1. Subsets of Euclidean Space, Vector Fields and Continuity
2. Differentiation in Higher Dimensions
3. Tangent Spaces, Normals and Extrema
4. Multiple Integrals
5. Line Integrals
6. Green's Theorem in the Plane
7. Div, grad and curl
8. Change of Variables, Parametrizations, Surface Integrals
9. The Theorems of Stokes and Gauss

There will be weekly homework assignments, a Midterm and a Final examination. The final grade will depend on a composite of these factors; to be precise, the final will be worth 40 percent, while the homework and midterm will each be worth 30 percent. No one will be excused from the final.

Recitations:

Please go to the recitations. Each week, a portion of the recitation will be dedicated to introducing some computational (or even theoretical) aspect which the Instructor will not have time to present in class. In general, get to know your TA and bug him/her to death (figuratively speaking) with your questions, and try to fill in all the holes in your understanding.

Homework:

Homework is due Mondays at 10am and will be posted on the course web site at least a week before it is due. All problems may be done in collaboration with others. However, each student must write down the solution in his/her own individual way and there should be no two identical solutions to any problem. Do not consult the solution sets from previous years in working this year's problems.

At most one late homework set will be accepted, and only at your TA's discretion, if arrangements have been made in advance with your TA, and if the work is less than a week late. Beyond this, late homeworks will NOT be accepted, except with a letter form the Infirmary or from the Dean (or Associate Dean). Every week, graded homeworks can be picked up from the TA during the recitation on Thursday.
 

Apostol, Vol. II, 2nd Ed., John Wiley, 1967, ISBN: 0-471-00007-8.