Instructor: Bjorn Poonen

Lectures: MWF 3-4pm, 213 Wheeler

Course Control Number: 54939

Office: 879 Evans, e-mail: poonen@math

Office Hours: MWF 9:30-10:30am, TuTh 1:30-2:30pm, or by appointment.

GSI: Aaron Greicius, office hours in 891 Evans: M 9-11am, 2-5pm and Tu 11am-1pm, 2-5pm.

Grader: Soroosh Yazdani. (Go to his website for solutions to the homework.)

Prerequisites: Math 104.

Syllabus: This is a standard introduction to the theory of analytic functions of one complex variable. The main topics are contour integration, Cauchy's Theorem, power series and Laurent series expansions of analytic functions, classification of isolated singularities, and the residue theorem with its applications to evaluation of definite integrals. If time permits, we will also discuss the argument principle and Rouché's Theorem, analytic continuation, harmonic functions, and conformal mapping (including fractional linear transformations).

Required Text: Sarason, Notes on complex function theory, published by Henry Helson.

Recommended Reading: The Sarason text is concise and without many figures or worked examples, so you are encouraged to look also at at least one other text, such as one of the following:

• Marsden and Hoffman, Basic complex analysis, 3rd edition, W. H. Freeman, 1998. (I used this book the last time I taught Math 185, but decided against it this time, since it now costs $153, nine times as much as Sarason's book!)
• Stewart and Tall, Complex analysis, Cambridge University Press, 1983.
• Lang, Complex analysis, 4th edition, Springer-Verlag.

Exams: There will be midterm exams in class on Wednesday, February 25 and Wednesday, April 14. The final exam will be Tuesday, May 18, 5-8pm in 50 Birge Hall.
Midterm 1 (solutions)
Midterm 2 (solutions)
Makeup midterm 2
Old final exam from 1997
Final exam (solutions)

Grading: 35% homework, 15% first midterm, 15% second midterm, 35% final. Each homework grade below the weighted average of your final and midterm grades will be boosted up to that average. The course grade will be curved. Click here for an example.

Homework: There will be weekly assignments due at the beginning of class each Wednesday. Late homework will not be accepted, but see the grading policy above. You should not expect to be able to solve every single problem on your own; instead you are encouraged to discuss questions with each other or to come to office hours for help. If you meet with a study group, please think about the problems in advance and try to do as many as you can on your own before meeting. After discussion with others, write-ups must be done separately. (In practice, this means that you should not be looking at other students' solutions as you write your own.) Write in complete sentences whenever reasonable. Staple loose sheets!