Assignments are due on Thursday, at the beginning of class. The row that an assignment appears in is the day that it is due.

Date | Topic | Book | Homework | Practice Problems | ||
---|---|---|---|---|---|---|

Sept. | 13 | Introduction to the course | §1.1–1.2 | 1.1: 8, 10; 1.2: 7, 10 | ||

15 | More about the complex numbers | §1.3 | 8, 11, 12 | |||

16 | Visualizing complex mappings | §1.3 | ||||

20 | Möbius transformations | §1.4–1.5 | 1.4: 5, 7, 11; 1.5: 6, 12, 18 | |||

22 | Exponentials of complex numbers | §3.3, 3.5 | 3.3: 1, 5; 3.5: 1, 4 | |||

23 | Limits and continuity | §2.1–2.2 | H1 | 2.1: 1, 6; 2.2: 6, 17 | ||

27 | Holomorphicity | §2.3 | 1, 4, 6, 10 | |||

29 | The Cauchy-Riemann equations | §2.4 | 1, 2, 3, 4 | |||

30 | Proof of the Cauchy-Riemann Theorem | §2.4 | H2 | 3, 5, 15 | ||

Oct. | 4 | Harmonic Functions | §2.5 | 1, 2, 3, 5 | ||

6 | Differentiation of elementary functions | §3.1–3.3 | 3.2: 8, 9, 10; 3.3: 6 | |||

7 | Contour integrals | §4.1–4.2 | H3 | 4.1: 5, 8; 4.2: 6, 12 | ||

11 | Thanksgiving |
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13 | Properties of contour integrals | §4.2–4.3 | 4.3: 2, 4, 5, 7 | |||

14 | Fundamental theorem of complex calculus | §4.3 | H4 | |||

18 | Cauchy's theorem | §4.4 | 1, 3, 4, 10, 11, 18 | |||

20 | More about Cauchy's theorem | §4.4 | ||||

21 | Proof of Cauchy's theorem | §4.4 | H5 | |||

25 | Cauchy's integral formula | §4.5 | 1, 2, 8, 13 | |||

27 | Some consequences of the integral formula | §4.6 | 1, 3, 5, 6, | |||

28 | Maximum modulus theorem and harmonic functions | §4.6–4.7 | H6 | 4.6: 8, 14; 4.7: 4, 6 | ||

Nov. | 1 | The Dirichlet problem and Poisson's formula | §4.7 | 8, 9, 10, 11 | ||

3 | Convergent series of analytic functions | §5.1, 5.4 | 5.1: 10, 11; 5.4: 5, 8 | |||

4 | Taylor series expansions of holomorphic functions | §5.2 | H7 | 5.2: 1, 2, 11 | ||

8 | Some corollaries of Taylor series expansions | §5.3 | 1, 4, 5, 10 | |||

10 | Laurent series | §5.5 | 1, 2, 6, 7 | |||

11 | Classification of singularities | §5.6 | H8 | 1, 2, 5, 6 | ||

15 | Residue theorem and calculation of residues | §6.1 | 1, 2 | |||

17 | More residue calculations | §6.1 | 5, 6, 7 | |||

18 | Definite integrals I | §6.3 | H9 | 1, 3, 4, 5 | ||

22 | Definite integrals II | §6.5 | 2, 3, 4, 5 | |||

24 | Definite integrals III | §6.4 | 1, 3, 4, 6 | |||

25 | Definite integrals IV | §6.2 | H10 | 1, 4, 6 | ||

29 | The principle of the argument | §6.7 | 1, 2, 3, 4 | |||

Dec. | 1 | Rouché's theorem | §6.7 | 6, 7, 8, 9 | ||

2 | Review | H11 | ||||

6 | ||||||

8 | ||||||

13 | H12 | |||||