I've been reinventing myself as an engineering student over the last couple years - I started taking classes at North Seattle Community College in January of 2010. I finished up my basic sciences and some lower-division engineering classes there, and at Seattle Central Community College, at the end of Winter Quarter this year. At the same time, I also applied to the graduate program at the University of Washington.
I wasn't exactly accepted, but I wasn't rejected in a final way either. I now have a really weird status at UW - I'm a Graduate Non-matriculated student. I think what it comes down to is that the designed the program I applied to, a Master's of Science in Engineering, for applicants with a BS in an engineering-related field who didn't want to do the extra requirements for the MS in Mechanical Engineering - a whole boatload of upper-division, industry-specific engineering classes. While I'm pretty close to being in technical compliance with the requirements for the MSE, I'm not the usual applicant either.
Which brings me to this quarter. I took four classes, for a 15-credit load. This isn't heavy by number of credits, but a little heavy because none of them were breadth requirements. Classes were Beginning Scientific Computing, Systems Dynamic Analysis and Design, CAD lab, and Fundamentals of Materials Science. My departmental adviser (kind of like a counselor) told me to be careful, and drop a class if I needed to.
It didn't take me long to decide that Systems was going to be my difficult class for the quarter. It has beginning scientific computing and a previous Systems class as prerequisites, but it's only offered once a year and my program coordinator said he thought I could just do it. It's actually a really cool class. I had an electrical circuits class about a year ago, that was concerned with the way that electrical circuits are mathematically modeled. This starts to get difficult when there are capacitors and inductors involved, especially if there's more than one, because these devices can store energy.
Electricity is one energy domain. The one that's most familiar to people is mechanical energy, in which energy is stored as kinetic energy, as in a moving mass, and in springs. It can also be stored as potential energy when something is higher in a gravity field, but Systems is concerned with systems that are in some sort of equilibrium state, or can achieve an equilibrium state, so that kind of potential energy is not addressed. Rotational energy is another energy domain, fairly equivalent to mechanical energy, and fluid systems are addressed too, with tanks acting as capacitors and long pipes acting as inductors. Resistors might model pipes or valves.
The thing that's cool about all of these systems is that they can all be described with a very similar set of mathematical techniques. Some specifics change, but not the approach. The next cool thing is that because the math is the same, in a system using multiple energy domains, the math can be linked up.
Once all the math is in place, a set of equations emerge that can predict the way a system responds to different inputs, based on the amplitude and frequency of the input. By the end of the quarter, we were also able to include some funky, but highly relevant inputs - impulses, like hitting something sharply with a hammer, and the Step function, which is a fair mathematical model of turning on a light switch.
What does all this have to do with real life? The one most people will have experienced is that driving on a rough road, like most of the freeways in Washington, there's a certain speed in many cars at which the car will start to shake and bounce in a really scary way. What's happening is that some regularly-spaced bump on the road, probably from successive trucks bouncing over bumps and crashing down into compressions, is hitting the suspension of the car at the suspension's resonant frequency. This causes the suspension system to amplify the input, instead of attenuating it. Uh-oh! There are similar problems with the engine mount and sometimes within the drivetrain of a car, and it applies to all kinds of other systems as well.
My favorite, of course, is bicycles. If one were to model the suspension of a bicycle as a system, it would want to do three things. First, it would need to sag appropriately under the weight of the rider. This is no big deal - most systems sooner or later respond to an input with zero frequency. If owners of fancy suspension components were wondering why the instructions for their forks and shocks say to sit on the bike for thirty seconds or so to measure sag, though, "sooner or later" is why. Next, the suspension needs to compress when something hits it hard. The math gets a little funky here, but as I understand it, a hard, fast hit, even if it's just one, can be described as having a certain period. The frequency is the inverse of the period, so for something hard and fast, it's quite high. So, the suspension has to pass high-frequency inputs without phase lag or attenuation. But here's the difficult part - people don't want their suspension to bounce under pedaling inputs or dive under braking. Pedaling is a relatively low-frequency input, probably 120-180 Hz for most people (remember, there are two pedals, and they alternate peak force.) Braking is usually done with less force, over longer, than a hit like a little rock or a root. So the ideal suspension for a mountain bike would be a high-pass filter with a range of attenuated inputs from 100-200 Hz. Lemme go out and invent that...
Systems was a class I did with my full "hard class" approach. I tried to start the homework about a week early, and finish it before section so I could ask questions. I freaked out about the tests, which was dumb - I was above average by less than a standard deviation on the first midterm, and right around average on the second. I felt really good about the final, though (knock on wood) and the professor says he has his thumb on the scale a little for score improvements at the end of the quarter. It's also an upper-division class, so I suspect that "merely average" actually is pretty good. It's just not what I'm used to.
The other classes were easier. Beginning Scientific Computing is required by a few classes, and offered as an alternative prerequisite to computer programming, linear algebra and differential equations for a few classes. I've already had a fair amount of programming and some linear algebra and differential equations classes, so I didn't miss a single point until the final. We had an electronic submission method for all tests and homework, and it's a poorly set up system. I went into the final with a 10% bonus for getting 100% on every homework, got a 90% on my first attempt, and then started having trouble with the submission system. While I'd like to know if I fixed the two problems that cost me those 10 points, I also realize I don't actually need them, so I didn't pursue the matter as much as I might have if they were going to affect my grade. I liked my teacher okay, but didn't like the class very much - I feel like it doesn't cover programming, differential equations or linear algebra particularly well, and because people don't necessarily come into the class knowing how to do any of those things, it doesn't address what's cool about MATLAB - the ability to solve nonlinear differential equations and calculus problems without analytical solutions - until the very end. I thought those were cool, and maybe we could have started them in the second or third week...
CAD lab was fun. It was concerned with learning to use SolidWorks, a solid modeling program, and also with a certain approach to modeling based on figuring out which pieces of information about an object are important, and basing everything else on that. For example, if I care about the inside width of something made out of sheet metal and also know how thick it is, I might draw it with the inside width and the thickness, and let the outside width be whatever it's going to be.
Fundamentals of Materials Science is actually a lot like chemistry, except that a few exponential formulae creep in and the strength of a material is one of the things that's discussed.
Anyway, I can't usefully take any classes for the summer, so now I'm trying to find a job, hopefully with some relevance to my new field, and hopefully I'll have time to ride my bike a lot and come into my 50-mile race in August in really good shape.