Class Schedule: Monday-Wednesday, 8:30-10:00 AM; East Hall (EH) 4096
Textbook: Complex Analysis with Applications, by R. A. Silverman, Dover Publications, Mineola, New York, 1984.
Office Hours: Wednesday 10:00 AM-12:00 PM; East Hall (EH) 3836
Homework Policy: Homework will be due every Monday at the end of class. No late homework will be accepted. Due to the grading policy, only emergency situations will be considered for extensions on homework.
Grading Policy: 40% Homework, 25% Midterm, 35% Final. The lowest homework score will be dropped. Each homework assignments will be graded out of 20 points. Four questions will be evaluated closely (4 points each) and the remaining 4 points are given for meaningful completion of the remaining problems.
Homework 1: due Wednesday, January 23
Chapter 1 (Silverman) #3, #16, #21, #23; Chapter 2 (Silverman) #6, #8, #13, #17, #21
Homework 2: due Monday, February 4
Chapter 3 (Silverman) #5, #12, #13, #14; Chapter 4 (Silverman) #1, #3, #6, #7, #8
Homework 3: due Monday, February 11
Chapter 4 (Silverman) #11 (see remark 4.35 on 42) page , #22 (see definition of entire in problem #16 page 44); Chapter 5 (Silverman) #8, #10, #12, #15, #16
Homework 4: due Monday, February 18
Chapter 5 (Silverman): #18, #21, #25; Chapter 6 (Silverman): #3, #4, #9, #12; read pages 228-232 of Silverman
Homework 5: due Monday, February 25
Chapter 6 (Silverman) #15, #17, #21; Chapter 7 (Silverman): #4, #11, #12, #15
Homework 6: due Monday, March 18
Chapter 8 (Silverman) #2, #6, #9, #10, #15, #22, #30 (see definition of group and subgroup from #28, #29)
Homework 7: due Monday, March 25
Chapter 9 (Silverman) #1, #3, #4, #5, #6, #13, #14, #18
Homework 8: due Monday, April 1
Chapter 10 (Silverman) #5, #8, #10, #16, #18, #21, #25, #27
Homework 9: due Monday, April 8
Chapter 11 (Silverman) #2, #10 (b,d,f,h), #11 (a, d, h), #21 (a, c, g, h), #22, #24, #31, #33
Homework 10: due Wednesday, April 17
Chapter 12 (Silverman) #4, #14 (c), #16, #17, #20 (b), #23 (c), #23 (d)
Homework 11 (Optional): due Monday, April 22
Revise one prior homework. You only need to rewrite the problems you got incorrect. Please turn in the corrections with your previous version. This revision is due by 9:50am in class, no exceptions.
Midterm: Wednesday, February 27 (in class)
The first midterm will cover material from Chapters 1-7 of the course textbook and any supplementary material covered in class.
Final: Thursday, May 2, 8:00-10:00 AM; East Hall 3836
Sample Problem to Do for the Final: Prove directly from the integral form of the solution, u(z), to the Dirichlet problem on the half-plane, G = {Im (z) > 0} that the maximum of u(z) is achieved on the boundary C= {Im (z) = 0}.
Assume that the function $g: \mathbb{R} \rightarrow \mathbb{R}$, such that $u(x) = g(x)$ on the boundary, is bounded and non-negative.