Math 103 Written Projects

Part of the work for Math 103 is a special project in which each student (or student collaboration) explores an aspect of multivariable calculus and/or solves a problem not addressed in class and writes a report of three to five typed (or word-processed) pages (not including figures) explaining the application. (If you have questions about putting mathematical notation in your paper, please ask.) This project will account for ten percent of your grade.

Project topics will ordinarily be selected from the topics list below. It is also possible to select an application of calculus from your major or another topic that is not on the list. After selecting a topic, you must write a project proposal of no more than one page explaining the project that you (or your collaboration) plan to carry out, and whom you will be collaborating with. (If you are picking a project from the list this only needs to be a few sentences so that I know you have looked the project over.) You may wish to consult with me before you do this; if you choose a topic which is not on the list, you should definitely consult with me before you turn in your proposal.

You are encouraged to work in collaboration with one or two other students on your project. However, no collaboration should involve more than three students. Each collaborator must turn in a proposal.

Project Deadlines

1.

Paper proposal due: November 12

2.

First draft of paper due: November 29

3.

Second draft of paper due: December 8

Project topics from the textbook

1.

Does a pitched baseball really curve? (p. 756)

2.

Exotic critical points (p. 834) (You should use the polar coordinate technique when investigate your own exotic critical points.)

3.

Numerical Investigation of Lagrange Multiplier Problems A (p. 872)

4.

Numerical Investigation of Lagrange Multiplier Problems B (p. 872) (Only attempt this if you have the means to solve six equations in six unknowns, probably using a calculator or computer.)

5.

Critical Point Investigations (p. 881) (Parts B or C, or both.)

6.

Midpoint Approximations of Double Integrals (p. 892)

7.

Optimal design of downhill race car wheels (p. 922) (You will need to read the section in the book about moments of inertia.)

8.

Archimedes' floating paraboloid (p. 932)

9.

The Earth's mantle (p. 940) (You will need to read the section in the book about moments of inertia.)

10.

Computer-generated parametric surfaces (p. 946) (Don't forget to calculate the area!)

11.

Green's Theorem and Loop Areas (p. 992) (You will need to do some reading ahead to do your first draft on this subject.)

12.

Surface integrals and rocket nose cones (p. 1003) (You will need to do some reading ahead to do your first draft on this subject.)

Notes

• Most of these projects will go much easier if you have access to a good calculator or a computer with a mathematical problem-solving package. In particular, you may need a good equation solver and you may need to be able to produce three-dimensional graphs. Free copies of Mathematica and other software can be downloaded from the Duke web site. Let me know if you would like some help with this.
• Wherever the projects say ``Show (such and such is true)'' you should give an explanation and probably derive some formulas.
• You should explain all of your steps.
• Some of these projects ask you to produce graphs and plots. By all means experiment with these and include them with your paper. However, merely giving me a collection of plots is not sufficient.
• Many of these projects encourage you to produce a ``personal'' equation using your student number. You may pick your equation using some other method if you prefer. I encourage you to try more than one ``personal'' equation in order to compare and contrast.
• Some of these projects are long. If you have three to five good pages of text and you have not done all of the parts of your project you may have done enough. If you have any questions about what is sufficient, please ask.

Plagiarism

If you are not familiar with what does and does not constitute plagiarism, you may wish to look at a web page such as

• <http://www.lib.duke.edu/libguide/plagiarism.htm>
• <http://uwp.duke.edu/sources.html> , or
• <http://library.ups.edu/research/guides/acadhon.htm> .

Briefly speaking, if you quote three or more words from a source without paraphrasing, you must put them in quotation marks and note where they came from. If you paraphrase information from a source, you must cite the source unless it is ``common knowledge''. The rule of thumb is that anything you find in three or more different sources is common knowledge. (Even if you find something in three or more sources, you may wish to give a citation for one of them.) Plagiarism is a violation of the University Honor Code.

This goes even more so for any pictures you find on the internet. If you copy a picture or any image from a web site and use it in your paper or on your web site without attributing it, that is not only unethical but illegal. Please make clear attributions of any images you copy and try not to go overboard with using too many of them!

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