http://interval.louisiana.edu/courses/302/spring2000math302_exam_hints.html
Math. 30202, Spring, 2000 Hints for the Exams
Instructor: R.
Baker Kearfott, Department
of Mathematics, University of Louisiana
at Lafayette
Office hours
and telephone, Email: rbk@louisiana.edu.
This page will change throughout the semester.
/ The
First Exam / The
Second Exam / The
Third Exam / The
Fourth Exam / The
Final Exam /
Note: Previously given exams are available below
in Postscript format, that can be printed with a Postscript printer.
The files can also be viewed and printed with Ghostscript
and GSview.
The First Exam:
There were no hints for this exam.
The answers on the key are not necessarily the only possible answers.
Postscript
copy of the first exam
Adobe
Acrobat (PDF) copy of the first exam
Answer
key for the first exam
The Second Exam:
The exam, on Friday, February 25, will be closed book. Be sure
to bring your student ID, as I (Prof. Kearfott) will not be proctoring
it. Here's a study guide:

Be able to write down the equation of the plane perpendicular to a particular
vector and through a particular point.

Be able to write down an equation for the plane that passes through three
points whose coordinates are given.

Be able to write down the tangent plane approximation to a function.

Be able to compute directional derivatives of a function in a particular
direction at a particular point.

Be able to find unit vectors in the direction of maximum increase and maximum
decrease of a function.

Be able to write down vectors parallel to contours of functions.
Postscript
copy of the second exam
Adobe
Acrobat (PDF) copy of the second exam
Second
exam answers, page 1
Second
exam answers, page 1b
Second
exam answers, page 2
The Third Exam:
The exam will be on Friday, March 17, and will be closed book. You
will need to bring a pocket calculator. Here is what to expect:

Expect a problem dealing with the chain rule for a function of two variables.

Be able to write down the Taylor polynomial of degree 2 for a function
of two variables. Be able to use that Taylor polynomial to approximate
the function for values of x and y near the base point.

Be able to find and classify the critical points of a function of two variables.

Be able to compute the maximum and minimum values of a function of two
variables subject to an inequality constraint.
Postscript
copy of the third exam
Adobe
Acrobat (PDF) copy of the third exam
Third
exam answers, page 1
Third
exam answers, page 2
The Fourth Exam
The exam will be on Monday, April 17, and will be closed book.
Be sure you know how to do the following.

Given a diagram of a region, write down a double integral over that
region, and evaluate it. It may be that the integral can be evaluated
if written one order as an iterated integral, but not in the other order.

Set up and evaluate an integral in polar or spherical coordinates.

Understand parametrizations of curves. Compute velocity, acceleration,
and speed of a parametrized curve. Be able to compute the intersection
of a parametrized curve with a surface.
Postscript
copy of the fourth exam (It was explained in class that, for problem
1, the region was that region between the curve and the xaxis.)
Adobe
Acrobat (PDF) of the fourth exam
Fourth
exam answers, page 1
Fourth
exam answers, page 2
The Final Exam
The final exam will be on Thursday, May 4, 2000, and will be closed
book. Be sure you bring your own paper, and you may want your calculator.
Here is a study guide:

Be able to compute a line integral over a curve described in words, by
first writing down a parametrization for the curve.

Know Green's theorem, and know how to apply it.

Know how to change a triple iterated integral between rectangular and spherical
coordinates, or between rectangular and cylindrical coordinates.
You will need to change such an integral and evaluate such an integral.

Know how to compute fluxes of vector fields through surfaces. You
may be given a special surface (a sphere or a plane segment), or you may
need to compute the flux by parametrizing the surface, then taking a dot
product of a cross product.

Know the divergence theorem, and know how to apply it.

Concerning finding maxima and minima,

know how to find the global minimum and global maximum of a function over
a region such as a disk or a rectangle;

know how to find and classify all critical points of a function;

know the difference between the above two procedures.

Know how to apply the chain rule for functions of more than one variable.

You should look at various examples and word problems associated with this.
Postscript
copy of the final exam (The z coordinate of the curve is slightly
different than on the copy of the exam handed out in class.)
Adobe
Acrobat (PDF) copy of the final exam
Final
exam answers, page 1
Final
exam answers, page 2
Final
exam answers, page 3
Final
exam answers, page 4