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, limits & continuity | Week 02 | HW2 |
| 3 | Derivatives of complex functions | Week 03 | HW3 |
| 4 | Cauchy-Riemann equations | Week 04 | HW4 |
| 5 | Möbius transforms, exponential functions | 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 | HW9 |
| 10 | Infinite sequences & series | Week 10 | HW10 |
| 11 | Sequences & series of functions | Week 11 | HW11 |
| 12 | Taylor series, Midterm 2 | Week 12 | HW12 |
| 13 | Zeros of analytic functions | Week 13 | |
| 14 | Harmonic functions | Week 14 |
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.
My office hours are shown above on my weekly schedule. I am also available by appointment. My office is Blake B-02, which is one of the Blake apartments. You can find it on this map. It looks like a student apartment, but I am using it as my office while the new science building is being built. During my regularly scheduled office hours the front door should be unlocked, so feel free to come in. I’ll be right upstairs. If you would prefer to schedule online office hours, let me know and I’ll be happy to set up a Zoom meeting.
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 three 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.
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.
If we need to switch to an online virtual course at any point during the semester, the basic outline and schedule of topics for the course will remain the same. I will provide asynchronous video guided notes and workshops to help learn the material. I will also divide the class into smaller groups and schedule Zoom meetings during our regular class time (MWF 10:00 - 11:10am & R 2:30 - 3:40pm) where we can go over the material in more detail. I may also incorporate a short oral examination as part of one or more of the midterm or final exams. If you know that you will have trouble with Zoom from home, please let me know.