Math 407-500 — Fall 2023

Assignment 1 - Due Friday, 9/1/23.

• Read sections ICA 1.1-1.4, 1.6 and Schaum's Chapter 1
• Do the following problems.
  1. ICA 1.3.1(d), 1.3.9(b), 1.3.10, 1.4.2(c), 1.4.5(k), 1.4.6 (Hint: Show that $(1-z)\sum_{k=0}^{n-1}z^k=1-z^n$.)
  2. Schaum's 1.89(e), 1.93(a), 1.97(b)

Assignment 2 - Due Monday, 9/11/23.

• Read sections ICA 1.6, 2.10-2.12 and Schaum's 2,6, 2.9 2.18
• Do the following problems.
  1. Schaum's 1.118-1.120, 2.46, 2.50, 2.59. 2.62(c), 2.68(b,c), 2.102, 2.103

Assignment 3 - Due Monday, 9/25/23.

• Read Schaum's sections 3.1-3.10
• Do the following problems.
  1. Schaum's 2.19, 2.20, 2.56, 2.77(a), 2.78(b), 3.47, 3.69(a), 3.70(b), 3.77(a), 3.77(b)

Assignment 4 - Due Friday, 10/13/23.

• Read Chapter 4 in Schaum's.
• Do the following problems from Schaum's: 4.32, 4.33(a,b), 4.36(a,c), 4.40(a,b), 4.45, 4.49, 4.52, 4.61(b)

Assignment 5 - Due Friday, 10/27/23.

• Read Chapter 5 in Schaum's.
• Do the following problems from Schaum's: 5.31-5.36 (For 5.36, see Solved Problem 5.3), 5.39, 5.46, 5.50(a)
• Suppose that $f(z)$ is an entire function (i.e., $f$ is analytic on $\mathbb C$) and that $|f(z)|\le A|z|+B$, where $A$ and $B$ are positive. Show that $f(z)$ is linear; that is, $f(z)=az+b$. (Hint: use Cauchy's inequality for $n=2$.)

Assignment 6 - Due Friday, 11/10/23.

• Read sections 55-59 in Chapter 5 of Brown/Churchill.
• Do the following problems from Brown/Churchill: 1, 3, 5, 7, pgs. 179-180; 2, 3, 4, 7, 8, 10, 11, pgs. 196-197.

Assignment 7 - Due Monday, 11/20/23.

• Read sections 59-62 in Chapter 5 of Brown/Churchill.
• Do the following problems from Brown/Churchill: 1-7, pgs. 205-206. BONUS (15 pts., no partial credit) 10, pg. 207.

Assignment 8 - Due Monday, 12/4/23.

• Read sections 72, 73, 76, in chapter 6, and sections 78, 79 and 85 in Brown/Churchill. (These are "how to do" sections. Section 85 is actually easier than the earlier ones in chapter 7.)
• Do the following problems from Brown/Churchill: 1(a,b,d), 2, 3, pg. 243; 4(a), 5, pg. 248; 2(a), 9, pgs. 255-256; 3, 6, pg. 267; 1, 2, pg. 290.

Updated 11/30/2023.