Stevens Institute of Technology West Point Military Academy Using Technology as a Teaching/Research Tool in a Special Topics Course in Differential Equations Lawrence E. Levine Stevens Institute of Technology and West Point Military Academy llevine@stevens-tech.edu

Using Technology in Teaching Web and Distance Learning Use in classroom State of the art classroom Laptops Wireless connections Software to monitor students’ laptops Scientific Notebook

What Do You Do With All of This? Prepare lecture notes using SNB Have students work in class and monitor their work Project the work of a student for all to see Have students make presentations Involve the student

Course Use of Technology I Presentation of material Review of basic techniques to solve Des Infinite series Series solution near an ordinary point Method of Frobenius Boundary value problems, Fourier series Separation of variables for PDEs

Course Use of Technology II Research Tool Polynomial solutions of nonhomogeneous DEs Chebyshev, Hermite, Legendre, Laguerre equations with right hand side What initial conditions yield a polynomial solution? Maple kernel in SNB will solve initial value problem By looking at examples one attempts to guess the general case Then one proves that this is indeed the result.

Another Approach Want a polynomial solution In these equations recurrence relation has “step 2” Set expression for equal to zero Work backwards to get the initial conditions.