The complex number system. Analytic functions. Cauchy's integral theorem and formula. Applications including the maximum modulus principle, Taylor expansion and Laurent expansion. Harmonic functions. The residue theorem with applications: the calculus of residues, the argument principle, and Rouché's theorem. Basics of analytic continuation. Additional topics at the instructor's discretion such as normal families, the Riemann mapping theorem, and Picard's theorem.
M W F 1500-1550 CAB 377
M W F 1600-1650 CAB 377/CAB 521 Tel: 780-492-0532 Email: email@example.com WWW: http://www.math.ualberta.ca/~bowman/m411
Gamelin, Theodore W. Complex Analysis, Springer, 2001. [QA 300 g25]
Freitag, Eberhard and Busam, Rolf. Complex Analysis, Springer, 2009. [QA 331 F7413]
|Midterms||30%||October 12, November 14||15:00-15:50 CAB 377|
|Final||40%||December 13||14:00-17:00 CAB 281|
|Deferred||40%||January 14||09:00-11:00 CAB 528|
Much of the learning in this course will be done outside the classroom, solving the exercises and homework problems. Discussion with your classmates on specific homework problems is encouraged provided that you clearly acknowledge collaborators on the last page of your assignment and that you independently write up your own solutions. Assignments may be submitted any time on or before the given due date in the box provided on the third floor of CAB. Please put your name on the first page of your assignment (it will be handed back directly to you during class).
On exams, you must work independently; questions of interpretation should be directed to the instructor. There will be two midterm examinations, each 50 minutes in length. Your midterm grade will be the maximum of your two midterm scores.
Material related to this course will be posted on the web page noted above. Additional material may be occasionally sent by email to your official U of A email address. If you do not regularly read your U of A email, it is your responsibility to forward your U of A email to your preferred email account. Instructions for doing this are available on the course web page.
Classroom interaction and questions are welcomed during the lectures!