The Final Exam will be in the usual classroom on Thursday, May 11, 2006, at 1:30 p. m. You may work as late as 3:45 p. m. if you wish.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided, so all you will need is something to write with. Also, along with your final exam, you will receive a copy of the formulas page.

The main emphasis of the exam is Chapter 17, especially surface integrals, Stokes' Theorem, and the Divergence Theorem. There will be material from earlier in the course, but most of it will be problems identical or similar to problems that appeared on the in-class exams. Assuming that you understand all of those well, it is probably best to use your studying time on Chapter 17. The following will definitely be covered:

1.	vector fields: examples, div, grad, curl, and all that
2.	parameterized surfaces: examples, r_u, r_v, and r_u \times r_v
3.	surface integrals: 1) definition and geometric interpretation, 2) case of surfaces that are the graph of a function, and 3) case of parameterized surfaces
4.	Stokes' Theorem
5.	The Divergence Theorem
6.	spherical coordinates--- triple integrals in spherical coordinates, parameterization of the sphere
7.	implicit differentiation, differential of a function, the Chain Rule for partial derivatives
8.	the gradient: geometric meaning, relation with directional derivatives
9.	change of coordinates in integration, the Jacobian

The following topics do not appear, at least not explicitly: material from Chapter 14, limits, continuity, equation of the tangent plane, moments and center of mass, derivation of the formulas relating spherical and Cartesian coordinates, proof of Clairaut's Theorem, critical points, second-derivative tests, Lagrange multipliers, polar coordinates other than routine use in integration, actually graphing vector fields from their formulas, integrating conservative vector fields to find the functions of which they are the gradient, the rotating drum example of curl, calculating the unit normal vector of a curve, proof of the Fundamental Theorem for Line Integrals, proof of Green's Theorem, Stokes' Theorem for general manifolds.

Exams from previous Honors Calculus classes can be found on their course pages (links to them appear on the course pages page). Some were 50-minute classes, but most were 75-minute classes. Of course, these were different classes, so the exams may be quite a bit different.