Complex Analysis

Math 444 - Winter 2021

Basic Info

Announcements

Tentative Schedule

Date Section Topic Notes Homework
1/11 1.3 Geometry of complex numbers HW1
1/12 1.4 Elementary topology of the plane HW2
1/13 2.1 Limits and continuity HW3
1/14 2.2 Differentiability and holomorphicity HW4
1/15 2.3 The Cauchy-Riemann equations HW5
1/18 2.4 Constant functions HW6
1/19 3.1 Mobius transformations HW7
1/20 3.4 Exponential and trigonometric functions HW8
1/21 3.5 Logarithms and complex exponentials HW9
1/22 Midterm 1
1/25 4.1 Complex integration HW10
1/26 4.2 Antiderivatives
1/27 4.3 Cauchy’s theorem
1/28 4.4 Cauchy’s integral formula
1/29 5.1 Variations of a theme
2/1 5.2 Antiderivatives again
2/2 5.3 Taking Cauchy to the limit
2/2 Midterm 2
2/3 8.1 Power series and holomorphic functions
2/4 8.2 Classification of zeros and the identity principle

Course Description

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 as time permits.

Attendance Policy

Regular attendance is essential in a fast paced course like Math 444. 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.

Office Hours

My office hours are shown above on my weekly schedule. I am also available by appointment. My office is Blake B-2, 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.

Grading Policy

Your final grade will be based on the following factors.

Component     Proportion    
Homework     60%
Midterm 1 10%
Midterm 2 10%
Final Exam 20%

Exams

There will be two midterm exams and a cumulative final.

Homework

I will assign homework problems every class. I recommend having a notebook for your homework solutions. I will check some problems during class and other problems I may ask you to turn in by e-mail. If you don’t get credit for a homework problem on the first try, you can resubmit solutions by e-mail. When you e-mail solutions to me, please scan them as PDF documents first. I recommend using the CamScanner app which is available for free for both Android and iOS. All homework problems are graded based on correctness, and your final homework grade will be the percent of problems completed correctly during the course.

Special Accommodations

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.

Virtual Learning Plan

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 try to provide asynchronous video guided notes and workshops to help learn the material. We will also use Zoom meetings for part of each class to 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.