Ordinary Differential Equations for Poolesville Students

Fall 2012 -- Spring 2013, Dr. Ron Lipsman

This page contains a few "Khan Academy"-type videos created for the course. Place your cursor on a video field to see a 'play' button and a time bar. There is also a button (to the right of the time bar) that toggles to full screen; and another button that offers a download of the video. I believe that you can't really download the video. Clicking that button will launch your default video player (e.g., Real Player or Windows Media Player), which will attempt to "play the video" off the Educreations server. (Educreations is the outfit that created the iPad app on which I created the video.) It appears to me that at no time is the video file ever realy downloaded to the local machine so that you could save it or share it. If anyone can figure out how to do that, I would like to know.

The various buttons obscure part of the video field. Roll your cursor off the field while the video is playing.

1. This first video serves as a transition from first order equations to second order equations. It describes two cases in which one can actually reduce a second order equation to a first order equation; so that one can then employ the methods we developed to treat first order equations.

   Please note that this was Dr. Lipsman's very first attempt to create such a gadget. In particular, since the software used does not permit editing, the video contans one or two obvious mathematical errors, a few misspoken words, several poorly executed transitions, and an awkward pause before the first example is discussed (due to confusion on the part of the creator). Despite these caveats, there is some good stuff in here and, hopefully, students will see how in a few special cases, the study of a second order equation can be reduced back to first order methods.

2. The second video introduces the concept of integrating factors. These are discussed in section 2.6 of B&DiP. They constitute a symbolic method for solving first order ODEs beyond the three basic methods that we have addressed in this course.

3. This third video discusses a symbolic method that is only tangentially treated in the course -- namely, the method of substitution. Unfortunately, there are two minor typos in the video between minutes 14 :00 and 15:00: there is a 'ct' that should be ''cy' and later on where it is written 'x=e^t' it should be ''x=ln t'.

4. This video studies an inhomogeneous, linear, constant coefficient 2nd order diff equation with a sinusoidal forcing term as a model for both a mechanical and an electrical system. The former is the damped, forced vibrating spring and the latter is a simple series LRC circuit. The concept of resonance is treated in a uniform fashion for both systems.

   Since Dr. Lipsman is still using the relatively primitive system in which no editing is possible, once again there a few minor mistakes that need to be acknowledged beforehand. First, the forcing term for the equation, is F₀ sin(ωt), but at least once in the video, the sine function is accidentally replaced by the cosine. Next, in reciting a formula for the genenral solution of a homogeneous equation, i.e., something of the form c₁y₁ + c₂y₂, the subscript '1' on the 'c' is omitted in the recitation. Finally, in the computation of the partial of R with respect to ω, a 'b²' is accidentally recited and written as 'b'.