Differential Equations
December 31st, 2005 by SplineGuy
I just have to say that one of the things I have been most looking forward to teaching has been Differential Equations. Actually, I am particularly fond of Numerical Analysis but Wayland Baptist University does not offer that class as part of its regular program, even though I did have the opportunity to teach it as a Special Topics course a few years back. Anyways, diff. eq. has somehow evaded me to this point in terms of being my class. When I first started teaching at Wayland, another professor was teaching it. He retired but was asked to return after we lost one of our faculty, our Statistician. Diff. Eq. was offered to him to give him something besides all freshman level stat courses. Being on a two year course rotation has meant that I’ve had to wait to teach the course for which I am most qualified. I really look forward to this semester for that reason.
I am a bit worried that, since it is my favorite course, I won’t be able to finish as I am so often sidetracked by over explanation. In fact, even now I am torn as I am preparing my lecture notes. Do I cover all the simple analytical techniques for first order systems such as separable equations, exact equations, linear (integrating factors), special integrating factors (to convert to exact), homogeneous equations, linear coefficients, and so on and on? Then, do I include a wealth of numerical methods for solving such as Euler, Improved Euler, Backwards Euler, Runge Kutta, Taylor series methods, and so on and on? How much emphasis is placed on existence and uniqueness of solutions? How much time should I spend on the development of the models themselves? It’s all so good!
