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. |
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/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.