COMPLEX ANALYSIS
Math 2101, Spring 2010

Instructor: Dr. Rachel Hall
Office: 229 Barbelin
Office Hours: M 2:30-4, W 2-3:30, F 1-2 and by appointment
Telephone: (610) 660-3096 (Office)
E-mail: rhall@sju.edu
URL: http://www.sju.edu/~rhall/Complex

Course Description:  Complex analysis, the theory of functions of complex numbers, is one of the crowning achievements of nineteenth century mathematics.  Although complex numbers are sometimes called imaginary numbers, complex analysis is far from imaginary; it has a multitude of real-world applications to engineering, physics, and applied mathematics.  We will cover Chapters 1-4 in the textbook, plus selected topics in Chapters 5, 6, and 8.  Topics include properties of complex numbers, analytic functions, mapping, contour integrals, the fundamental theorem of algebra, and Cauchy’s residue theorem.   I will pay special attention to the geometric properties of complex functions.

Prerequisite: Real Analysis or consent of instructor

Text: Complex Variables and Applications, James Ward Brown and Ruel V. Churchill, seventh edition.  McGraw Hill, 2003.

Homework:  Homework assignments will be posted at http://www.sju.edu/~rhall/Complex/homework.html.   There will be about ten homework assignments; the lowest grade will be dropped.  You should start working on the homework problems for a section as soon as that section is covered in class.  Although you are encouraged to consult with other students and seek help from me, your homework should ultimately represent your own work. For more information, see the department’s Academic Honesty guidelines. Answers unsupported by work will not receive credit.  Homework should be neatly handwritten or typed, on one side of the page only.  Please remove messy edges and staple.

Function diary:  Each of you will be assigned a function at the beginning of the semester.  You will be asked to keep a diary of how each new topic applies to your function.  You will also be asked to present examples relating to your function in class.  The project will culminate in a paper.

Tests:  There will be two midterms and a final. Makeup tests will only be given to students who contact me within 48 hours of missing a test.  Students with a valid, verifiable reason for missing a test may take a makeup without penalty; those who have missed a test without a valid, verifiable reason may take a makeup with a 30% penalty.   The final will be cumulative.


Grades:  Grades will be assigned on the following basis:

3%       class participation
7%       function diary project (includes presentation and paper)
25%     homework (lowest grade dropped)
40%     two midterms
25%     final (may replace your lowest midterm grade, if it is lower than your grade on the final)

The grade cutoffs are 90% A, 86.7% A-, 83.3% B+, 80% B, 76.6% B-, 73.3% C+, 70% C, 65% C-, 60% D+, 55% D, and below 55% F.

Academic Honesty: Dishonesty includes cheating on a test, falsifying data, misrepresenting the work of others as your own (plagiarism), and helping another student cheat or plagiarize. Academic dishonesty will result in a grade of zero on that particular assignment; serious or repeated infractions of the Academic Honesty policy will result in failure of the course. All violations of the Academic Honesty policy will result in the filing of a violation report.  For complete information about the University's policy on Academic Honesty, consult the department’s Academic Honesty guidelines and the Student Handbook 2009-2010.

Attendance:  If you do miss a class, it is your responsibility to make up the material and make sure your homework is turned in on time.

Schedule: 

Weeks

Topics

2

Chapter 1

3

Chapter 2

2

Chapter 3

1

Chapter 8

2

Chapter 4

1

Chapter 5

1

Chapter 6