http://interval.louisiana.edu/courses/302/spring-2000-math-302_exam_hints.html

### Math. 302-02, 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.

/ 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

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

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 x-axis.)
Adobe Acrobat (PDF) of the fourth exam

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