Math 440/508  Complex Analysis  Fall 2017
Instructor: Malabika Pramanik
Office: 214 Mathematics Building
Email: malabika at math dot ubc dot ca
Lectures: Mon,Wed,Fri 11:00 AM to 12:00 noon in Room 105 of Mathematics Building.
Office hours: Wed, Fri 121PM or by appointment.
Marker/TA : Robert Fraser
Email : rgf at math dot ubc dot ca
Weekly quizzes
 Quiz 1 held on Monday September 11.

Quiz 2, based on week 2 material, will be held in class on Monday September 18.
Homework
 Week 1
 Practice problems: Chapter 1, Exercises 113 of the textbook. These are not to be turned in.
 Homework set 1: Exercises 5, 7, 13. (due on Friday Sept 15 at the beginning of lecture)
 Weeks 2 and 3
 Practice problems: Chapter 1 Exercises 1426. Chapter 2 Exercises 510. These are not to be turned in.
 Homework set 1: Chapter 1 Exercises 22, 25. Chapter 2 Problem 1. (due on Friday Sept 29 at the beginning of lecture)
Course information
Weekbyweek course outline
Here is a tentative guideline of the course structure, arranged by week. The textbook pages are mentioned as a reference and as a reading guide. The treatment of these topics in lecture may vary somewhat from that of the text. Please stay tuned for possible changes.
 Week 1: (pages 113)
 Properties of complex numbers
 Definition of holomorphy
 CauchyRiemann equations
 Week 2: (pages 1436)
 Power series
 Integration along curves
 Goursat's theorem
 Week 3: (pages 3750)
 Cauchy's theorem on the disc
 Toy contours
 Cauchy integral formulae
 Week 4: (pages 5053, 4145)
 Power series representation of holomorphic functions
 Liouville's theorem
 Fundamental theorem of algebra
 Principle of analytic continuation
 Evaluation of some integrals
 Week 5: (pages 7187)
 Morera's theorem
 Extended complex plane  stereographic projection
 Isolated singularities
 Removable, pole and essential singularities
 Week 6: (pages 8993)
 Residue theorem
 Argument principle
 Homotopies and simply connected domains
 Week 7: (pages 93101)
 Cauchy's theorem on homotopies
 The complex logarithm
 Week 8: (pages 205212, 218)
 Conformal mappings
 Schwarz lemma
 Automorphisms of the disc
 Week 9:
 Mobius transformations
 Crossratio
 Preservation of generalized circles
 Week 10: