Instructor: Brendan Pawlowski
Email: salmiak[_a_t_]math.washington.edu
Office: Padelford C-109
Office hours: Monday 4:30-5:30, Tuesday 3:30-4:30 (in my office), or by appointment
Lecture: MWF 11:30-12:20, More 234
Text: Elementary Differential Equations and Boundary Value Problems, 9th edition, Boyce and DiPrima. The 8th edition is also usable, but you will need to keep track of the differences from the 9th edition, given here (thanks to Hart Smith for this list).
→ Syllabus ←
Course description: This course is an introduction to differential equations. We'll talk about first-order equations, second-order equations, and the Laplace transform, along with some nice applications. Of course, there is much more to be said about differential equations than we can cover in this course (we only cover Chapters 2, 3, 6 of Boyce and DiPrima, which is itself an introductory text!). Often it's too much to hope to be able to solve a differential equation exactly, and instead one can look towards numerical methods to get approximations, or to geometric/topological methods in order to get a qualitative understanding of solutions; we won't do either of those things very much, and most of our equations will be more or less solvable exactly. We also only consider ordinary differential equations (those having derivatives with respect to just one variable), and won't say anything at all about partial differential equations (where there are derivatives with respect to multiple variables).
As the link to Wolfram Alpha below suggests, a computer can solve almost all of the differential equations we'll deal with better than you or me. Thus we'll try not to focus too hard on computations; nevertheless, doing explicit computations builds intuition, and so we'll certainly solve plenty of differential equations ourselves. Many of these computations involve integrals, so you should be sure that you have a decent handle on the material of Math 125 (integral calculus): substitution, integration by parts, partial fractions, etc. (although I will review partial fractions once we get to Laplace transforms).
Extra credit problem. Some parts of this problem may be tricky (part (c)), and other parts are a bit open-ended (part (d)). But, that's why it's extra credit: if you find some parts confusing, don't worry too much about it, this is somewhat off on a tangent from the central course material. Mainly, I just thought that what happens in part (d) is really cool, and figured an extra credit bribe would be the best way to inspire you to take a look at it. Due Friday, Mar. 11.
Extra credit. I'd like to continue giving a problem to be written up nicely, but there's no homework due this week, and there are only two after that, one of which you may or may not get back. With that in mind, I'll give an extra credit problem this week, which will be worth a little more than one regular homework problem. Both the mathematics and the written argumentation in your solution will be graded (although part of the point I'm trying to make with these problems is that one shouldn't think of those two things as separate!). Grading note: at the end of the course, the curve will be set before the extra credit is counted, otherwise it's not really "extra" at all. Here's the problem. Due Wednesday, Feb. 23.
Here's an example of what I'd consider to be a well-written solution; the solution to the reduction of order problem is another.