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Complex Analysis
Math 7350
Louisiana State University
Fall Semester, 2014
Prof. Stephen Shipman
Place: Lockett 111
Time: 11:3012:20 Monday, Wednesday, Friday
Office: Room 314 of Lockett Hall
Telephone: 225/5781674
Email: shipman@math.lsu.edu
Office Hours: Monday 1:304:00 and Thursday 1:303:30, or by appointment
Textbook
Complex Analysis by Elias Stein and Rami Shakarchi; Princeton Lectures in Analysis.
Course Description
Theory of holomorphic functions of one complex variable; path integrals, power series, singularities, mapping properties, normal families,
special functions (Gamma, Zeta, Theta, Elliptic) Fourier transform, special topics.
Prerequisite
The prerequisite is a good graduate or very good undergraduate analysis course.
Course Topics
 Holomorphic functions and power series
 Cauchy's integral formula; Runge's approximation theorem
 Meromorphic functions and the logarithm
 The Fourier transform
 Infinite products and entire functions
 The gammafunction
 The Riemann zetafunction and the prime number theorem
 Conformal mappingsautomorphisms of the disk, the Riemann mapping theorem, and polygons
 Elliptic functions
 Theta functions
 The Jordan curve theorem
 Some asymptotics
Assignments
The book has lots of exercises and problems; see the schedule of weekly problem sets below.
Students may discuss problems with each other and other people (including me, of course) and consult other literature; in fact students are encouraged to search the literature and discuss ideas. However, all work that is turned in must ultimately be that of the submitter alone. If a student receives aid on an assigned problem from discussions with people or other sources, he or she must begin from scratch in writing the solution so that the result is the product of his or her own understanding alone.
Evaluation
 Regular assignments: 50%
 Midterm exam: 20% Friday, October 17
 Final exam: 30% Monday, December 8 from 10:00 to 12:00 in Lockett 111
The final exam will be based on the following themes:
 Chapter 9, Exercise 2 (p. 278)
 Chapter 9, Problem 2 (p. 281)
 Chapter 4, Exercise 7 (p. 128)
 Computing definite integrals by complex contour integration and residue calculus
Problems to do
Due date 
Section 
Problems to do 
Fri., Sept. 5
 Chapter 1
 3, 7, 9, 13, 15, 16, 17, 18, 19, 23, 25

Mon., Sept 22
 Chapter 2
 Exercises 1, 4, 6, 9, 13, 15; Problem 4

Mon., Oct 6
 Chapter 3
 Exercises 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 22

. . .
 Chapter 4
 None

Fri., Oct. 17
 Midterm Exam
 Topics in residue calculus

Mon., Nov. 3
 Chapter 5
 Exercises 1, 2, 3, 5, 16, Problems 1, 2

. . .
 Chapter 6
 None

. . .
 Chapter 7
 None

Wed., Nov. 26
 Chapter 8
 Exercises 3, 13, 15; Problem 4

