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.
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.