- Week of 1/15: Sarason I, §1–11; Schaum, §1.1–1.14;
§1.18 for review
- Week of 1/22: Sarason II. Schaum, §3.1–3.7. Needham, 4.I–4.V
- Week of 1/29: Sarason II, §12–15; IV, §1–16. Schaum,
§3.1–3.7; §3.12, 3.13, 3.15. Needham, 2.IV–2.VII.
- Week of 2/5: Sarason II, §13–15; V. Schaum, §2.12–2.17 (review),
§6.1–6.8.
- Week of 2/12: Sarason VI. Schaum, §4.1–4.9 (4.6–4.8 for information)
and §3.16 (review)
- Week of 2/19 (midterm week): Will cover the material from the preceding four weeks.
Here, here, and here are three old midterms, with their
solutions.
(Ignore questions about Möbius transformations and Cauchy's theorem, which are
not covered.)
Note: No class on Monday 2/19. Office Hours: Tu 2–4. Review, Tuesday
4–5:30 pm, 732 Evans.
- Here is the midterm and its
solution.
- Week of 2/26: Schaum, Chapts. 4, 5 (omit theorems 5.2.9–5.2.11).
Sarason, VII (we'll vary the order)
- Week of 3/5: Sarason VII, §8–23; X, §11, 12.
- Week of 3/12: Sarason, VIII. Schaum, §7.1–7.6
- Week of 3/19: Sarason, odd topics from IX and X.
- Week of 4/2. The exam will cover :
- Line integrals, real and complex, and the relation between them
- Green's theorems, real and complex forms
- Cauchy's theorem and formula
- Argument Principle and Rouché's theorem
- Theoretical consequences for holomorphic functions
- Isolated singularities, residues and Laurent series
- Important! Calculation of integrals via residues
- Here, here and
here are some old midterms, with some solutions
- Week of 4/9: Möbius transformations (Sarason III, Needham 3)
- Week of 4/16: The Dirichlet problem; Needham 12; Schaum §9.1–9.9
- Week of 4/23: Conformal maps. The Schwarz-Christoffel map. Schaum §8.10–8.12
- RRR Week: Office hours Monday 2–4 and Friday 2–4:30
- FINAL EXAM: Friday 5/11, 3:00–6:00 pm, Cory 237. OPEN BOOK exam (but no
old homeworks or solutions).
- Here are some review problems from Schaum. The exam will be problem-centric.
- 3.5 (for your review), 3.7, 3.25, 3.53, 3.82, 3.112
- 4.10 (for your review), 4.35 (the first z should be an integral sign),
4.78 (assume R is large), 4.80
- 5.20, 5.28, 5.43, 5.63, 5.64, 5.66, 5.67, 5.83 (the correct assumption is that
f is analytic on the closed disk of radius 1 centered at a), 5.84, 5.98
- 6.12, 6.15 (you must *find* the region), 6.24, 6.25 (for your review), 6.26,
6.27, 6.39, 6.56, 6.57, 6.68, 6.95, 6.98, 6.99, 6.121, 6.137, 6.141, 6.149.
For fun: 6.163—6.165
- 7.13, 7.14, 7.17, 7.20, 7.37, 7.41, 7.42, 7.43, 7.44, 7.62
- 8.5, 8.12, 8.13, 8.33, 8.56, 8.62, 8.101, 9.7, 9.40
- Finally, here and here are two older
final exams. (I will not include a T/F section this time.)