F 1/19 -- The text is still not in, so xeroxes of the first
few sections are distributed. First homework is passed out, Homework One
, to be due F 1/26. Cover 1.1.1 and most of 1.2.
M 1/22 -- Handouts include two missing pages from the text, a
list of sines in multiples of pi/60, and How to Solve It
guide. Finish 1.2 and most of 1.3.
W 1/24 -- Discussion of 1.3 and 1.4. A couple of homework
questions, posted to the newsgroup. The text is still not in.
F 1/26 -- Unexpected cancellation of class due to power outage!
M 1/29 -- Homework 1 collected, Homework One
Solutions are distributed, along with Homework Two
, to be due M 2/5. (Homework three will be out on 2/2, and we'll
return to having homework on Fridays. Other handouts (not TeX'd) are
more of the book (the text is still not in) and some notes on
stereographic projection.
W 1/31-- Homework 1 returned. Some questions about Homework 2.
1.4 completed and we move on to 1.5. Still more of the book passed out.
F 2/2 -- We finish 1.5 and begin 1.6. Homework Three
distributed, due 2/9. Some more questions on Homework 2. What
happens when you keep trisecting the sides of a triangle and snipping
off the corners? (Answers 2/9.)
M 2/5 -- Homework 2 collected. Homework Two
Solutions are distributed. [Note the absence of pictures, as well
as an error to 5c, corrected in class.] We get through most of 1.6. Yet more
of the book passed out. We begin to talk about the first exam.
W 2/7 -- Homework 2 returned, along with a handwritten sheet of
additional comments. We finish 1.6 and begin 2.1. Green's Theorem and
its variants are temporarily postponed.
F 2/9 -- There seems to be consent that Monday 2/19 is ok for the
first test, at night 7-8, but I won't collect the exams until
8:30. This will be finalized on 2/12. Homework Three
Solutions are distributed, as before, without pictures. Homework Four
is distributed.
M 2/12 -- Homework 3 returned, with a handwritten sheet of
additional comments (and relatively minor corrections.)
and a handwritten explanation of the analyticity
of log z, that goes beyond the book's over-simplistic formula
arg z = arctan (y/x). If you didn't get these handouts, ask. We finish
2.1 and begin 2.2.
W 2/14 -- A hint on HW4 #5: think of {x < 1, y < 1} as the
intersection of {x < 1} and {y < 1}. We continue through 2.2. There is
a handout giving a more detailed play-by-play of the inequality on
pp. 98-99, handwritten. It looks like, except for the homework and its
solutions, all handouts will be handwritten. If you don't have the
text yet, go to the web hints suggested on the newsgroup. If this
problem persists into mid-next week, I'll start xeroxing the text again.
F 2/16 -- Homework Four
Solutions are distributed, 2.2 is finished, and we begin a brief
discussion of Green's theorem. Review notes on Green's theorem
(unlinked) are distributed.
M 2/19 -- Homework 4 returned, along with a sheet
of supplemental remarks. Some time spent discussing the exam, as well
as Green's Theorem.
M 2/19 -- First exam, in 145 Altgeld, 7-8:30. Class cancelled on
F 3/9 as a result. Here is a copy (with some typos corrected) of the
exam. First Test
.
W 2/21 -- First exam returned. The score distribution follows
| Scores | #Undergrads | #Grads |
|---|---|---|
| 100 | 0 | 4 |
| 90s | 6 | 2 |
| 80s | 4 | 1 |
| 70s | 5 | 1 |
(My first table in HTML!) No solutions are written up for exams. Work problems you don't get right, and you can ask me to look at your work. In class, we start 2.3 and prove Cauchy's Theorem. Homework Five is distributed
F 2/23 -- We continue through Cauchy's Theorem to Cauchy's
Formula. This is powerful stuff! A set of alternative problems, Test 1
Worksheet, is distributed. If you want to do this, and it is
optional,
turn it in to me by F 3/2, so I can look at all of them at once.
M 2/26 -- We discussed the Cauchy Theorems and gave a few
examples. This takes a while to be fully assimilated. Also,
if f is analytic, then |f| has no local maxima, and no local minima,
except where f = 0.
W 2/28-- Homework Five
Solutions are distributed. Homework Six
is distributed, to be due after Spring Break, on 3/19. The
Cauchy-Goursat Theorem (2.3.1) and the
beginnings of 2.4, which is one of the key sections of the course.
A short handwritten and unlinked handout gives some geometric series
identities.
F 3/2-- Homework 5 returned, with a handwritten and unlinked
sheet of additional comments, and some discussion therein. We complete
the proof of Theorem 1 in 2.4, which says that if f is analytic on
a domain D which contains a simple closed curve C and its interior,
then so is f' (so that f is differentiable to all orders), and f is
representable by its Taylor series in a disk contained within C.
Some applications to variations on the geometric series and a muddled
discussion of Liouville's Theorem, which will be fixed in a handout
on 3/5.
M 3/5 --
W 3/7 --
F 3/9 -- Class cancelled because of evening exam, 2/19.
M 3/19 -- Homework 6 due, Homework 7 out
W 3/21 --
F 3/23 --
M 3/26 --
W 3/28 --
F 3/30 --
M 4/2 --
W 4/4 --
F 4/6 --
M 4/9 --
W 4/11 --
F 4/13 --
M 4/16 --
W 4/18 --
F 4/20 --
M 4/23 --
W 4/25 --
F 4/27 --
M 4/30 --
W 5/2 --
Sat 5/5 -- Final Exam (1:30 -- 4:30)