General Information and Course Policies

Course Overview. This is an advanced undergraduate course covering fundamental aspects of functions in one complex variable. We start with the definition and properties of complex numbers including their geometric interpretation. Then we define the notion of complex differentiable function (aka holomorphic) in one complex variable and study some basic examples. We continue with Cauchy integral formula and derive some striking properties of holomorphic functions such as analyticity. We also study isolated singular points of holomorphic functions (Laurent series, residues, Cauchy's Residue formula). Then we apply residues to evaluation of improper integrals. We also cover such topics as harmonic functions and iterated maps (i.e. fractals).

Why would you want to take this course?  Complex numbers may seem at first to be a difficult abstraction, but in fact they provide a mathematically simple framework which has many beautiful and useful properties. There are many surprising relationships which turn hard questions (calculating integrals, counting roots of a polynomial in a region) into easy ones. There is geometry - which means pictures! - underlying many of the ideas. Moreover, the theory of complex variables proves useful to other fields of mathematics (like number theory, for example) and there are countless applications to physics and engineering. Indeed, this course is a highlight of the undergraduate mathematics curriculum.

The Textbook. E.B. Saff & A.D. Snider, Fundamentals of Complex Analysis with Applications to Engineering and Science 3rd ed., Prentice Hall. You might be able to find the book at a cheaper price online:
http://www.amazon.com/gp/product/offer-listing/0139078746/qid=1137015329/sr=1-1/ref=sr_pb_a//002-7509553-6718452?condition=all

Grades. Your grade will be based on two hourly exams, periodic quizzes, the daily homework, participation, a Mathematica project, and a final exam. Each will be weighted as follows.

 Graded "Event" % of Total Homework 15 Mathematica project 5 Participation 10 Exam I 15 Exam II 15 Quizzes 15 Final Exam 25 TOTAL: 100

Daily Homework. As with any math class, homework is the most important aspect of the course. Homework exercises will be collected and graded regularly (typically about 1 assignment per week.) Your homework must be legible, with problem number and final answer clearly indicated. Explanations should be written in complete sentences. Random math expressions floating in space will receive no credit.

 HOMEWORK POLICY Homework is due at the START of class on the assigned due date, unless I specify otherwise. Late homework will not be accepted. If you know you will be missing class for some reason (e.g., an athletic event), turn in your assignment BEFORE you leave. Under extenuating circumstances extensions may be granted, but this should be discussed with me in advance. Your homework will be evaluated on neatness, completeness, and correctness. Group work is encouraged, but assignments must be written up INDIVIDUALLY unless you are told otherwise. Copied work will receive no credit - even if the work was discussed in collaboration with a classmate before write-up.

Exams. There will be two hourly exams and a comprehensive final exam. Their dates are given below.

 Exam I Wednesday, February 13 Exam II Wednesday, April 2 The Final Exam Friday, May 9, 8:30-11:30AM in RBH 203 ***Note: The final will be 3 hours long***

Note: the final exam will be in-class and cumulative.

Academic Honesty. In general, the rules set forth in the 2007-2008 Course of Study apply. Presenting the work of others as your own is strictly prohibited. In the case of homework, you may collaborate with others in discussing how a problem may be solved, but your write-up must be your own. If you submit work that contains the ideas or words of someone else, then you must provide proper citation. Assistance can not be given nor received (other than by the instructor) on any quiz, or exam associated with this course, except where explicitly allowed by the instructor. In the case of a group assignment, all members of the group should contribute equally to writing the final product. And every member of the group is responsible for the content of the entire paper, not just the section(s) that are written by that person. Don't put your name on a paper written by others. For further information, consult your instructor.
Learning Disabilities. If you have a disability which requires an accommodation in this class, please feel free to discuss your concerns with me, but you should also consult Ms. Erin Salva, (Coordinator of Disability Services; Office of the Dean for Academic Advising, PBX 5453) as soon as possible. Ms. Salva (in consultation with the L.E.A.R.N. committee) has the authority and the expertise to decide on the accommodations that are proper for your disability. Though I am happy to help you in any way I can, I cannot make any accommodations for learning (or other) disabilities without proper authorization from Ms. Salva.

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