2/3-2/5

Complex numbers: arithmetic and polar form

Brown & Churchill, chap 1, secs 1-8

In the Google Drive folder, you’ll find some very nice notes by Dennis Snow. They parallel the textbook, and they’re nice enough that you might find you even prefer them.

2/8-2/12

Roots of complex numbers

Regions and mappings

Chap 1, secs 9-11

Chap 1, sec 12; Chap 2, sec 13-14

1^st hwk is now posted in Drive

As discussed in class today, lectures will now take place MW from 3:30-4:45 and I’ll use the Friday slot for office hours (still Bond 104 & virtual).

2/15-2/19

Limits and continuity

Derivatives and the Cauchy-Riemann equations

Chap 2, secs 15-18

secs 19-23

1^st hwk due Monday 2/15. I put a link in the contact folder that will take you to a Google form where you can upload your solutions.

2/22-2/26

Analytic and harmonic functions.

Some basic egs: exponential, trig fns

Chap 2, secs 25-27

Chap 3, secs 30-38

I’ll likely skip over sec 26 (polar coords) and secs 28-29.

I mostly skipped the stuff about z and zbar partial derivatives. Hence you don’t need to do Prob 7 on Assignment 3.

3/1-3/5

Log fns and exponents

Contours and integration

Chap 3, secs 31-36

Chap 4, secs 41-45, 47

Minibreak March 2

3/8-3/12

Antiderivatives and Cauchy’s Theorem

(review &) midterm

Chap 4, secs 48-51 (I might give a Green’s Thm based pf of Cauchy, rather than the book’s proof)

1^st midterm Friday, March 12 in class

3/15-3/19

Cauchy’s Integral Formula, derivatives of analytic functions

Chap 4, secs 52-57

Please turn in corrections for exam 1 (along with your exam) on Monday 3/22.

3/22-3/26

Liouville’s Theorem, Maximum modulus principle and the Fundamental Theorem of Algebra

Chap 4, secs 58-59

3/29-4/2

Sequences, series and power series

Chap 5, secs 61-62, 69-71

No office hours April 2: Good Friday. I’ll hang around after class Wed if you have any questions.

4/5-4/9

Power series and Taylor series

Chap 5, secs 63-64, 72

4/12-4/16

Isolated singularities and Laurent series

Chaps 5/6, secs 66-67, 74, 78

4/19-4/23

(cont)

No class April 21: minibreak

4/26-4/30

The Residue Theorem

Chap 6, secs 75-76, 80-84, 85

There’s a short review sheet for the 2^nd midterm in the Drive folder

2^nd midterm, Friday April 30

5/3-5/7

Integration via the Residue Theorem

Chap 7, secs 85-92

5/10

What I didn’t tell you

Homework 10 due on 5/10; homework 11 won’t be collected, but it’ll help you prepare for the final.

Office hr (prior to final) Sunday, May 16, 4:30-5:30 in Hayes-Healy 129

Final exam Tuesday, May 18 from 4:15-6:15 PM, Bond 104.