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Unformatted text preview: DEPARTMENT OF MATHEMATICS, NORTHEASTERN UNIVERSITY MTH G131 : Introduction to mathematical methods and modeling. Ideas for course project 1) This project concerns determining the trajectory of a rocket. The equation of motion is deduced using Newtons Law; assuming a constant rate of burn for the fuel and a constant rate at which exhaust gases are emitted, you can compute the trajectory as a function of time. In this project you will include the effects of air resistance and decreasing gravity as the rocket ascends. So you will need to (a) get the equation of motion, (b) solve it for some special cases, (c) get a numerical solution for the general case, (d) use realistic numbers for the parameters, (e) output a nice graph showing altitude as a function of time. 2) The TCP protocol on the Internet can be modeled as a community of users all competing for a finite resource (in this case bandwidth). Each user probes the network for available bandwidth, and slowly increases its transmission rate. When the combined transmission rates exceed the capacity, the users are notified andits transmission rate....
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