http://interval.louisiana.edu/courses/302/fall2001math302_exam_hints.html
Math. 30202, Fall, 2001 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 Fifth Exam / The
Sixth 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. I have also provided Adobe Acrobat (PDF) copies.
The First Exam:
Postscript
copy of the first exam
Adobe
Acrobat (PDF) copy of the first exam
First
exam answers, page 1
First
exam answers, page 2
First
exam answers, page 3
The Second Exam:
The exam will be closedbook, and will be on Friday, September 21.
It will cover the material in Chapter 12 of the book, including displacement
vectors, velocity and acceleration, the dot product, and the cross product.
Pay particular attention to the word problems, such as numbers 1215 on
page 75 of the text, the concept of work, and equations for planes.
Postscript
copy of the second exam
Adobe
Acrobat (PDF) copy of the second exam
Second
exam answers, page 1
Second
exam answers, page 2
Second
exam answers, page 3
The Third Exam:
The third exam will be closedbook, and will be on Tuesday, October
9. It will cover the material in Chapter 13 of the book. Here
are some hints:

You will need to compute algebraically the first and secondorder partial
derivatives of a function of two variables.

There will be a word problem dealing with linear (tangent plane) approximation
of a function of two variables.

There will be a word problem dealing with gradients and directional derivatives.

There will be a word problem that deals with the chain rule for a function
of three variables. (The chain rule for a function of three
variables is the same as the chain rule for a function of two variables
given in §13.6 of the book, except that there are three terms.
That is,
df / dt = f_{x }dx/dt + f_{y}
dy/dt + f_{z }dz/dt.
Postscript
copy of the third exam
Adobe
Acrobat (PDF) copy of the third exam
Third
exam answers, page 1
Third
exam answers, page 2
Third
exam answers, page 3
Third
exam answers, page 4
The Fourth Exam
The fourth exam will be closedbook, and will be on Friday, November
9, 2001. It will cover the material in Chapter 14 of the book.

You will need to find and classify all critical points of a function.

You will be given a list of several functions, and you will need to state
whether or not each of the functions has a global maximum, a global minimum,
or both. In all cases, you will need to state why you answered the
way you did.

You will need to find all global maxima and minima of a function within
a bounded region defined by an inequality constraint.
Postscript
copy of the fourth exam
Adobe
Acrobat (PDF) copy of the fourth exam
Fourth
exam answers, page 1
Fourth
exam answers, page 2
Fourth
exam answers, page 3
Fourth
exam answers, page 4
The Fifth Exam
The fifth exam will be closedbook, and will be on Monday, November
12, 2001. It will cover that part of the material in Chapter 15 of
the book that is listed on the syllabus. You will need to:

Sketch the region of integration, then evaluate a double integral.

Find the average value of a function of three variables; this problem will
be posed as a word problem.

Find the volume of an object by taking the area integral of its height.

Rewrite a threedimensional integral using a change of coordinates, then
evaluate it.
Postscript
copy of the fifth exam
Adobe
Acrobat (PDF) copy of the fifth exam
Fifth
exam answers, page 1
Fifth
exam answers, page 2
Fifth
exam answers, page 3
Fifth
exam answers, page 4
The Sixth Exam
The sixth exam will be closedbook, and will be on Tuesday, November
27, 2001. It will cover that part of the material in Chapters 16,
17, and 18 of the book that is listed on the syllabus. You will need
to:

Determine if a particular parametrized curve intersects a particular parametrized
surface.

Compute the length of a parametrized curve.

Write down parametric equations for a particular surface.

Compute a line integral.
Postscript
copy of the sixth exam
Adobe
Acrobat (PDF) copy of the sixth exam
Sixth
exam answers, page 1
Sixth
exam answers, page 2
Sixth
exam answers, page 3
Sixth
exam answers, page 4
The Final Exam
The final exam will be closedbook, and will be on Tuesday, December
4, 2001, at 7:30 AM. Pay particular attention to the following items:

Computing equations of planes, given points on the planes, normal vectors,
etc.

Applying the chain rule for multivariate functions.

Finding and classifying critical points of multivariate functions.

Reading contour diagrams of functions, and discerning maxima, minima, and
saddle points from the contour patterns.

Using Green's theorem.

Computing the mass of threedimensional objects.

Computing triple integrals in rectangular, cylindrical, and spherical coordinates.

Exhibiting f, given the gradient of f.
Postscript
copy of the final exam
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
Final
exam answers, page 5
Final
exam answers, page 6
Final
exam answers, page 7