| Date | Topic | Book | HomeworkHmwk | Practice ProblemsProbs | |
|---|---|---|---|---|---|
| Sept. | 5 | Good things about complex functions | §1.1–1.2 | 1.1: 8, 10; 1.2: 7, 10 | |
| 9 | The complex numbers | §1.3 | 8, 11, 12 | ||
| 11 | Visualizing complex mappings | §1.3 | |||
| 12 | Möbius transformations | §1.4–1.5 | 1.4: 5, 7, 11; 1.5: 6, 12, 18 | ||
| 16 | Exponentials of complex numbers | §3.3, 3.5 | H1 | 3.3: 1, 5; 3.5: 1, 4 | |
| 18 | Limits and continuity | §2.1–2.2 | A1 | 2.1: 1, 6; 2.2: 6, 17 | |
| 19 | Holomorphicity | §2.3 | 1, 4, 6, 10 | ||
| 23 | The Cauchy-Riemann equations | §2.4 | H2 | 1, 2, 3, 4 | |
| 25 | Proof of the Cauchy-Riemann Theorem | §2.4 | A2 | 3, 5, 15 | |
| 26 | Harmonic Functions | §2.5 | 1, 2, 3, 5 | ||
| 30 | Conformal Maps | §2.5 | H3 | ||
| Oct. | 2 | Differentiation of elementary functions | §3.1–3.3 | A3 | 3.2: 8, 9, 10; 3.3: 6 |
| 3 | Contour integrals | §4.1–4.2 | 4.1: 5, 8; 4.2: 6, 12 | ||
| 7 | Properties of contour integrals | §4.2–4.3 | H4 | 4.3: 2, 4, 5, 7 | |
| 9 | The fundamental theorem in complex analysis | §4.3 | A4 | ||
| 10 | Cauchy's theorem I | §4.4 | 1, 3, 4, 10, 11, 18 | ||
| 14 | Thanksgiving | ||||
| 16 | Cauchy's theorem II | §4.4 | H5 | ||
| 17 | Cauchy's theorem III | §4.4 | A5 | ||
| 21 | Cauchy's integral formula | §4.5 | H6 | ||
| 23 | Integrals of Cauchy Type | §4.6 | A6 | 1, 3, 5, 6, | |
| 24 | Fall Break | ||||
| 28 | More on integrals of Cauchy type | §4.6 | |||
| 30 | The maximum modulus principle | §4.6–4.7 | H7 | 4.6: 8, 14; 4.7: 4, 6 | |
| 31 | The Dirichlet problem and Poisson's formula | §4.7 | A7 | 8, 9, 10, 11 | |
| Nov. | 4 | Convergence of functions | §5.1, 5.4 | H8 | 5.1: 10, 11; 5.4: 5, 8 |
| 6 | Convergence of holomorphic functions | §5.2 | A8 | 5.2: 1, 2, 11 | |
| 7 | Analyticity of holomorphic functions | §5.3 | 1, 4, 5, 10 | ||
| 11 | Laurent series expansions | §5.5 | H9 | 1, 2, 6, 7 | |
| 13 | Classification of singularities | §5.6 | A9 | 1, 2, 5, 6 | |
| 14 | Residue theorem and calculation of residues | §6.1 | 1, 2 | ||
| 18 | More residue calculations | §6.1 | H10 | 5, 6, 7 | |
| 20 | Definite integrals I | §6.3 | A10 | 1, 3, 4, 5 | |
| 21 | Definite integrals II | §6.5 | 2, 3, 4, 5 | ||
| 25 | Definite integrals III | §6.4 | H11 | 1, 3, 4, 6 | |
| 27 | Definite integrals IV | §6.2 | A11 | 1, 4, 6 | |
| 28 | The principle of the argument | §6.7 | 1, 2, 3, 4 | ||
| Dec. | 2 | Review | H12 | ||
| 4 | A12 | ||||
| 6 | |||||