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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.

Send me an e-mail

Please send me an e-mail at 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 Mathematics 241A
Time Wednesday/Friday 10:30-11:45
Place Mathematics 124
Office Hours Wednesday 1:30PM-3:30PM, or by appointment
Prerequesites Math 275 (Calculus III)

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Required textbook and other resources

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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
Codes written or demonstrated in class :
Friday -- 

Week #3 (Jan. 23)
Wednesday -- 
Friday -- 

Week #4 (Jan. 30)
Wednesday -- 
Friday --  Midterm #1

Week #5 (Feb. 6)
Wednesday -- 
Friday -- 

Week #6 (Feb. 13)
Wednesday -- 
Friday -- 

Week #7 (Feb. 20)
Wednesday -- 
Friday -- 

Week #8 (Feb. 27)
Wednesday --  Midterm #2
Friday -- 

Week #9 (Mar. 6)
Wednesday -- 
Friday -- 

Week #10 (Mar. 13)
Wednesday -- 
Friday -- 

Week #11 (Mar. 27)
Wednesday --  Branch cuts
Friday --  Finish Chapter 5
Other resources :
Branch_Points_B_Cuts.pdf  -- Discussion of branch points and branch cuts

Week #12 (Apr. 3)
Wednesday --  Midterm #3 (Chapters 4 and 5)
Friday -- 

Week #13 (Apr. 10)

Week #14 (Apr. 17)

Week #15 (Apr. 24)

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Homework assignments

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 theoretical questions.

Login into WebAssign here.

Supplemental homework assignments are listed here below.

Homework #1

Due 1/18 (WebAssign)

Assignment :

Homework #2

Due 1/25 (WebAssign)

Assignment :

Homework #3

Due 2/1 (WebAssign)

Assignment :

Homework #4

Due 2/10

Assignment :

Homework #5

Due 2/22 (WebAssign)

Assignment :

Homework #6

Due 3/17 (WebAssign)

Assignment :

Homework #7

Due 3/31 (WebAssign)

Assignment :

Homework #8

Due 4/21 (WebAssign)

Assignment :

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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.

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Grading policy

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!).

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