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Complex Variables
Math 4036-1
Louisiana State University
Fall Semester, 2009
Prof. Stephen Shipman
Place: Room 130 of Lockett Hall
Time: Tuesday and Thursday from 12:10 to 1:30
Office: Room 314 of Lockett Hall
Telephone: 225/578-1674
Email: shipman@math.lsu.edu
Office Hours: Monday 9:00-11:00 and Wednesday 1:00-3:00 or by appointment
For a PDF version of the basic course information on this page,
click here: 4036syl.pdf
Textbook
Complex Variables and Applications, by J. W. Brown and R. V. Churchill.
Course Description
Complex functions of one complex variable; analytic functions, integration, power series, residues, and conformal mapping.
The prerequisite for this course is Math 2057, multivariable calculus.
Course Content
The content of the course will span most of the text book, with some subsections being omitted. Some of the key ideas are the following:
- Algebraic, geometric, and analytic structure of the set of complex numbers.
- Complex-analytic functions and the differential and integral calculus thereof.
- Power series.
- Poles of complex functions and their "residues".
- Mapping by elementary functions; conformal mapping (preservation of angle).
- Applications to boundary-value problems for harmonic functions.
Assignments
Due date |
Section |
Problems to do |
| Tues., Sept. 1
| Chapter 1
| p.12: 5, 6; p.22: 5, 9, 10; p.29: 4, 5, 8.
|
| Tues., Sept. 8
| Chapter 2
| p.55: 10, 11; p.62: 2, 9; p.71: 1, 6, 8, 10; p.77: 6, 7.
|
| Tues., Sept. 15
| Chapter 3
| p.92: 1, 3, 6; p.97: 3, 10; p.100: 4; p.104: 1; p.108: 16; p.111: 1.
|
| Tues., Sept. 22
| Chapter 4
| p.135: 1, 3, 6, 7; p.140: 1, 3, 5, 7.
|
| Thurs., Oct. 15
| Chapter 5
| p.188: 3; p.196: 7, 12; p.206: 7, 11; p.220: 5, 8; p.225: 4, 8.
|
| Tues., Nov. 3
| Chapter 6
| p.239: 2, 6; p.243: 4, 5; p.248: 6, 7; p.255: 5, 7.
|
| Tues., Nov. 24
| Chapter 7
| p.267: 4, 8; p.276: 8, 10; more to come
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Exam schedule
- Exam 1: September 24
- Exam 2: November 10
- Final Exam: Thursday, December 10, from 12:30 to 2:30
Evaluation
Evaluation of performance in the course is based on scores on the exams, assignments and the final exam as follows:
- Assignments: 25%
- Exam 1: 25%
- Exam 2: 25%
- Final exam: 25%
In calculating the grade, the lower of the scores on Exam 1 and Exam 2 will be replaced by the score on the final exam, given that the final exam score is higher.
Ethical Conduct
Students may discuss problems with each other and other people and consult other literature; 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. No joint work in any capacity may be submitted for evaluation.
Students must abide by the LSU
Code of Student Conduct .
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