Each group will choose one of the options below as a project. You will have most of the quarter to work on your problem of choice and will submit both a Preliminary and Final Report as a group. Methods and techniques you learn in this course will be applicable to these projects and will requre you to read ahead to identify them. If you wait until the topic is discussed in class you will likely not have sufficient time to complete your project and prepare your report. You MUST use something from this course in your model!
Remember, these are GROUP projects. That does not mean you "divy" up the work. It means that you work together. That is, every member of the group should be able to explain the model and report. For example, if you use a computer simulation to test your model, every member of the group should be able to explain the simulation. Learn from the members of your group!
Please feel free to use computer simulations, collect physical data, and do experimentation whenever safe, reasonable, and applicable.
In the movie GI Joe, there are several scenes where characters essentially traverse an obstical course. Suppose you are choreographing the stunts and want to use as little CGI as possible (meaning you want the stunt doubles to actually traverse the course without being killed). Design such a course so that it can be used in a 5 minute chase scene (it need not be 5 consecutive minutes in actual time, only in movie time). (e.g., when the stunt man jumps through a window of a moving train, you will want to know the trajectory of the man).
Alpha Centauri is a multiple star system. Suppose a planet exists within such a system. Can you describe (mathematically) a situation in which this planet would be able to sustain life (e.g. not too hot and not too cold). Remember, first approaches should always be simple models.
Suppose you have a job ordering supplies for an organization (military, coffee shop, law firm, take your pick) with a certain budget (hint, this is a constraint). Suppose that you need three specific different types of products that each have their own amounts, costs, etc. Come up with a measure of the usefulness of these products to the smooth operation of the company (e.g. come up with a function U(x,y,z)--utility function). How should you best go about designing your order?
Come up with a model for the daily temperatures in Chicago. What can you say about the average temperature? Once you have done this for temperature, do the same for precipitation or humidity. What is the relationship between the two? What conclusions can you make? What do you expect the temperature and humidity (or precipitation) to be on the day of the final?
Suppose you are designing a container (what ever kind of container you like). Describe how you might optimize your container for its purpose given the logical constraints (this us up to you). Describe your results and give some real world measurements and examples. How sensitive is/are the volumes or surface areas of your containers to small changes in dimensions? What are the consequences of this on your design and subsequent use or marketing?
Suppose zombi-ism is plaguing the world. Model the the change in populations of zombies and humans as a flow line of a vector field. What conclusions can you make? Will all humans die out?
Propose your own project. If you choose this option, you must have your topic approved by me before you submit the preliminary report.