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 |
|
1-3 |
Set Theory. Introduction |
5 |
|
4-5 |
Algebraic and Order
Properties of R |
2 |
|
6-7 |
Completeness Property,
Nested Cells |
3 |
|
8-9 |
Vector Spaces. Rn. Topology in Rn |
3 |
|
10 |
The Bolzano-Weierstrass
Theorem |
2 |
|
11 |
The Heine-Borel Theorem |
2 |
|
12 |
Connected Sets |
1 |
|
14-16 |
Convergence of Sequences |
5 |
|
17-18 |
Convergence of Functions |
5 |
|
20 |
Continuous Functions |
2 |
|
22 |
Global Properties of
Continuous Functions |
3 |
|
23 |
Uniform Continuity. Fixed
Points. |
2 |
|
24 |
Bernstein Approximation
Theorem |
3 |
|
26 |
The Stone-Weierstrass
Approximation Theorem |
3 |
Math 745, Complex
Analysis I; 9:30-10:20am MWF, 336 HH
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 |
|
Ch.1/1.1-2.4 |
Complex numbers |
3 |
|
Ch. 2/1.1-2.5 |
Analytic function.
Power series. |
6 |
|
Ch.2/3.1-3.4 |
Some elementary
functions. |
3 |
|
Ch. 3/1.1-2.4 |
Conformal mappings. |
5 |
|
Ch. 3/3.1-4.3 |
Linear
transformations. Riemann surfaces. |
3 |
|
Ch. 4/1.1-1.5 |
Cauchy theorem in a
disk. |
5 |
|
Ch.4/2.1-2.3 |
Cauchy Integral
formula |
3 |
|
Ch. 4/3.1-3.4 |
Local theorems for
analytic functions |
3 |
|
Ch.4/4.1-4.7 |
Cauchy theorem:
general form |
5 |
|
Ch.4/5.1-5.3 |
The calculus of
Residues |
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 Monday, December 8,
2025.