The project must demonstrate a substantial application of differential equations. Related articles from the American Mathematical Monthly and useful websites for the course are listed at the end of this page. Surface area of Minimum Resistance through a Medium. Chaos via the Lorenz equations Modeling the Spread of an Infectious Disease by Rachel Brik Modeling physical, biological, and social phenomena using differential equations is a powerful tool for providing attainable answers to obscure questions. The group of susceptibles is reduced by one person each time one of them becomes infected.
Infection can occur during the times when susceptibles are in contact with infecteds.
This system was solved numerically by Maple 6 using feasible values for a and b and initial conditions provided by examining AIDS data for the state of Pennsylvania from 1990 to the present. The vector field and trajectory are shown below. The graphs for x and y versus t were then compared to the actual data. The rate of a chemical reaction is the change in concentration of a substance per unit time. During a reaction the concentration of reactants decrease and the products increase.