Math 201, Fall 2007
Freshman Seminar. How Mathematicians Think: Multivariable Calculus
Instructor John E. McCarthy
Class
MTuThF 11.00-12.00 in
199, Cupples I
Office
105 Cupples I
Office Hours M 3:00-4:00, Tu 3:00-4:00, F:
12:00-1:00.
Phone
935-6753
Text
Multivariable Mathematics by
T. Shifrin, Wiley, First edition
Exams There will be three exams in the course:
1) Exam 1 In class, Tuesday, October 2
2) Exam 2 In class, Friday, November 2
3) Exam 3 Final exam, on Wednesday December
19, 10.30-12.30.
There will be weekly homework sets during the semester, handed out on Thursday in class and due the following Thursday.
Prerequisites
Calculus I & II.
Content
This course is an honors level, rigorous treatment of calculus in two and three dimensions. It is aimed at students who want a deeper understanding of multivariable calculus than they would get in the regular 233 course, and are willing to work hard to achieve this understanding.
We shall start out with a rigorous discussion of continuity for functions of one variable. We shall discuss vectors in two and three dimensions. We shall discuss differentiation, partial derivatives, and extrema of functions of several variables. We shall move on to discussing vector valued functions and vector fields. Then we shall discuss integrals of functions of two and three variables, and then line and surface integrals. Finally we shall get to the multi-variable analogues of integration by parts: the theorems of Green, Stokes and Gauss.
Basis for Grading
Each midterm and the homework will be 20% of your grade, the final will be
40%. If you do well on the final, this grade can be substituted for one of your
midterms.
Homework
Homework is an extremely important part of the course. Whilst talking to
other people about it is not dis-allowed, too often this degenerates into one
person solving the problem, and other people copying them (often justified to
themselves by saying "I provide the ideas, X does the details" - but
the details are the key. If you can't translate the idea into a real proof, you
don't understand the material well enough). So I shall introduce the following
rules:
(a) You can only talk to some-one else about a problem if you have made a genuine
effort to solve it yourself.
(b) You must write up the solutions on your own. Suspiciously similar write-ups
will receive 0 points.
Class
I do expect you to come to class every day, and to participate in class discussions. I also expect you to stay abreast of the material we are covering, and may call on you at any time to answer a question.
Additional Reading
Transition to Higher Mathematics: Structure and Proof by Bob Dumas and John McCarthy
Vector Calculus by J. Marsden and A. Tromba