# MATH 451

## Introduction to Complex Variables

(Updated
)
### News

The class is over. Check back in January for udpated information for Math 452.
### General Information

**Meets**: MWF 3:10-4:00 in Ritter 217.
**Instructor**: Dr. Bryan Clair
**Syllabus**: 451syllabus.pdf
**Textbook**: E.B. Saff, A.D. Snider, Fundamentals of Complex Analysis (with applications to engineering and science) (3ed), 2003.

### Links

### Homework Assignments

- 1. Due Friday 8/28
- Ch. 1.1 # 4, 5, 7, 9, 11, 13, 14, 15, 17, 19, 20, 23.

Problem A: Solve *x*^{3} = 6*x* + 6 and check your answer.
- 2. Due Friday 9/4
- Ch 1.2 # 4*, 7ij, 9, 10, 14, 15

Ch 1.3 # 4, 5*, 11, 12*, 13, 19

Ch 1.4 # 1*, 2*, 3*, 4*, 5, 7, 8.
- 3. Due Friday 9/11
- Ch 1.4 # 10, 11, 12a, 17*

Ch 1.5 # 5*, 8, 10, 18

Problem A: Find the primitive 12th roots of unity (see bottom pg. 34).
- 4. Due Friday 9/18
- Ch 1.7 # 5

Problem A: Describe how f(z) = z-bar (complex conjugation) acts on the Riemann Sphere.

Problem B: Describe how f(z) = -z acts on the Riemann Sphere.

Ch 2.1 # 6, 7a, 8a, 9, 12

Ch 1.6 # (2-8)*, 11, 13, 17, 18.
- 5. Due
*Wednesday* 9/23
- Ch 2.2 # 4, 7*, 11*, 14, 16, 17, 21*, 25*

Ch 2.3 # 1, 2, 3, 4, 7*, 13
- 6. Due Friday, 10/2
- Ch 2.4 # 2, 6, 7, 8, 10, 11, 15
- 7. Due Friday, 10/9
- Ch 2.5 # 1b, 3e, 4, 5, 6, 14, 16, 21

Ch 2.6 # 1*, 2*, 3*

Ch 2.7 # 1, 3a, 5, 10
- 8. Due Friday, 10/16
- Ch 3.3 # 1*, 3, 5, 6, 7, 9, 10, 15

Ch 3.5 # 1*, 3*, 5, 7, 15a

Ch 3.2 # 5*, 12*, 13*, 14c, 25
- 9. Due
*Wednesday*, 10/28
- Ch 3.4 #1, 2, 3, 4, 6

Ch 4.1 #1, 3, 8

Ch 4.2 #7, 8, 11, 14a, 15

Ch 4.3 #1*, 6, 7, 12
- 10. Due Monday, 11/9
- Ch 4.4 #1*, 3*, 5*, 9*, 10*, 11, 16, 18, 19

Problem A: Show that homotopy is an equivalence relation. That is, for
curves C1, C2, C3 in a domain D, show:
- (Reflexive)C1 is homotopic to C1.
- (Symmetric)If C1 is homotopic to C2 then C2 is homotopic to C1.
- (Transitive)If C1 is homotopic to C2 and C2 is homotopic to C3 then
C1 is homotopic to C3.

- 11. Due Monday, 11/16
- Ch 4.5 # 1, 2, 3ab, 5, 9, 10, 14, 16, 17
- 12. Due Monday, 11/23
- Ch 4.6 # 3, 4, 5, 7, 10, 11, 14, 16

Ch 4.7 # 1, 2, 4, 5
- 13. Due Friday, 12/4
- Ch 5.1 # 1*, 2*, 3, 5, 6, 11*

Ch 5.2 # 1be, 4, 5

* : Multipart exercise. Do as many parts as you feel you need to learn the
material.