Math 444 is an introduction to analysis (calculus) with complex variables. We will cover the arithmetic and geometry of complex numbers, followed by complex differentiability and the analysis of holomorphic functions. We will finish the course looking at applications of Cauchy’s theorem. Along the way, we will incorporate material on Taylor and Laurent series, and harmonic functions, as time permits.
| Week | Topic | Notes | Homework |
|---|---|---|---|
| 1 | Complex numbers | Week 01 | HW1 |
| 2 | Topology of C | Week 02 | HW2 |
| 3 | Complex limits & continuity | Week 03 | HW3 |
| 4 | Complex exponentials and logarithms | Week 04 | HW4 |
| 5 | Complex differentiability | Week 05 | HW5 |
| 6 | Complex logarithms, Midterm 1 | Week 06 | HW6 |
| 7 | Complex integration | Week 07 | HW7 |
| 8 | The Cauchy integral formula | Week 08 | HW8 |
| 9 | Entire functions | Week 09 | |
| 10 | Singularities and residues | Week 10 | |
| 11 | Applications of the residue theorem | Week 11 | |
| 12 | Möbius transforms, Midterm 2 | Week 12 | |
| 13 | Discrete applications of residue | Week 13 | |
| 14 | Harmonic functions | Week 14 | |
| 15 | The heat equation | Week 15 |
The schedule above is tentative, and may be subject to change. Changes will be announced in class, and you are responsible for knowing about any changes even if you miss the class when they are announced.
Attendance in this class is expected, and you are responsible for any material that you miss. However, if you have a fever or are not feeling well, then please do not come to class that day. As long as you let me know the reason for your absence, I will do my best to help you stay caught up and make up any material that you missed. The key is to communicate with me when you aren’t able to attend class.
The term grade will be based on the following.
| Component | Proportion |
|---|---|
| Homework | 30% |
| Midterm 1 | 20% |
| Midterm 2 | 20% |
| Final Exam | 30% |
There will be two in-class midterm exams and a cumulative final. You will be allowed to use your notes and old homework sets during the exams.
There will be homework problems assigned every week. These will be collected on Fridays. I don’t accept late homework, but I will drop the lowest homework grade. If you know in advance that you won’t be able to make class when a homework assignment is due, please make arrangements to turn in the homework before class.
My office hours are shown on my weekly schedule. I am also available by appointment. If you can’t stop by during my regular office hours, just ask me after class or by e-mail, and I’ll be happy to make an appointment that works for both of us.
In compliance with the Hampden-Sydney College policy and equal access laws, I am available to discuss appropriate academic accommodations that may be recommended for students with disabilities. Requests for academic accommodations are to be made at the beginning of the semester (except for unusual circumstances) so that appropriate arrangements can be made. Students are required to contact the Office of Academic Success in order to verify their eligibility for appropriate accommodations.