Differential equations are the language in which physical and natural laws are expressed. This course covers 1st and 2nd order ordinary differential equations and Laplace transforms, always centering applications to science and engineering.
I've taught this course 10 times in total, most recently during the Spring 2023 quarter.
Lectures
Recorded lectures from Spring 2020 are available on the following youtube playlist:
Problem Solving
My key contribution to this course was the development of a collaborative problem solving activity.
Once a week, I'd present the class with a short word problem that's easy to state but quite difficult to solve. Then, we'd work together over the next hour to solve the problem, with the students always steering the discussion. The problems were chosen to emphasize recently-taught course concepts. However the overarching theme of these sessions is the process of modeling, which includes first making appropriate assumptions and then constructing a mathematical model to describe the situation. In this way, students can study differential equations as they actually arise, in contrast to the all-too-typical exam problem where an artificial equation is handpicked to illustrate a particular mathematical trick.
Here is a sampling of the problem prompts I've used:
How fast must a rocket be launched in order to escape the earth's gravitational pull?
Two medieval armies are fighting each other. One army has superior weapons that deal double the damage, but the other army has double the numbers. Who wins?
A clepsydra is a large urn that keeps time by the slow draining of water through a hole in the bottom of the vessel. What shape should the clepsydra be so that the water level in the vessel decreases at a steady rate?
A dog jumps into a river and swims directly toward his owner on the other side. How fast must the dog swim relative to the current in order to reach his owner?
Four snails start at the corners of a square table. If each snail follows the snail to its right, what shapes are the resulting slime trails?
Suppose a hole is drilled through the earth from Seattle, WA to Beijing, China. If you were to jump down the hole, how much time would pass before you come out the other end?
A 10 meter long rope is hanging on a smooth peg, but with a slight excess of its length on one side. How long until the rope slips off the peg?
What is the shape formed by a hanging chain, suspended from both ends?
Is it possible to design a ski slope in such a way that any skier will reach the finish line at the same time regardless of where they start on the slope?
In the past I've made additional resources available to other instructors who wish to implement this kind of activity. Please feel free to reach out if you are interested.
Exams
[My exam archive will be uploaded shortly]
Last updated Oct 12, 2023 by Thomas Carr (tjcarr@uw.edu)