Spring 2011
Course Syllabus: Math 656 - 002
Course
Title: |
Complex
Variables I |
Textbook: |
Complex
Variables, M. Ablowitz & A. Fokas + Notes |
Prerequisites: |
Math 545 or Math
645 |
COURSE OUTLINE |
|||
Lect. |
Sections |
Topic |
Assignment |
1 |
1.1, 1.2 |
Complex Numbers
and Fucnctions |
Select Probs. |
2 |
1.2 , 1.3 |
Complex
Functions and Derivatives |
Select Probs. |
3 |
2.1, 2.2 |
Analytic
Functions and Integration |
Select Probs. |
4 |
2.3, 2.4 |
Analytic
Functions and Integration |
Select Probs. |
5 |
2.5, 2.6 |
Complex Integration: Cauchy’s Theorem and
Formulas |
Select Probs. |
6 |
2.6 |
Liouville, Morera and Maximum Modulus Theorems |
Select Probs. |
7 |
3.1, 3.2 |
Series and
Singularities for Complex Functions |
Select Probs. |
8 |
3.2, 3.3 |
Taylor and
Laurent Series |
Select Probs. |
9 |
3.3, 3.4 |
Laurent Series and Singularities |
Select Probs. |
10 |
3.4, 3.5 |
Singularities and Continuation |
Select Probs. |
11 |
3.5, 3.7 |
Singularities and Painlevé
Equations |
Select Probs. |
12 |
3.7, 3.8 |
Computations and Applications for
Singularities |
Select Probs. |
13 |
1.1-3.8 |
Complex Functions: Representations and Applications |
Select Probs. |
14 |
* |
Review
for Midterm Exam |
* |
15 |
* |
MIDTERM
EXAM |
* |
16 |
* |
Spring
Recess |
*. |
17 |
* |
Spring
Recess |
* |
18 |
4.1 |
Residue
Calculus: Cauchy’s Theorem |
Select Probs. |
19 |
4.2, 4.3 |
Applications of Residue Theory: Definite
Integrals |
Select Probs. |
20 |
4.3 |
Applications of Residue Theory: More
Integrals |
Select Probs. |
21 |
4.4 |
Applications of Residue Theory: Argument
Principle |
Select Probs. |
22 |
4.4 |
Applications of Residue Theory: Rouché’s Theorem |
Select Probs. |
23 |
4.4, 4.5 |
More
Applications: Fourier and |
Select Probs. |
24 |
4.1-4.6 |
Overview of
Residue Theory and Applications |
Select Probs. |
25 |
5.1, 5.2 |
Conformal Maps
and Their Inverses |
Select Probs. |
26 |
5.2, 5.3 |
Conformal Maps
and Their Applications |
Select Probs. |
27 |
5.3, 5.4 |
Conformal Maps
and Their Applications |
Select Probs. |
28 |
5.5, 5.6 |
Riemann Mapping
and Schwarz-Christoffel Theorems |
Select Probs. |
29 |
5.1-5.6 |
Overview of
Conformal Maps |
Select Probs |
30 |
* |
Review
for FINAL EXAM |
* |
IMPORTANT DATES |
|
FIRST DAY OF SEMESTER |
|
MIDTERM EXAM |
|
LAST |
|
LAST |
|
FINAL EXAM PERIOD |
|
Grading Policy
Assignment Weighting |
|
Homework |
15% |
Midterm Exam |
35% |
Final Exam |
50 % |
Course Policies (optional)
Important Departmental and University Policies
Prepared by Prof. Denis Blackmore,