Math 440/508 - Complex Analysis - Fall 2017
Instructor: Malabika Pramanik
Office: 214 Mathematics Building
E-mail: 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 12-1PM or by appointment.
Marker/TA : Robert Fraser
E-mail : rgf at math dot ubc dot ca
- Quiz 1 held on Monday September 11.
Quiz 2, based on week 2 material, will be held in class on Monday September 18.
- Week 1
- Practice problems: Chapter 1, Exercises 1-13 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 14-26. Chapter 2 Exercises 5-10. 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)
Week-by-week 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 1-13)
- Properties of complex numbers
- Definition of holomorphy
- Cauchy-Riemann equations
- Week 2: (pages 14-36)
- Power series
- Integration along curves
- Goursat's theorem
- Week 3: (pages 37-50)
- Cauchy's theorem on the disc
- Toy contours
- Cauchy integral formulae
- Week 4: (pages 50-53, 41-45)
- Power series representation of holomorphic functions
- Liouville's theorem
- Fundamental theorem of algebra
- Principle of analytic continuation
- Evaluation of some integrals
- Week 5: (pages 71-87)
- Morera's theorem
- Extended complex plane - stereographic projection
- Isolated singularities
- Removable, pole and essential singularities
- Week 6: (pages 89-93)
- Residue theorem
- Argument principle
- Homotopies and simply connected domains
- Week 7: (pages 93-101)
- Cauchy's theorem on homotopies
- The complex logarithm
- Week 8: (pages 205-212, 218)
- Conformal mappings
- Schwarz lemma
- Automorphisms of the disc
- Week 9:
- Mobius transformations
- Preservation of generalized circles
- Week 10: