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.
|
Sec # |
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 |
Math 845, Complex
Analysis II; 9:30-10:20am MWF, 207 JB
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. |
2 |
|
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. |
2 |
|
5.1.3-5.2.2 |
The Laurent
Series. . Infinite Products. |
3 |
|
5.2.4-5.2.5 |
The Gamma
function and the Sterling 's Formula. |
3 |
|
5.4.1-5.4.4 |
The Riemann
Zeta Function. |
4 |
|
5.5.1-5.5.2 |
Equicontinuity,
Normality, and Compactness. |
2 |
|
5.5.3-5.5.4 |
Ascoli-Arzela's Theorem
Normal family of analytic functions |
2 |
|
6.1.1 |
The Riemann
Mapping Theorem. |
4 |
|
6.2.1-6.2.3 |
Conformal
mapping of polygons. The Schwarz-Christoffel Formula. |
4 |
There will be individual projects/tests
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 8, 2026