Current Courses and Seminars

Spring 2024 (under construction)

Office hours: MWF 10:30-11:30 am and by appointment

Math 640, Advanced Calculus II; 8:30-9:20am MWF, 109 LH

Text: The Elements of Real Analysis, by Robert G. Bartle, Second Edition.

The number of classroom hours to be spent on each topic is approximate.

 

Sections

Topic

Class meetings

27-28

The Mean Value Theorem and Applications

4

29-30

Riemann-Stieltjes Integral

12

32-33

Improper Integrals

3

34-36

Infinite series

5

37

Series of Functions

3

39-40

The Derivative in Rn

5

41

Mapping Theorems

3

42

Extremum Problems

3

There will be individual projects/tests during the semester (about 100 pts. each). Final exam (200 pts.) is scheduled for 7:00 - 8:50 AM (notice different time!) on Wednesday, May 8, 2024

 

 

Math 845, Complex Analysis II; 9:30-10:20am MWF, 109 LH

Text Complex Analysis by Lars V. Ahlfors, 3rd ed.

The number of classroom hours to be spent on each topic is approximate.

 

Chapters/Sections

Topic

Class meetings

4.6.1-4.6.2

Harmonic functions. Laplace's equation. Mean value theorem.

 

4.6.3-4.6.5

Poisson formula. Schwarz’s Theorem. The Reflection Principle.

 

3

5.1.1-5.1.2

Weierstrass's Theorem. Theorem of Hurwitz. The Taylor Series.

 

5.1.3-5.2.2

The Laurent Series. . Infinite Products.

5.2.4-5.2.5

The Gamma function and the Sterling 's Formula.

 

5.4.1-5.4.4

The Riemann Zeta Function.

       

5.5.1-5.5.2

Equicontinuity, Normality, and Compactness.

 

5.5.3-5.5.4

Ascoli-Arzela's Theorem Normal family of analytic functions

 

6.1.1

The Riemann Mapping Theorem.

6.2.1-6.2.3

Conformal mapping of polygons. The Schwarz-Christoffel Formula.

 

 

There will be individual projects/tests/presentations during the semester (about 100 pts. each). Final exam (200 pts.) is scheduled for 9:00-10:50 AM (notice different time!) on Monday, May 6, 2024.

 


Research interests and publications

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