- Week of 1/16: Sarason I, §1–11; II, §1–6; Schaum, §1.1–1.14;
§1.18 for review; §3.1–3.7
- Week of 1/23: Sarason II, §7–9 and §13–16; IV §9–13.
Schaum, 3.1–3.7, 3.14–3.15. Needham, 4.I–4.V; 5.I–5.VI
- Week of 1/30: Sarason IV (less §17)
- Week of 2/6: Sarason V; Schaum, §6.1 6.8 (skip comments about integrals for now)
ALSO: please revise real line integrals in the plane, div, grad curl and all that
(e.g. Schaum §3.16, §4.2)
if you have not done that yet
- Week of 2/13: Sarason VI, VII§1–8; VII.10. Schaum, Chapts. 4, 5.
- Week of 2/20 (midterm): No new reading, just do lots of practice problems such as HW4.
Many more problems in Schaum. We have covered Complex Line Integrals including Cauchy's theorem and formula,
up to Sarason, §VII.5, but have not proved many applications of Cauchy's theorem.
Specifically, we did not discuss §VI.11 and §VII.6–10.
- Week of 2/27: Sarason, 7sect;VII; Schaum, Chapts 4, 5.1, 5.2 through the Maximum
- Week of 3/6: Sarason VIII; Schaum 6, §9-12
- Week of 3/13: Schaum 7, §1–5
- Week of 3/20: Topics from Sarason IX and X: IX.4; X, §8–12; Schaum, 7.6
- Week of 4/3 (midterm 2): Sarason, VII, VIII and the covered topics from X.
The midterm will test: isolated singularites and their residues,
Laurent series, and evaluation of definite integrals via residues. Do practice those integrals.
In addition, there will be a theory question. You will be asked to write a neat
proof of one of the following: convergent Taylor expansion of holomorphic functions in
a disk; convergent Laurent expansion of holomorphic functions in an annulus; the mean
value theorem for holomorphic functions; or one of the proofs of the Fundamental Theorem of
algebra. (There will be no True-False questions, as in the old midterm).
- Week of 4/10: Sarason III; Schaum, §8.17–8.4, §8.10, § 8.11;
§9.1, §9.2, § 9.6 (ignore the Neumann problem for now).
- Week of 4/17: The Dirichlet problem, the Poisson Kernel for the disk and the upper
- Week of 4/24: Schaum, Ch.8: Examples of conformal maps: §8.1–11 (known),
§8.14, A1–A4 and A6; Fluid FLow, §9.7–9.9, §.9.12
- RRR Week: There will be a review class on Tuesday, 5/2 at the usual time and place.
I will hold office hours as usual on TuWed.
- FINAL EXAM: 11:30–2:30 pm, 3107 Etcheverry. OPEN BOOK exam (but no notes
or old homeworks).
The exam will have two parts, independently graded: a review section with problems about
complex differentiation, power series, Residue formulas and calculation of contour integrals;
and a section on Moebius transformations, conformal maps and their use in solving the
Laplace equation with Dirichlet boundary conditions (the April material).
- Here is an old final exam (remember the format will
be different, see above).