MATH 411  Honors Complex Variables (Fall 2015)
Time and Location
Time: MWF 3:00  3:50 pm Room:
CAB
377
Instructor
Dr. Arno Berger (CAB 683,
berger@ualberta.ca)
Office hours
MWF 4:15  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

Wed 2 Sep

The complex numbers: Algebraic foundations.


2

Fri 4 Sep

Geometric properties.



Mon 7 Sep

No class  Labour Day.


3

Wed 9 Sep

Sequences and series of complex numbers.


4

Fri 11 Sep

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


5

Mon 14 Sep

Limits and continuity.


6

Wed 16 Sep

Linear functions. Complex differentiability.

Handout  Lemma II.6

7

Fri 18 Sep

The CauchyRiemann equations.


8

Mon 21 Sep

Power series: Examples.


9

Wed 23 Sep

More on power series.

Homework deadline changed to Thursday, 3:00 pm.

10

Fri 25 Sep

Path integrals.


11

Mon 28 Sep

The Cauchy Integral Theorem.


12

Wed 30 Sep

The Cauchy Integral formula.

Handout (corrected!)  arbitrary paths

13

Fri 2 Oct

Sequences of analytic functions.


14

Mon 5 Oct

Weierstrass' Theorem.


15

Wed 7 Oct

Morera's Theorem.


16

Fri 9 Oct

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

Handout  Theorem III.32 (proof corrected).


Mon 12 Oct

No class.

Happy Thanksgiving! 

Wed 14 Oct

MIDTERM TEST 1.

Good luck!!

17

Fri 16 Oct

The Open Mapping Theorem and Maximum Modulus Principle.


18

Mon 19 Oct

Isolated singularities.


19

Wed 21 Oct

The CasoratiWeierstrass Theorem.


20

Fri 23 Oct

Laurent series.


21

Mon 26 Oct

More on Laurent series.


22

Wed 28 Oct

The Index (or Winding Number).


23

Fri 30 Oct

The General Cauchy Integral Theorem.


24

Mon 2 Nov

Simply connected regions.


25

Wed 4 Nov

Homotopy. Residues.

Homework 7 deadline changed to Monday, 3:00 pm.

26

Fri 6 Nov

Discrete sets. The Residue Theorem.

Handout  discrete sets.




Enjoy Reading Week. 
27

Mon 16 Nov

Applications of the Residue Theorem.

Handout  Sec. IV.5.


Wed 18 Nov

MIDTERM TEST 2.

Good luck!!

28

Fri 20 Nov

A few theoretical consequences of the Residue Theorem.


29

Mon 23 Nov

The Rouché and Hurwitz theorems.


30

Wed 25 Nov

Conformal mappings.


31

Fri 27 Nov

Conformal automorphisms.


32

Mon 30 Nov

Groups of conformal automorphisms. Examples.


33

Wed 2 Dec

The ArzelàAscoli Theorem.

Handout  ArzelàAscoli Theorem.

34

Fri 4 Dec

The theorems of Montel and Riemann.


35

Mon 7 Dec

Proof of the Riemann Mapping Theorem. Concluding
remarks. 







Good bye and good luck !!







Fri 11 Dec

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

Good luck !! 




