This will be updated as the semester progresses.
Read Chapter 1.
Do Ch 1 exercises 2, 12, 13, 20, 27, 29, 36, 49 (do not hand in)
Do Chapter 1, Exercise 42; Chapter 2, Exercises 2, 4, 14, 23 (do not hand these in).
Hand in Chapter 2, Exercises 3 and 5. Try to do Exercise 3 directly (using the Fundamental Theorem of Calculus) rather than using Cauchy's Theorem or the proofs of Theorems 1.5.3 or Section 2.3.
In addition hand in the following exercise: Suppose Omega is a connected open set in the complex plane. Suppose f:Omega --> C is holomorphic with |f(z)|=1 for all z in Omega. Show f is a constant function on Omega.
Do Chapter 2 #18 (do not hand in)
Hand in Chapter 2 # 15, 23, 36, 43. Ignore the hint in Exercise 43 (referring to 6 and 42). The hint should be to use Exercise 5, which you did for the previous homework assignment.
Assignment due 9/28 is the following hand-out (in pdf format).
Do, but do not turn in Chapter 3 #3, 11, a, d, e, f, g, h. Also prove the ratio test: the series sum(a_n, n=1..infinity) converges absolutely provided the limsup |a_{n+1}|/|a_n| <1 as n -> infinity; here, a_n is sequence of nonzero complex numbers.
Turn in the following problems: Chapter 3 # 10, 18, 21 and 33.
Do, but do not turn in Chapter 4, #5, 13, 17
Turn in the following problems: Chapter 3 # 39 and Chapter 4, #1, 3, 8, 14.
Do, but do not turn in Chapter 4, #35, 36 42.
Turn in the following problems: Chapter 4 # 50, 53, 58, 61. Hint for #61, use a contour integral over the unit circle, with z=e^{it}.
Midterm due
Turn in the following problems: Chapter 5, # 3, 11 (do only the first part - the formula for f^{-1} (w)). Also do # 12 and 16. For extra credit, do #13 (but no hints will be given for extra credit problems).
Hand-out
Hand-out
Hand-out