Vector Calculus and Complex Variables

Course Description: The published course description reads ``Functions of several variables, implicit and inverse functions, Jacobians, multiple integrals, Green's theorem, divergence, curl, the Laplacian, Stoke's theorem, analytic functions, Laurent expansions, residues, argument principle, and conformal mapping.'' In practical terms, we will discuss Chapters 8, 9, 12-16 in Kreyszig.

Goals: In this course you will review vector calculus, learn how to generalize the Fundamental Theorem of Calculus to vector calculus, learn how multiplication on R^2 yields calculus of complex numbers, compute with this complex calculus, study applications, and learn a topic on your own and present it to your fellow students.

Prerequisites: MATH 374, Differential Equations and Linear Algebra.

Text: Advanced Engineering Mathematics by Erwin Kreyszig. You will be required to read the text and homework problems will be assigned from the text, but you are not required to carry the text to class every day.

Coursework: For every class, you will be told which sections will be covered and some routine problems you should be able to do before you come to class. These problems will be collected at the beginning of each class meeting. Every week, you will also have some longer problems. You are encouraged to talk with other people to learn the material and complete these problems, but you should always write a final draft of your homework on your own. Each solution in the final draft should be written in complete sentences, as if you were trying to explain to someone else how to do the problem. The longer problems will be due once every week. Occasionally, you may be asked to present a solution to the class.

Presentation: You will plan and present a 20 minute talk on a subject which extends the material in this course. Early in the semester, you will make an appointment to come to my office so that we will discuss possible topics for your presentation. By October 20, you will have chosen a topic, and I will determine a schedule of the talks. At least a week before your talk, you will come to my office prepared to give a trial run of your talk. Beginning November 15, you will present your talks to the class.

Grades: Coursework 37% , Midterm Exams (2) 28% , Presentation 10%, and Final exam 25% . I reserve the right to lower your grade for poor attendance.

Makeups: Makeup exams will be made only in the case of a genuine medical or personal emergency. It is your responsibility to prove that your absence is due to an emergency.

Communications: Academic correspondence must be through wmich.edu accounts. I will respond to email at least once per weekday.

Academic Dishonesty: You are responsible for making yourself aware of and understanding the policies and procedures in the Undergraduate or Graduate Catalog that pertain to Academic Integrity. These policies include cheating, fabrication, falsification and forgery, multiple submission, plagiarism, complicity and computer misuse. If there is reason to believe you have been involved in academic dishonesty, you will be referred to the Office of Student Conduct. You will be given the opportunity to review the charge(s). If you believe you are not responsible, you will have the opportunity for a hearing. More details about this procedure can be found at website of the office of student conduct, and an outline of the procedure can be found at this website. You should consult with me if you are uncertain about an issue of academic honesty prior to the submission of an assignment or test.

Disabilities: Any students with a documented disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable accommodations must contact Ms. Beth Denhartigh at telephone 387-2116 or by email at the beginning of the semester. A disability determination must be made by that office before any accommodations are provided by the instructor.

Important Dates:

Last day to drop/add classes : September 2
Exam 1: Approximately October 4
Deadline for choice of topic for talk: October 20
Last day to withdraw from classes: October 31
Exam 2: Approximately November 1
In class presentations begin: November 15
Final Exam: Tuesday December 6, 12:30-2:30