Exam I will be in the usual classroom on Tuesday, September 18, 2007. It will cover sections 15.1 and 15.3-15.8.

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.

Most of the exam will be similar to the homework problems, but some will be drawn from the lectures. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others.

The following topics are likely to appear, although the exam is not necessarily limited to these topics:

1.	Functions of more than one variable, domains and ranges, graphs, level curves and surfaces.
2.	Partial derivatives, computation and geometric interpretation. Implicit differentiation.
3.	Tangent planes. Linear approximation and differentials.
4.	The Chain Rule.
5.	The gradient and its properties.
6.	Extreme values of functions of two variables, critical points, examination of the values of a function on the boundary of a domain.
7.	Lagrange multipliers.

The following topics do not appear, at least not explicitly: limits, continuity, mathematical justification of Clairaut's theorem, error of linear approximation, mathematical justification for the fact that dot product of the gradient with a unit vector u equals the rate of change in the direction of u, finding equations of straight lines in 3-dimensional space

Exams from some of my previous Calculus IV classes can be found on their course pages. Some were 50-minute classes, but most were 75-minute classes. Of course, these were different courses, so the exams may be quite a bit different.