MATH 353 - COURSE SYLLABUS

Instructor:	Adrian Rice
Office:	Copley 233
Phone:	752-7230
e-mail:	arice4@rmc.edu
Web Site:	http://faculty.rmc.edu/adrice/public_html/math353.html
Office Hours:	Tu Th 2:00 - 3:00 and by appointment

Useful Books:

Complex variables: introduction and applications, by Mark J. Ablowitz
& Athanassios S. Fokas, Cambridge: Cambridge University Press, 1997.

Complex variables, by Stephen D. Fisher, Pacific Grove, Calif.:
Wadsworth & Brooks/Cole Advanced Books & Software, 1990.

Complex variables for mathematics and engineering, by John H. Mathews,
Dubuque, Iowa: W.C. Brown, 1988.

For historical background, see An Imaginary Tale: The Story of i, by Paul Nahin,
Princeton University Press, 1997.

Objectives:

This course is an introduction to the calculus of analytic functions. As such, it does for complex variables what regular calculus does for real variables. In other words, it extends existing methods and introduces new ones to enable the differentiation and integration of complex functions. This subject is one of the most beautiful and intricate branches of mathematics, containing some interesting results and powerful methods, which facilitate the solution of otherwise impenetrable problems. Consequently, the chief aims of this course will be to equip you with some of the necessary theory and techniques to enable to you solve such problems and derive further results.

Homework:

Problem sets will be regularly assigned. Homework solutions will not be collected. However, at least 75% of the problems on each exam will be drawn directly from the assigned homework exercises.

In-Class Activities:

Time during a typical class meeting will be spent on a lecture covering the main points, and working on in-class problems and examples.

Attendance:

You are expected to attend class, as it will contribute to your final grade.
LATE ARRIVAL TO CLASS WILL BE COUNTED AS AN ABSENCE.

Quizzes:

There will be a number of quizzes throughout the course. The purpose of these quizzes is to ensure that you are keeping up with the homework and the lectures.
NO MAKE-UP QUIZZES WILL BE GIVEN.

Topics to be covered in the course will include:

The algebra of complex numbers

The geometry of complex numbers

Functions of a complex variable

The Cauchy-Riemann equations

Analytic Functions

Paths and Connectedness

The complex integral

The Cauchy integral theorem

Contour integration

Taylor and Laurent series

Theory of Residues

Exams:

There will be two midterm tests, and the course will conclude with a comprehensive final exam of three hours. The dates of the exams can be found in the Examination Schedule.
AN UNEXCUSED ABSENCE FROM AN EXAM WILL RESULT IN A SCORE OF ZERO.

Course Grade:

Your course grade will be based on scores received on the two midterm tests, the final, and the quizzes. Attendance will also be taken into consideration. The course grade scale is given below:

Grade Scale
Exam 1		25%
Exam 2		25%
Quizzes		15%
Attendance		5%
Final exam		30%

Technology Policy:

The only form of technology that is permitted in my classroom is a calculator. Cell phones, iPods, and ALL OTHER ELECTRONIC DEVICES ARE STRICTLY PROHIBITED. Anyone listening to music, sending texts, reading messages, making phone calls, or whose cell phone rings in class will have HALF A LETTER GRADE deducted from their final grade on every occasion this policy is violated.

Disabilities:

If you have a physical or psychological disability that requires an accommodation, you must first register with the Office for Disability Support Services. Please arrange a meeting with the course instructor to discuss your needs and how to register for support services.