Index to course material for Math 251:01, 02 & 03, spring, 1997 (in GIF)

This material is also available in Postscript format.

Preparing for the final

I recommend this strategy to prepare for the final exam. The material discussed below is all on the Web, and almost all of it can be reached using links from this page.
Please review the two exams given already this semester. These exams, with answers and comments, are included here. You should also review the three quizzes we gave this semester. They, along with answers, are included here. There is also a review sheet for the final exam. Look over this material. If I thought it was important before, I probably still believe it's important. The final exam is cumulative, with somewhat heavier emphasis on the material covered since the last exam ("vector calculus"). If you insist on having even more questions to look at, consider glancing at the Web pages for the Math 251 course I taught last semester. I don't think that's necessary and don't recommend it. What I've suggested is already enough to prepare for the exam thoroughly and well.
Time and place of the final exam Thursday, May 8, 1997, from 12:00 PM - 3:00 PM, in SEC-117. Please note that this is not the same as was listed on the syllabus for the course.
Additional office hours; review session I'll have office hours in Hill 542 on Monday, May 5, from 1 to 4 PM, and on Tuesday, May 6, from 10 AM to Noon. I also am teaching Math 152, so there may be competition for my time. There will be a review session on Wednesday evening, May 7, from 7:30 to 9:30 PM in SEC 203.
The final exam itself is now (5/20/97) available here. Two minor misprints have been corrected, and the formatting has been rearranged to make the exam shown more compact.


Here's the syllabus and textbook problem assignments as initially distributed. There have been some changes in the timing of the second exam and the syllabus.

Workshops & Quizzes

The first "workshop" was designed to be a diagnostic exam. The questions asked were about material which will be used frequently in Math 251. Solutions of workshop problems won't usually be given, but since these problems were to be done in a limited time in the classroom, here are solutions
The second workshop was a more standard model with problems about lines and planes. We want students to hand in problem 3. A few extra problems were written on the way but weren't given to students.
The third workshop was about curves. One problem dealt with tangent lines to the twisted cubic. The second problem, which we wish students to hand in, is a more qualitative question on curvature.
The fourth workshop had two problems, one about a linear approximation where one variable of a several variable function was perturbed, and one about graphs of functions. We'd like students to hand in the first problem.
During the next period we gave a quiz about some "elementary" computations of two-variable limits, partial derivatives, and the chain rule. Here are some solutions to one version of this quiz.
The next workshop had two problems, one about the best-fitting straight line to ex on [0,1], and the other a geometrically pleasing but analytically slightly intricate Lagrange multiplier problem. Both of the problems could certainly benefit from Maple's help. We'd like students to hand in solutions to the first problem.
Vacation begins in only a few days. Here to celebrate are the beginning of the integration problems. The first one, very carefully written, asks readers to discover which iterated integrals compute geometric volumes. One of the parts of this problem is very tricky. The next two problems deal with simple improper two-dimensional integrals, and the last problem asks students to closely consider the signs of the functions and signs of their integrals. We'd like students to hand in the second and fourth problems of this set.
In this workshop we give a "simple" double integral to be evaluated three different ways, and a problem about center of mass, and a problem about surface area. The engineering students and everyone else should hand in the problem about center of mass.
Here is a sample workshop solution , with a companion Maple worksheet . Students may find it useful to examine the style of this sample.
During the next period we gave another quiz to help students review for the next exam which will be given on April 15. The quiz included a question about critical points, and some additional questions about double and triple integrals. Here are some solutions to these questions.


Introductory material similar to what was done last semester was distributed. Then a first lab on curvature computations was handed out. This lab included some background expository material and was rather different from what was given out last semester.
The second Maple lab was about surfaces defined by second-degree polynomial equations. It was a simpler version of last semester's second lab.
The third Maple lab was about discovering maximum and minimum values of functions of two variables. It was a simplified and changed version of last semester's third lab.
The last Maple lab is optional and should be handed in sometime before the end of the semester to be considered for credit.


The first practice exam was the same as last semester's. Students should also be aware that there's also an actual first exam from last semester on line, together with answers . Here is the first exam given in this course, together with answers. Last semester's second practice exam will serve as an adequate review for our second exam. Students should omit problem #13 which covers material no longer on our syllabus. There will be a review session before the second exam. Last semester's second exam may not be very useful since it consisted of homework problems which all had been done in class so solutions were not written up. Now we have the second exam given in this course, together with answers. Most of the problems on this exam were taken directly from the text.
Here is review material for the final exam. Please ignore problems 19c and 20 since I will not discuss Stokes' Theorem in class.
Here is the final exam for the course. Two minor misprints have been corrected, and the formatting has been rearranged to make the exam shown more compact.

Comments? Questions??

Here is a pointer to a page giving information which might be of interest to students in the course. It was last modified April 8, 1997.

Back to Stephen Greenfield's home page

Maintained by and last modified 5/20/97.