| Week |
Lecture |
Subject |
reading |
| Week0 |
Lecture0 (9/24) |
Course Introduction, Catesian and polar forms |
NA |
| Week1 |
Lecture1 (9/27) |
Review of complex arithmetic,Powers and roots |
1.1-2 |
| |
Lecture2 (9/29) |
Subsets of the complex plane
Complex limit |
2.1 |
| |
Lecture3 (10/1) |
Complex derivatives, Complex analytic functions |
2.1-3 |
| Week2 |
Lecture4 (10/4) |
Harmonic functions, Complex maps1 |
2.4-5, 3.3 |
| |
Lecture5 (10/6) |
Complex maps2:Translation, Rotation, Dilation, Inversion |
2.6-7 |
| |
Lecture6 (10/8) |
fractional linear transformation |
2.7 |
| Week3 |
Lecture7 (10/11) |
Exponential functions,
Trig and hyperbolic function |
1.5, 1.8 |
| |
Lecture8 (10/13) |
The complex logarithm |
1.6 |
| |
Lecture9 (10/15) |
Multi-valued functions, Reviews |
1.7 |
| Week4 |
Lecture10 (10/18) |
Midterm1 |
NA |
| |
Lecture11 (10/20) |
Curves and contours, Contour integration1 |
3.1-2 |
| |
Lecture12 (10/22) |
Contour integration2, Fundamental theorem of Calculus |
4.1-2 |
| Week5 |
Lecture13 (10/25) |
Cauchy's theorem |
4.3 |
| |
Lecture14 (10/27) |
Cauchy integral formula1 |
4.4 |
| |
Lecture15 (10/29) |
Louville's theorem, Fundamental theorem of Algebra |
4.6-7 |
| Week6 |
Lecture16 (11/1) |
Power Sries1 |
5.1-7 |
| |
Lecture17 (11/3) |
Power Sries2, Taylor Series1 |
|
| |
Lecture18 (11/5) |
Taylor Series2, Review |
|
| Week7 |
Lecture19 (11/8) |
Midterm2 |
NA |
| |
Lecture20 (11/10) |
Laurent Series |
6.1 |
| |
Lecture21 (11/12) |
Classification of Isolated Singularities, Zeros and poles |
6.2 |
| Week8 |
Lecture22 (11/15) |
The point at infinity |
1.3, 6.3 |
| |
Lecture23 (11/17) |
Residues; The residue theorem |
7.1-2 |
| |
Lecture24 (11/19) |
Trigonometric Integrals |
7.3 |
| Week9 |
Lecture25 (11/22) |
Indefinite integrals |
7.4 |
| |
Lecture26 (11/24) |
Indefinite integrals, Principal value integrals |
7.6 |
| |
Lecture27 (11/26) |
Holiday |
NA |
| Week10 |
Lecture28 (11/29) |
Integrals of multi-valued functions |
NA |
| |
Lecture29 (12/1) |
Argument principle, Rouche's theorem |
8.1-2 |
| |
Lecture30 (12/3) |
Reviews |
|
| Final |
12/9 (Thurs) |
11:30AM-2:30PM at TBA |
|
