Spring 2003

MA362 Complex Analysis with Applications

Course Policy Statement

Associate Professor Erik M. Bollt

Office: Science Center 369 e-mail: bolltem@clarkson.edu

Course Text: Complex Variables and Applications, Mark J. Ablowitz, Athanassios S. Fokas.

Dear Students:

Welcome back to academics and welcome to Complex Variables! This is the math class you have been waiting for! I look forward to a great semester of learning with you. The key to success is effort and determination; a good attitude and a good work ethic is at least as important as talent. Remember too that no matter how much effort I show, I won’t be able to learn the material for you. You have to make the effort! . . .

Topics. We will cover topics in Chapters 1-4. Complex variables is an invaluable tool for students and professionals in engineering, and the physical sciences. It is also a beautiful mathematics topic in its own right. Complex analysis is the development of the ideas of calculus (differentiation and integration) to functions of a complex variable. Topics we will cover include the complex plane, complex functions, derivatives of complex functions, contour integrals, Cauchy integral formulas, Taylor and Laurent series, residues, and conformal mapping. We will discuss applications of complex analysis to problems in circuits, signals, heat conduction, electrostatics, fluid flow, as well as fractals. If time permits, we will discuss transform methods and applications.

On the Web: At my website, www.clarkson.edu/~bolltem, I will regularly post useful information about the class, such as homework info, and updates to the syllabus.

Grading. Listed below are the items I will be using to evaluate your progress this semester.

Homework: 30%

2 Midterm Exams: 2 x 20%

Final Exam: 30%

Attending the lectures is required; a significant number of unexcused absences will result in downward adjustment of your grade.

Homework : Working through problems on you own is a crucial part of learning mathematics. I encourage you to work together on homework. My policy is to encourage unlimited help on homework, but all work must be in your own hand: you may neither electronically nor manually copy other’s work. Probably the best way to really learn something is to teach it to someone else. Please note that homework is weighted extremely highly in your course evaluation.

I will assign homework regularly, and collect homework approximately once a week. Work handed in late will generally not be accepted. If you have to be absent on the day homework is collected, see me as soon as possible.

Exams. There will be two in-class exams. The final exam will be comprehensive. All exams are closed-book and closed-notes. Calculators will not be allowed on exams.

Academic Integrity. The Clarkson Regulations read, "a student will not claim as his or her own, the work of another, or any work that has not been honestly performed, will not take any examination by improper means, and will not aid and abet another in any dishonesty." (p. 19) Any violations will result in an F for the course and will be reported to the Academic Integrity Committee.

Reading the text: Remember that you do not read a math text like a paperback novel. To understand a math text, you need to keep paper and pencil at your side, and work/sketch details as you read each step, and you may need to re-read a step many times. The point is not to skim your eyes over a the text, but rather to understand. The same goes for the homework. Don’t let the details go. If you are stuck, try again, then try again. If you stay stuck, seek help from a classmate, or me. Again, I encourage you to work together on homework. An efficient and fun way to do math can be to find a regular study partner, and do the reading and homework at the same time. Even when you are not the one who is stuck, the best way to deepen your own understanding is through helping your peers. This also develops good teamwork skills.

Dr. Erik M. Bollt

Associate Professor of Mathematics