Mathematics 134, Spring 2017

Functions of a Complex Variable and Applications

Lectures:

Section 1: Tuesdays and Thursdays, 9-10:15am
Room 122, Sequoia Hall



Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Office Hours: Mondays and Wednesdays 9-10am and Thursdays 10:30-11:30am.


A description of the course: Math 134, Spring 2017 (pdf)

Drop Policy


Announcements:

We will be using the following textbook:
Complex Variables (2nd Edition) by Stephen D. Fisher.
We will cover the first two chapters and (as time allows) parts of the third chapter, as listed in the schedule below.


Final Exam Schedule:
Tuesday, May 16, 10:15am-12:15pm




Homework:

Homework 1, due Tuesday, January 31:
Section 1.1 (1, 2ac, 3, 4, 5, 6abcf, 7, 8, 10, 17, 18)
Section 1.1.1 (4)
I won't grade odd problems, since the answers are in the back of the book, but I expect you to know how to do them on exams.

Homework 2, due Tuesday, February 7:
Section 1.2 (3, 4, 6, 10, 12, 14, 22, 24, 26, 28)

Homework 3: Do not turn it in, but expect to see problems like this on the exam on Tuesday, February 14.
Section 1.3 (1-9, 26)

Homework 4, due Tuesday, February 28:
Section 1.4 (3, 7, 8, 13, 14, 16, 19, 40ab)
Section 1.5 (2, 10, 11, 12, 19, 23)

Homework 5, due Tuesday, March 7:
Section 1.6 (1, 2, 3, 4, 5, 6, 7, 8, 12a)
I will grade your homework on the same day, and you can pick it up on Wednesday, March 8, if you want.
(The exam is on Thursday, March 9.)

Homework 6, due Thursday, March 30:
Section 2.1 (1ab, 3, 6, 9, 14, 15, 17, 21, 22, 24, 26)
Also, for Problems 2, 3, and 4 in Section 2.1.1: The given function represents a vector field in the plane.
(a) is the vector field conservative? (i.e. the gradient of a function U)
(b) is the vector field locally sourceless? (i.e. is its divergence zero?)
(c) if your answers to (a) and (b) lead you to a harmonic function U, find an analytic function f(z) having U as its real part.

Homework 7, due Thursday, April 6:
Section 2.2 (8, 9, 10, 18, 19, 23)

Homework 8, due Thursday, April 13:
Section 2.3 (1, 2, 3, 4, 7, 9, 10, 12, 13, 14, 15, 16)
Hint on 13.

Homework 9: Do not turn it in, but expect to see problems like this on the exam on Thursday, April 20.
Section 2.4 (13, 14, 17, 18)
And also work on the review problems I passed out in class.

Homework 10, due Thursday, May 4:
Section 2.5 (1, 2, 3, 8, 10, 14, 15, 19, 20, 21)

Homework 11: Do not turn it in, but it's good practice for the final exam.
Section 2.6 (1, 5, 9, 13, 17)




Exams:

Exams and Solutions are posted on Sac CT.




Lecture Schedule

DateTopicsBookNotesCode
1. T 1/24 Complex Numbers and the Complex Plane, I. § 1.1
2. R 1/26 Complex Numbers and the Complex Plane, II. § 1.1
3. T 1/31 Geometry of Complex Numbers, I. § 1.2
4. R 2/2 Geometry of Complex Numbers, II. § 1.2
5. T 2/7 Subsets of the Plane. § 1.3 sketch of 1/z
6. R 2/9 Review.
T 2/14 EXAM 1
7. R 2/16 Functions and Limits. § 1.4
8. T 2/21 The Exp, Log, Trig Functions. § 1.5
9. R 2/23 Line Integrals and Green's Theorem, I. § 1.6
10. T 2/28 Line Integrals and Green's Theorem, II. § 1.6
11. R 3/2 Line Integrals and Green's Theorem, III. § 1.6
12. T 3/7 Review
R 3/9 EXAM 2
13. T 3/14 The Cauchy-Riemann Equations, I. § 2.1
14. R 3/16 The Cauchy-Riemann Equations, II. § 2.1
M-F 3/20-24 NO CLASS (Spring Break)
15. T 3/28 Power Series, I. § 2.2
16. R 3/30 Power Series, II. § 2.2
17. T 4/4 Cauchy's Theorem, I. § 2.3
18. R 4/6 Cauchy's Theorem, II. § 2.3
19. T 4/11 Consequences of Cauchy's Formula, I. § 2.4
20. R 4/13 Consequences of Cauchy's Formula, II. § 2.4
21. T 4/18 Review.
R 4/20 EXAM 3
22. T 4/25 Isolated Singularities, I. § 2.5
23. R 4/27 Isolated Singularities, II. § 2.5
24. T 5/2 The Residue Theorem and Definite Integrals, I. § 2.6
25. R 5/4 The Residue Theorem and Definite Integrals, II. § 2.6
26. T 5/9 The Residue Theorem and Definite Integrals, III. § 2.6
27. R 5/11 Review.
FINAL EXAM: 5/16, 10:15am-12:15pm