental Theorem of
Algebra. Identity Theorem.



Mon 10 Oct

No class.

Happy Thanksgiving! 
16

Wed 12 Oct

The Open Mapping Theorem and Maximum Modulus Principle.


17

Fri 14 Oct

Zeros. Isolated singularities.


18

Mon 17 Oct

The CasoratiWeierstrass Theorem.


19

Wed 19 Oct

Laurent series.



Fri 21 Oct

MIDTERM TEST 1.

Good luck!!

20

Mon 24 Oct

More on Laurent series.


21

Wed 26 Oct

Examples.


22

Fri 28 Oct

The Index (or Winding Number).


23

Mon 31 Oct

The General Cauchy Integral Theorem.


24

Wed 2 Nov

Simply connected regions. Homotopy.


25

Fri 4 Nov

Residues.





Enjoy Reading Week. 
26

Mon 14 Nov

The Residue Theorem.


27

Wed 16 Nov

Applications of the Residue Theorem.

Handout  Sec. IV.2.

28

Fri 18 Nov

More applications of the Residue Theorem.


29

Mon 21 Nov

A few theoretical consequences of the Residue Theorem.


30

Wed 23 Nov

Conformal mappings.



Fri 25 Nov

MIDTERM TEST 2.

Good luck!!

31

Mon 28 Nov

Groups of conformal automorphisms. Examples.


32

Wed 30 Nov

Principles of (pre)compactness.


33

Fri 2 Dec

The ArzelàAscoli Theorem. Montel's Theorem.

Handout  ArzelàAscoli Theorem.

34

Mon 5 Dec

The Riemann Mapping Theorem.


35

Wed 7 Dec

Proof of the Riemann Mapping Theorem. Concluding
remarks. 







Good bye and good luck !!







Tue 20 Dec

Final exam !
Please see box on the left for details.

Good luck !! 




