Mathematics 2443-005 - Calculus IV - Spring 2003
Information about Exam I
Exam I will be in the usual classroom on Thursday, February 6,
2003. Please take your usual seat.
Only a basic, non-graphing calculator may be used. Actually, there is no
need to use a calculator. Scratch paper will be provided, so all you will
need is something to write with.
The exam will be worth 52 points, and will cover sections 15.1-15.6. The
approximate point breakdown by section of the text is as follows:
| 15.1 | 4
|
| 15.2 | 7
|
| 15.3 | 18
|
| 15.4 | 4
|
| 15.5 | 7
|
| 15.6 | 12
|
| Total | 52
|
The following topics will definitely be covered (of course, the exam is not limited to
these topics):
| 1.
| partial derivatives --- calculation and geometric meaning,
including implicit differentiation and the Chain Rule
|
| 2.
| gradient --- its geometric meaning, its computation, and its use
|
| 3.
| differential of a function
|
| 4.
| Clairaut's Theorem
|
You do not need to memorize the formula for the tangent plane to the graph
of a function, but you should know the general formula for the equation of
a plane given a normal vector and a point in the plane. There will be
emphasis on computation of partial derivatives, and on the gradient. Many
of the problems are very similar to the homework problems, others make use
of the ideas emphasized in class, and one or two of the problems may be new
to you.
Exams that I wrote for this course in previous semesters can be found (both
with and without solutions) on
their course pages (links are on the
course pages page).
Our exam may be a bit longer than those from courses which had 50-minute
classes.