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One of the ways to earn points in Math 21a is to complete a short project
related to multivariable calculus. This project is worth up to 200 points
towards your term total. The goal is to let you personalize Math 21a by
exploring a topic that interests you for course credit. A variety of
potential projects are described below. You can use them as your
starting point and expand on these suggestions according to your
interests, or you can also design a project of your own so long as it is
approved by your section leader first.
By the beginning of December, you will be asked to commit to one of the
options above by filling out a form distributed in class and on the web.
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With the exception of the section test, all projects are due in your
instructor's mailbox by 5 pm on Friday, January 10. As a rough guide,
most written projects should be five to ten pages long. The work you turn
in should be your own. It need not be typed, but should be neat,
well-presented, and self-contained. Try to create an exposition rather
than just a series of calculations, and treat the assignment with at least
as much care as you would give a short paper in an English course or a lab
report in a Chemistry class. We might post on the website some of the best
projects and pictures.
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- Mathematica Lab.
Mathematica is a very versatile program for
performing and displaying computations. It was, for example, used to
produce some of the graphics on the Math 21a website. This project
involves learning to use Mathematica for drawing curves, surfaces, vector
fields, etc. Just download the Mathematica Lab instructions from the
course web page. Work through the entire lab, then print out and hand in
the material listed. Mathematica is available on public computers at
Harvard, and Harvard students can download it for use on their own
machines. See instructions on our web page for obtaining your own copy.
More instructions to get started can be found here.
- Challenge Problems. Throughout the term, we are posting challenge
problems on the course website through links on the homework page. These
problems are less routine than the homework exercises, and should require
some real thought and imagination on your part. Many deal with
generalizations of our coursework to higher dimensions, for example.
Problems with four stars are harder than those with three. To do this
project, solve and hand in 16 or more stars worth of challenge problems
(say,for example, 4 of the four star problems or 6 of the three star
ones). Your solutions should be neat and thoroughly explained.
- Textbook Projects. The table of contents of the text lists a number
of "Discovery Projects" and "Applied Projects." For example, there is one
in Chapter 11 that investigates measurements of a dumpster. Any of these
would make an appropriate project. To take this option, just complete,
write up, and hand in all parts of a project described in the book.
- Section Test. Each section leader
will make up a section test covering material
specific to his section, mostly from the last few weeks of class. The
exact format and contents of the test will vary from section to section.
Your section leader will provide details about the test for your section.
To do this project, tell your section leader that you want to take the
section test and follow his instructions.
- Your Own Idea. You can also design your own project. Topics related
to other fields and applications are encouraged, but what you hand in
should not duplicate work in another class. The use of Math 21a
techniques should be clear and explicit. If you are interested in doing
such a project, speak with your instructor. He or she will consider your
idea, perhaps make some suggestions, and approve it if the subject matter
and workload seem appropriate.
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