MATH 451

Introduction to Complex Variables

News

General Information

• Fall 2009 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

• The whole point of this class (maybe). And Euler's formula. And Complex Conjugation.
• Cubic equations and their history: History of quadratic, cubic, and quartic equations. The cubic formula at CTK.
• The complex exponential function: 24 views, more visualizations.
• Stereographic projection:
  • Animated demo.
  • The Earth: Polar, Transverse, centered on Japan.
  • Mathematica demo.

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 x³ = 6x + 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