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 Laplace Transforms

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

January 22, 2013

MIDTERM EXAM

March , 2013

LAST DAY TO WITHDRAW

March 26, 2013

LAST DAY OF CLASSES

May 8, 2013

FINAL EXAM PERIOD

May 9-15, 2013

 

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, January 9, 2013