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21:640:403 Complex variables (Fall 2016)
Special announcements
- 09/14/2016: The classroom is permanently changed to Hill Hall 202.
- 09/21/2016: Please note that we will be using the online textbook A first course in complex analysis (see here).
Syllabus & Textbook
Download the course syllabus here. This contains essential information about the course (textbook, prerequisites, material covered...). Please note that the textbook mentioned in this syllabus is incorrect.
The official textbook for this class is: Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Cartan. Follow this link for the full reference. Even though I recommend buying this textbook, we will not be using it very often and instead will follow the online textbook A first course in complex analysis: see here for details and a download link (pdf file).
Course schedule
For general important dates in the semester, see the academic calendar here.
Refer to the course schedule below for the homework assignments as well as for the files of the past quizzes and exams.
This course schedule is very much subject to change, refer to last version online (and make sure you refresh the page).
Class time and location:
Monday: 2:30pm-3:50pm, Hill Hall 202
Wednesday: 1pm-2:20pm, Hill Hall 202
Office hours:
Monday: 10:30am-11:30am, Smith Hall 308
Wednesday: 10:30am-11:30am, Smith Hall 308
Contact: brice@loustau.eu
| Date | Topic | Homework assignment | Special |
|---|---|---|---|
| Wed 09/07 |
Welcome, Introduction Chapter 1: The complex plane. 1.1: Basics |
- | First day of class |
| Mon 09/12 | Chap. 1.2: Polar form | Review lecture notes | |
| - | - | - | 09/13: Last day of Add/Drop period without "W" grade |
| Wed 09/14 | Chap. 1.3: Complex exponential | Review lecture notes | Last day of Add Only period without "W" grade |
| Mon 09/19 | Chap. 1.4: Topology of $\mathbb{C}$ |
Review lecture notes Homework exercises #1 |
Quiz #1 |
| Wed 09/21 | Chap. 1.4: topology of $\mathbb{C}$ |
Review lecture notes Exercise: prove that $\displaystyle{\lim_{n \to +\infty}e^{i/n} = 1}$. |
|
| Mon 09/26 | Chap. 1.4: Topology of $\mathbb{C}$ | Review lecture notes Homework exercises #2 |
Quiz #2 |
| Wed 09/28 |
Chap. 1.5: Complex algebraic equations. Chapter 2: Functions of a complex variable. Chap 2.1: Basics |
Review lecture notes Homework exercises #2: Ex.3 |
|
| Mon 10/03 | Chap. 2.2: Continuity | Review lecture notes Homework exercises #3 |
Quiz #3 |
| Wed 10/05 | Chap. 2.2: Continuity and 2.3: Real differentiability (crash review) | Review lecture notes Homework exercises #4 |
|
| Mon 10/10 | - | List of topics | TEST #1 |
| Wed 10/12 | Chap. 2.3: Real differentiability (crash review) | Review lecture notes |
|
| Mon 10/17 | Chap. 2.4: Complex differentiability (holomorphicity) | Review lecture notes Homework exercises #5 |
Quiz #4 |
| Wed 10/19 | Chap. 2.4: Complex differentiability (holomorphicity) | Review lecture notes | |
| Mon 10/24 | Quiz #5 + Exercises session | Review lecture notes Homework exercises #6 |
Quiz #5 Replacement by Prof. Gilman |
| Wed 10/26 |
Chapter 3: Examples of holomorphic functions Chap 3.1: Polynomials, Taylor expansions for polynomials Chap 3.2: Rational fractions, Möbius transformations |
Review lecture notes | |
| Mon 10/31 |
Chap 3.2: Rational fractions, Möbius transformations Chap 3.3: Exponential and trigonometric functions |
Review lecture notes Homework exercises #7 |
Quiz #6 |
| Wed 11/02 | Chap 3.4: Logarithms | Review lecture notes | |
| Mon 11/07 |
Chapter 4: Power series. Chap 4.1: Series of complex numbers |
Review lecture notes Homework exercises #8 |
Quiz #7 Last day for dropping courses to receive a "W" grade |
| Wed 11/09 | Chap 4.2: Series of complex functions | Review lecture notes | |
| Mon 11/14 | - | Homework exercises #9 List of topics | TEST #2 |
| Wed 11/16 | Chap 4.2: Series of complex functions | ||
| Mon 11/21 | Chap 4.3: Power series and analytic functions | ||
| Wed 11/23 | - | - | Class cancelled (Wed 11/23 follows a Friday schedule) |
| - | - | - | 11/24-11/27: Thanksgiving recess |
| Mon 11/28 | Chap 4.4: Theorem of isolated zeros and Identity theorem | Review lecture notes Homework exercises #10 |
Quiz #8 |
| Wed 11/30 |
Chapter 5: Cauchy theory Chap 5.1: Integration along paths |
Review lecture notes | |
| Mon 12/05 | Exercises session | Review lecture notes Homework exercises #11 |
Quiz #9 |
| Wed 12/07 | Chap. 5.2: Cauchy's integral formula and first consequences | Review lecture notes |
|
| Mon 12/12 | Chap 5.2: Exercises | Review lecture notes Homework exercises #12 |
Quiz #10 |
| Wed 12/14 |
Chapter 6: Overview of fundamental theorems for holomorphic functions Review session |
Review lecture notes |
12/14: Regular classes end |
| - | - | 12/16-12/23: Fall exams period | |
| Mon 12/19 | - | List of topics | FINAL EXAM 3pm-6pm (regular classroom) |
Students: please take the SIRS survey by following this link. The deadline is Friday December 16 at 11:59pm.