# MATH 452

## Introduction to Complex Variables II

(Updated
)
### News

This course is over.
### General Information

**Meets**: MWF 3:10-4:00 in Ritter 217
**Instructor**: Dr. Bryan Clair
**Syllabus**: syllabus.pdf
**Textbook**: E.B. Saff, A.D. Snider, Fundamentals of Complex Analysis (with applications to engineering and science) (3ed), 2003.

### Resources

For the Mobius transformations part of the course, we are using:
- Needham,
Visual Complex Analysis, Chapter 3, and particularly sections
II, V, and VI.
- Saff & Snider, Ch 7.3 and 7.4

The Non-Euclid applet.

Applets demonstrating inversion in a circle:
Circle Inversion,
Inverting an F,
The
Peaucellier Linkage.

An article about the history of the problem of
changing circular
motion into straight-line motion by Daina Taimina.

Mobius Transformations Revealed (YouTube video).

For the infinite product/Gamma/Zeta function part of the course, we are using pages 164-194 of Conway,
Functions of One Complex Variable (2ed).

Pictures of the Riemann Zeta function ζ(z):

- |ζ(z)| on [-5,5]x[-60,60]: Image.
- 1/|ζ(z)| on [-2,2]x[0,100]: Image.
- |ζ(½ + iy)| for y in [0,100]: Image.

Pictures of the Gamma function: |Γ(z)|,
Γ(x).

XKCD on the Riemann Zeta funtion.

### Homework Assignments

- Due Wednesday, 1/20:

Week 1 problems #1-4.
- Due Wednesday, 1/27:

Ch 5.3 # 2, 3*, 4, 5, 6, 7, 11, 16

Ch 5.4 # 3, 14

- Due Wednesday, 2/3:

Ch 5.5 # 1*, 2, 3*, 4*, 5*, 6*, 7*, 9, 10

Ch 5.6 # 1*, 2, 3*
- Due Wednesday, 2/10:

Ch 5.6 # 5, 6, 7, 9, 12, 15, 19

Ch 5.7 # 1*, 2, 3*, 5
- Due Wednesday, 2/17:

Ch 6.1 # 1*, 3*, 4, 5, 7
- Due Friday, 2/26:

Ch 6.3 # 1, 3, 4, 5, 11

Ch 6.5 # 12
- Due Wednesday, 3/24:

Conway Pg. 173 # 1, 4, 5, 6, 7, 8

Plus problems on a handout.
- Due Wednesday, 4/7:

Problems on a handout.
- Due Monday, 4/19:

Conway Pg. 185 # 2

Conway Pg. 194 # 2, 3, 4

Plus one problem on a handout.
- Due Friday, 4/30:

Check (3) on page 124 of Needham

S-S: 7.3 # 3, 5, 7, 9, 11

S-S: 7.4 # 14, 19, 22bc

Needham: Ch 3 # 2, 10, 11, 12

* Routine problem - do as many as you need to.