Introduction to Complex Analysis (Math 426)
In this course, we will explore complex numbers and functions of a complex variable. Many of the ideas learned in Calculus will be revisited for complex numbers, including the idea of an "analytic function", infinite series and integration. While the approach of this course will be applied, we will also discuss proofs of basic results, including the Residue Theorem and the Riemann mapping Theorem. Other topics that will discuss include the Cauchy integral formula and conformal mapping.
- Basic course information
- Required textbook and other resources
- Homework assignments
- Grading policy
Send me an e-mail
Please send me an e-mail at firstname.lastname@example.org so that I can compile an e-mail list for the class. At the very least, include a subject header that says "Math 426". You may leave the message area blank, if you wish, or send me a short note about what you hope to get out of this course.
Basic course information
|Instructor||Prof. Donna Calhoun|
|Office Hours||Wednesday 1:30PM-3:30PM, or by appointment|
|Prerequesites||Math 275 (Calculus III)|
Required textbook and other resources
- Complex Analysis : A First Course with Applications (3rd Edition), by Dennis G. Zill and Patrick D. Shanahan. Jones and Bartlett Learning, (2015) (required).
- WebAssign, by Dennis G. Zill and Patrick D. Shanahan. Jones and Bartlett Learning, (2015) (required).
We will stick the following schedule as much as possible.
|Week #1 (Jan. 9)||
Wednesday -- Section 1.1 : Complex Numbers and their properties; 1.2 : Complex Plane
Friday -- Section 1.3 : Polar Form of Complex Numbers; 1.4 : Powers and Roots
|Week #2 (Jan. 16)||
Wednesday -- Section 1.4 : Powers and Roots; 1.5 : Sets of points in the complex plane
|Week #3 (Jan. 23)||
|Week #4 (Jan. 30)||
Friday -- Midterm #1
|Week #5 (Feb. 6)||
|Week #6 (Feb. 13)||
|Week #7 (Feb. 20)||
|Week #8 (Feb. 27)||
Wednesday -- Midterm #2
|Week #9 (Mar. 6)||
|Week #10 (Mar. 13)||
|Week #11 (Mar. 27)||
Wednesday -- Branch cuts
Friday -- Finish Chapter 5
|Week #12 (Apr. 3)||
Wednesday -- Midterm #3 (Chapters 4 and 5)
|Week #13 (Apr. 10)|
|Week #14 (Apr. 17)|
|Week #15 (Apr. 24)|
Homework assignments will be typicall due on Friday. All students will turn
in WebAssign assignments.
These assignments will be supplemented with written assignments.
Graduate students will have additional assignments that will involve more
Login into WebAssign here.
Supplemental homework assignments are listed here below.
Due 1/18 (WebAssign)
Due 1/25 (WebAssign)
Due 2/1 (WebAssign)
Due 2/22 (WebAssign)
Due 3/17 (WebAssign)
Due 3/31 (WebAssign)
Due 4/21 (WebAssign)
We will have two midterms and one final exam
|Midterm #1||Date: Friday, February 3|
|Midterm #2||Date: Wednesday, March 1|
|Midterm #3||Date: Wednesday, April 5|
|Midterm #4 (in place of a final)||Date: Friday April 28th
This is an in-class regular length midterm
You can find the Final Exam calendar here.
Homework and quizzes will count for 20% of your final grade and each of the three exams and final will be 20% of your final grade. A 90% and above will earn you an A, between 80% and 90% will earn you at least a B, between 70% and 80% will be at least a C, and below 60% will be a D or F. If there is any deviation from this grading policy, it will be to lower the percentages, i.e. you could still earn an A with less than 90%, but you will never need more than 90%. Quizzes will be mostly on the homework, and you will be given plenty of notice (no pop quizzes!).