|
Date |
|
Day |
Chapter |
Topics |
| Jan |
9 |
M |
|
Ellipses to Riemann Surfaces |
| |
11 |
W |
|
Cubics, Cardano to Euler and de Moivre |
| |
13 |
F |
|
Complex and Extended Complex Planes |
| |
16 |
M |
|
Holiday |
| |
18 |
W |
|
Riemann Sphere. Stereographic
Projection |
| |
20 |
F |
|
Differentiation |
| |
23 |
M |
|
Entire functions and Mappings |
| |
25 |
W |
|
Meromorphic functions |
| |
27 |
F |
|
Fractional Linear
Transformations/Mobius Transformations |
| |
30 |
M |
|
Integration in Complex Plane/Cauchy's Theorem |
| Feb |
1 |
W |
|
Cauchy Integral Formula |
| |
3 |
F |
|
Generalized
Cauchy Formula |
| |
6 |
M |
|
Power Series/Analytic Functions |
| |
8 |
W |
II.1 |
Laurent Series |
| |
10 |
F |
II.2 |
Calculus of Residues/Rouche's Thm |
| |
13 |
M |
II.4 |
Mapping UHP to Rectangle |
| |
15 |
W |
II.4 |
Schwarz-Christoffel Theorem |
| |
17 |
F |
II.5 |
Harmonic Functions - Poisson's
Integral |
| |
20 |
M |
II.5 |
Dirichlet Problem |
| |
22 |
W |
II.6 |
Fluid
Flow |
| |
24 |
F |
II.6 |
Kutta-Joukowski Theorem |
| |
27 |
M |
II.10 |
Infinite Products/Gamma Function |
| Mar |
1 |
W |
II.10 |
Gamma Function & Watson's Lemma/Laplace's Method |
|
3 |
F |
|
Midterm |
|
Spring
Vacation - Mar 4-12 |
| |
13 |
M |
III.1 |
Conformal Mapping |
| |
15 |
W |
III.2 |
Riemann Mapping Theorem |
| |
17 |
F |
|
Analysis on a Torus - Prelude to Elliptic and Theta Functions |
| |
20 |
M |
|
Modular Transformation - Connect Lattices to Riemann Surfaces |
| |
22 |
W |
III.4 |
Periodic Meromorphic Functions |
| |
24 |
F |
III.4 |
Periodic Entire Functions |
| |
26 |
M |
III.5 |
Weierstrass Elliptic Functions |
| |
29 |
W |
III.5 |
Elliptic Integrals |
|
|
31 |
F |
III.5 |
Spherical Pendulum |
| Apr |
3 |
M |
III.6 |
Jacobi Elliptic Functions |
| |
5 |
W |
III.6 |
Jacobi Elliptic Functions -
Applications |
| |
7 |
F |
III.6 |
Theta Functions |
| |
10 |
M |
III.7 |
Topology of Riemann Surfaces |
| |
12 |
W |
III.7 |
Triangulation and
Classification |
| |
13 |
R |
|
No
Class |
| |
14 |
F |
|
No
Class |
| |
17 |
M |
III.8 |
Analytic Continuation |
| |
19 |
W |
III.8 |
Analytic Continuation |
| |
21 |
F |
|
Riemann Zeta Function |
| |
24 |
M |
|
Huritz Zeta Function |
| |
26 |
W |
|
Prime Number Theorem/The
Riemann Hypothesis |
|
Apr |
28 |
W |
|
Final 11:30-2:30 |