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

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.

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 e

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

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.

The second

The third

The last

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.

Back to Stephen Greenfield's home page