131F06.proj-ideas - DEPARTMENT OF MATHEMATICS NORTHEASTERN...

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DEPARTMENT OF MATHEMATICS, NORTHEASTERN UNIVERSITY MTH G131 : Introduction to mathematical methods and modeling. Suggestions for course project 1) This project concerns determining the trajectory of a rocket. We started the analysis in one of the Problem sessions. The equation of motion is deduced using Newton’s 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
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