Math 311: Complex Analysis, Spring 2019
MWF 11:00-11:50am, Lib 389Office Hours: MWF 2:00-3:30pm in Lib 306
Text: Complex Variables by Joseph Taylor
Math 311 on Slack
Week 1: January 28 - February 1 [notes]
- M: Course overview. Review of the complex number system.
- W: Syllabus, §§1.1-2. Convergence and power series in $\mathbb{C}$.
- F: §§1.3-4. The exponential function and polar form for complex numbers. HW1 due.
Week 2: February 4 - 8 [notes]
- M: §1.4 and §2.2. Review of polar form, holomorphic functions I.
- W: §2.2. Holomorphic functions II.
- F: §2.3. Contour integrals. HW2 due.
Week 3: February 11 - 15 [notes]
- M: §2.4. Properties of countour integrals.
- W: §2.5. Cauchy's theorem for a triangle.
- F: §2.6. Cauchy's theorem for a convex set. HW3 due.
Week 4: February 18-22 [notes]
- M: In-class exam. One two-sided sheet of notes allowed, no other resources.
- W: §2.7. The index function.
- F: More fun with indices. HW4 due.
Week 5: February 25 - March 1 [notes]
- M: §3.1. Uniform convergence.
- W: §3.2. Power series expansions.
- F: §3.3. Liouville's theorem. HW5 and Exam 1 Redo due.
Week 6: March 4 - March 8 [notes]
- M: §3.4. Zeroes and singularities.
- W: More singularities. Examples.
- F: Examples, examples, examples. HW6 due.
Week 7: March 11 - March 15 [notes]
- M: §3.5. The maximum modulus principle.
- W: §4.1. Chains and cycles.
- F: §4.2. Cauchy's theorems. HW7 due.
Week 8: March 18 - March 22 [notes]
- M: §4.3. Laurent series.
- W: §4.4. Finish Laurent series. Start the residue theorem.
- F: Finish the residue theorem. HW8 due.
Spring Break: March 24 - March 28
- Make sure you complete HW9 for Monday, April 1's class.
- Review problems in advance of Exam 2.
- Complete the midterm feedback form.
Week 9: April 1 - April 5 [notes]
- M: §4.6. Homotopy. HW9 due. Exam 2 distributed at the start of class.
- W: §5.1. Computing residues.
- F: §5.2. Evaluating integrals using residues. Exam 2 due.
Week 10: April 8 - April 12 [notes]
- M: §5.5. Summing infinite series.
- W: §6.1. Conformal mappings. Mathematica notebook with visualizations.
- F: §6.2. The Riemann sphere. HW10 due.
Week 11: April 15 - April 19 [notes]
- M: §6.3. Linear fractional transformations.
- W: More with $PGL_2(\mathbb{C})$.
- Updated Mathematica notebook (thanks, Yunjia!).
- Möbius transformations revealed video and paper.
- Möbius transformations with Geogebra.
- Spherical video editing with linear fractional transformations.
- F: §6.4. The Riemann mapping theorem. HW11, Exam 2 Metacognative redo due.
Week 12: April 22 - April 26 [notes]
- M: Elliptic functions: period lattice and modular group.
- W: Elliptic functions: canonical basis of the period lattice.
- F: Elliptic functions: general properties. HW12 due.
Week 13: April 29 - May 3 [notes]
- M: Elliptic functions: the Weierstrass $\wp$-function. Course evaluations.
- W: Elliptic functions: the field of functions for $\mathbb{C}/L$. HW13 "due."
- F: Review session and donuts 🍩. (Free HW extension to today.)
Final exam: Thursday 16 May, 9am-12pm in Bio 19
- Comprehensive final exam with emphasis on material from weeks 8-13. One two-sided sheet of notes permitted; no other resources.
- Reading and finals week office hours: Tuesday 7 May 3-4pm, Wednesday 8 May 11am-noon, Friday 10 May 3-4pm, Monday 13 May 3-4pm, Tuesday 14 May 3-4pm.
The $\LaTeX$ document preparation system
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- $\LaTeX$ at Reed.
- A short guide [pdf] to writing mathematics with $\LaTeX$.
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Kyle M. Ormsby