MATH 451

Introduction to Complex Variables

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

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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:
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.