Stephen P. Shipman
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Department of Mathematics
Louisiana State University
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Complex Variables

Math 4036-1
Louisiana State University
Fall Semester, 2017

Prof. Stephen Shipman


Place: Room 111 of Lockett Hall
Time: Monday, Wednesday, and Friday from 2:30 to 3:20

Office: Room 314 of Lockett Hall
Telephone: 225/578-1674
Email: shipman@math.lsu.edu
Office Hours: Monday 1:00-2:20; Wednesday 3:30-5:00; or by appointment


Course Synopsis

Textbook

Complex Variables and Applications, by J. W. Brown and R. V. Churchill, 9th ed.

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 Chapters 1-9 of the text book. 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.
Computing integrals using poles of complex functions and their "residues".
Mapping by elementary functions; conformal mapping (preservation of angle).

Assignments

Problems will be assigned weekly and will usually be due on Fridays. All submitted work must adhere to the statement of ethical conduct at the bottom of this page. There is a grader for this course, but I (SS) will also review some of your work. I encourage you to discuss your mathematical thoughts with me and with others and to seek enlightenment (not copy solutions) from other sources, such as books, Wikimedia, etc. I am aware that solutions to problems in standard textbooks are easily available, and students must resist any temptation to use them. Trying to solve a problem on your own, even if you don't succeed completely, is infinitely more valuable and ethical than using someone else's solution.

In the problems listed below, I also list some suggested problems for practice. Your rule should be to do as many problems as you can and to keep practicing until you are confident with the material.

This is a 4000-level mathematics course, and all submitted work is expected to be logically coherent. This applies to all problems, whether they emphasize computation, verification, or proof.

Page numbers refer to the page on which the problem set begins.

Due date Chapter Problems to do; those in red are to be submitted.
Friday, Aug. 25 Chapter 1 p.12: 8, 9, 11; p.7: 1, 8; p.13: 3, 6, 7, 8; p.16: 2, 6, 7, 9, 10, 13, 14.
Friday, Sept. 1 Chapter 1 p.23: 1, 5, 6, 7, 8, 9, 10, 11; p.30: 5, 6, 8; p.34: 1, 4, 5, 10.
Friday, Sept. 8 Chapter 2 p.43: 3, 4, 5, 8, 9; p.54 2, 3, 5, 9, 10, 11, 13; p.61 1, 3, 7, 8, 9.
Friday, Sept. 15 Chapter 2 p.70: 1, 2, 4, 6, 7, 8; p.76 1, 2, 4, 5, 6; p.79 1, 2, 5, 6; p.84 2, 4, 5.
Wed., Sept. 20 Chapter 3 p.89: 3, 5, 6, 7, 8, 12, 13; p.95 1, 2, 3, 4, 5, 10; p.99 1, 2, 3; p.107 4, 7, 11, 12; p.111 4; p.114 1, 3.
Friday, Sept. 22 Chapters 1-3 Exam 1.
Friday, Sept. 29 Chapter 4 p.119: 1, 2, 3, 4; p.123 2; p.132 1-13, 6, 9, 10, 13; p.138 1-8, 4.
Monday, Oct. 9 Chapter 4 p.147: 1-3, 4, 5; p.159: 1, 2, 3, 4, 6, 7; p.170: 1-3, 4, 5, 6, 7, 10.
Friday, Oct. 13 Chapter 5 p.195: 1-11, 4, 6, 9, 11.
Wed., Oct. 23 Chapter 5 p.205: 1-10, 3, 7, 10; p.218 1-8, 3, 6, 8; p.224 1, 2, 3.
Mon., Oct. 23 Chapters 4-5 Exam 2.
Fri., Nov. 3 Chapter 6 p.237: 1, 2, 3, 4, 5, 6, 7; p.242: 1, 2, 3; p.246 1, 2, 3, 4, 5, 6, 7, 8.
Fri., Nov. 10 Chapter 7 p.264: 1-8, 6, 9, 10; p.273: 1-11, 1, 3, 7, 10, 12.
Fri., Nov. 20 Chapter 7 p.282: 1-6, 1, 2, 4, 5; p.287: 1-6, 5; p.293: 7, 8.
Mon., Nov. 20 Chapters 6-7 Exam 3.

Exam schedule

Exam 1: Friday, September 22
Exam 2: Monday, October 23
Exam 3: Monday, November 20
Final Exam: Tuesday, December 5, from 5:30 to 7:30

Evaluation

Evaluation of performance in the course is based on scores on the exams, assignments and the final exam as follows:
Assignments: 15%
Exam 1: 20%
Exam 2: 20%
Exam 3: 20%
Final exam: 25%

Grading scale:
A+: at least 95% A: at least 90% A-: at least 88%
B+: at least 85% B: at least 80% B-: at least 78%
C+: at least 75% C: at least 70% C-: at least 68%
D+: at least 65% D: at least 60% D-: at least 50%
F: less than 50%

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.

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