The last project in Calculus 1 at Fitchburg State. Students work through steps to develop two different formulations of Simpson's Rule for estimating integrals.
A New Definition of Pressure Based on Kinetic Theory Derivations
Typical derivations of kinetic theory equations often exchange the contact time of the particle on a wall with the period of the particle's motion between walls. In this paper we redefine pressure as time-dependent in order to solve this issue and show that this definition makes much more intuitive and theoretical sense than our old definition of pressure.
This project introduces the idea of recursive sequences. Students then prove that a given recursive sequence converges and find its limit. The final portion of the project is a derivation and investigation of the Fibonacci Sequence and the Golden Ratio.
V-Formation as Optimal Control
We present a new formulation of the V-formation problem for migrating birds in terms of model predictive control (MPC).