Mathematics 4156a   //   9056a
Complex Variables II   //   Complex Analysis I

Summer 2012

Instructor:
André Boivin
Phone: 661-2111   x86512
Office: MC 118

Prerequisite:
Mathematics 3124a/b or equivalent

Textbook:

Course Outline:
The Argument Principle, Rouché's Theorem, Hurwitz's Theorem Open Mapping and Inverse Function Theorems, Critical Points, Winding Numbers, The Jump Theorem for Cauchy Integrals, Simply Connected Domains, The Schwarz lemma, Conformal Self-Maps of the Unit Disc, Hyperbolic Geometry, The Poisson Integral Formula, The Scwarz Reflection Principle, The Riemann Mapping Theorem, Marty's Theorem, Theorems of Montel and Picard, Runge's Theorem, The Mittag-Leffler Theorem, Infinite Products, The Weierstrass Factorization Theorem.

This corresponds, approximately, to Chapters VIII to XIII in the textbook:

Evaluation of Student Performance:
70%       Assignments
30%       Class Presentation

Assignments

• Homework #1:
• Chapter VIII, Section 1, Exercises #8 (you can also use Rouché's Thm) and #9.
• Chapter VIII, Section 2, Exercises #3, #7 and #8.
• Chapter VIII, Section 3, Exercises #1 and #2.
• Chapter VIII, Section 4, Prove that (4.1) depends analytically on w. Do any two problems at the end of the Section.
• Homework #2:
• Chapter VIII, Section 5, Exercises #1, #4, and #8 as a bonus question.
• Chapter VIII, Section 6, Exercises #3, #4, #5 and #6.
• Chapter VIII, Section 7, Exercises #1, #2, and #4.
• Chapter VIII, Section 8, Exercises #4, #5, and read (only!) #7 and #8.
• Homework #3:
• Chapter IX, Section 1, Exercise #4.
• Chapter IX, Section 2, Exercises #1, #5 and #7.
• Homework #4:
• Chapter X, Section 1, Exercises #2, #4, and #3 as a bonus question.
• Chapter X, Section 2, Exercise #1.
• Chapter X, Section 3, Exercises #1, #6, and #7 as a bonus question.
• Homework #5:
• Chapter XI, Section 1, Exercise #2.
• Chapter XI, Section 2, Exercise #1.
• Chapter XI, Section 5, Exercises #1, #4a, #4b as a bonus question, and read (only!) #5.
• Chapter XI, Section 6, Exercises #1, #2.