Spring 2014 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

1/23

1.1

Complex Numbers and Their Properties

Select Probs.

1/27

1.2

Elementary Functions and Stereographic Projection

Select Probs.

1/30

1.3, 1.4

Limits, Continuity, Analyticity

Select Probs.

2/3

1.4, 2.1

Analytic Functions

Select Probs.

2/6

2.1

Analytic Functions

Select Probs.

2/10

2.1, 2.2

Multivalued Functions

Select Probs.

2/13

2.2

Multivalued Functions

Select Probs.

2/17

2.3

Multivalued Functions and Riemann Surfaces

Select Probs.

2/20

2.4

Complex Integration

Select Probs.

2/24

 2.4, 2.5

Complex Integration and Cauchy’s Theorem

Select Probs.

2/27

2.5, 2.6

 Cauchy’s Theorem and Cauchy’s Integral Formula

Select Probs.

3/3

2.6

Extended Cauchy’s Integral Formula

Select Probs.

3/6

2.6

Liouville, Morera and Maximum Modulus Theorems

Select Probs.

3/10

Review for Midterm Exam

3/13

MIDTERM EXAM: March 13, 2014

3/17-22

Spring Recess

3/24

3. 1

Complex Series and Basic Properties

Select Probs.

3/27

3.2

Taylor Series

Select Probs.

3/31

3.3

Laurent Series

Select Probs.

4/3

3.4

Theoretical Results for Series

Select Probs.

4/7

3.5

Singularities, Analytic Continuation, and Natural Boundaries

Select Probs.

4/10

3.6

Infinite Products and Mittag-Leffler Expansions

Select Probs.

4/14

4.1

Cauchy Residue Theorem

Select Probs.

4/17

4.2

Applications: Evaluation of Improper Definite Integrals

Select Probs.

4/21

4.2, 4.3

Applications: Evaluation of Certain Definite Integrals

Select Probs.

4/24

4.3

Applications: Integrals with Branch Points

Select Probs.

4/28

4.4

The Argument Principle and Rouche’s Theorem

Select Probs.

5/1

 

Applications: Mappings, Inviscid Fluid Flow, Electrostatics

Select Probs.

5/5

Review for FINAL EXAM

 

 

IMPORTANT DATES

FIRST DAY OF SEMESTER

January 21, 2014

MIDTERM EXAM

March 13, 2014

LAST DAY TO WITHDRAW

March 31, 2014

LAST DAY OF CLASSES

May 6, 2014

FINAL EXAM PERIOD

May 8-14, 2014

 

Grading Policy

 

Assignment Weighting

Homework

20%

Midterm Exam

35%

Final Exam

45%

 

 

Course Policies (optional)

 

 

­Important Departmental and University Policies

 

 

Prepared by Prof. Victor Matveev, December 8, 2014