Math 201, Fall 2005
Freshman Seminar. How Mathematicians Think: Multivariable Calculus

Instructor          John E. McCarthy
Class                  MTuThF 12.00-1.00 in 199, Cupples I
Office                 105 Cupples I
Office Hours      M 2:00-3:00, Tu 1:00-2:00, F: 1:00-2:00.
Phone                 935-6753

Text                    Vector Calculus (Fifth Edition) J. Marsden and A. Tromba
Structure and Proof (Chapters 1 -5)

Exams    There will be three exams in the course:

                        1) Exam 1       In class, Friday, September 30
                        2) Exam 2       In class, Friday, November 4
                        3) Exam 3       Final exam, on Thursday December 22, 10.30-12.30.

Homework

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.