http://interval.louisiana.edu/courses/302/fall-2001-math-302_exam_hints.html

### Math. 302-02, 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.

/ 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
The Second Exam:
The exam will be closed-book, 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 12-15 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

The Third Exam:
The third exam will be closed-book, 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 second-order 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 = fx dx/dt + fy dy/dt + fz dz/dt.
Postscript copy of the third exam
Adobe Acrobat (PDF) copy of the third exam

The Fourth Exam
The fourth exam will be closed-book, 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

The Fifth Exam
The fifth exam will be closed-book, 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 three-dimensional integral using a change of coordinates, then evaluate it.
Postscript copy of the fifth exam
Adobe Acrobat (PDF) copy of the fifth exam

The Sixth Exam
The sixth exam will be closed-book, 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

The Final Exam
The final exam will be closed-book, 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 three-dimensional 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