You have now completed Multivariable Calculus and hopefully learned some applications of Multivariable Calculus along the way. However, some of the best ways to solidify new content is by working with it on your own applied to an area that really excites and interests you. This is what we will be doing for the thrid trimester of Multivariable Calculus; you will each individually pick a project that related Multivariable Calculus with something that you are passonate about.
The goal is to have fun! I want you to explore something that you're interested in so that it doesn't feel like work. I want you to know what it's like to work on one focused mathematical idea for a long time. I want you to gain the sense of accomplishment that can come from dedication, and for you to recognize that you can produce something that is your own! Also, this will be a great warm up for your senior year when you work on your senior research project.
Your prospectus is an initial, explicit, clear explanation of exactly (a) what your project is, (b) how you plan to accomplish it, (c) what the product of your project is (e.g. website, video, paper, teaching tool, computer program, poster, powerpoint presentation), (d) your approximate timeline (what should be done in your project by when), and (e) you should have at least 3 souces for the project. Your prospectus should be a minimum of 1 page (single spaced, typed, 12pt font), but I anticipate for most of you, it will be longer.
Advice: You should write the prospectus as if someone who is a little less capable than yourself is going to be reading it. Be explicit and clear, spelling everything out. You want to be extraordinarily detailed - err on the side of being more detailed than less detailed. Lastly, you should recognize that the prospectus is an initial plan. You might plan to, say, work on writing a paper which explains all four of Maxwell's Equations. However, you might realize that you bit off more than you could chew, and can only write on two of them. That's okay. The prospectus is simply to give you clear directions.
Your rubric is a breakdown of how your grade for you final project should be calculated at the end of your project. I think that it is a good skill to learn how to judge your work. When you complete the project, you should honestly self-evaluate your project based on the rubric you created.
Your self-evaluation will consist of two parts:
1. Your rubric honestly filled out by yourself.
2. One paragraph discussing what you got out of this project and what you liked about doing a project like this. A second paragraph explaining whether you think what you got out of the project was worth the effort you put into it or not. Be honest, this will not be factored into your final grade.
Here are some final project ideas that others have come up with. You can choose one and expand on it, or pick something on your own but you'll need to consult with me about it. You can also look through out textbook by Stewart as there are a few projects sprinkled throughout. Also, I have a few copies of the Multivariable Calculus Textbook by Jon Rogawski which is cited as a scource for a few of the projects in the first link.
As a note: I have not explored nor done many of these projects, though I would love to given the time. So you choosing a project will not only be a learning experience for you but for myself and your fellow peers. However, I will be here to help you whether you need more resoures, to discuss a problem, or just in general aren't sure where to go nex.
Remember the most important thing to think about when choosing a topic is: does this excite me?