Saturday, January 09, 2010

2010: Already Better Than 2009

I think most of my readers already know I'm planning on a career change, starting with going back to school. I want to study mechanical engineering, and before I can apply for Master's programs, I need to do a lot of prerequisites in math, basic sciences and engineering.

I've just finished my first week at North Seattle Community College. I was nervous about it because while I've done this sort of thing before - I earned my certificate in lighting technology at the New York City College of Technology in Brooklyn - I expect the coursework to be more demanding this time around. Anyway, it was fine.

The courses I'm taking this quarter are General Chemistry, Engineering Physics and Differential Equations. So far, Chemistry and Physics are no big deal. The math class is significantly more challenging.

General Chemistry is an on campus/online hybrid course. That means I only go to class on campus twice a week, although since it meets for two hours both times it's pretty close to the same hard commitment as my other classes. I've already done some of the online coursework. It's sort of like taking a very long standardized test, and relatively easy. I also remember a surprising amount of high school chemistry, which is something I was nervous about.

Engineering Physics is the upper-level physics class, and I think anyone studying science would take it too. The first quarter is all mechanics. So far, it hasn't dealt with calculus, but the problems we've done have all been either vector addition and multiplication or constant acceleration problems. I think that where this class will diverge from my high school physics class is that using calculus, it should be possible to solve problems involving changing acceleration. The next quarter deals with electricity and magnetism, something my physics class didn't get to, and the third deals with wave phenomena, sound and optics.

Math is the Big Deal this quarter, though. I've never had trouble with any other class, but calculus and higher math require my full attention. I was actually pretty nervous about this one going in because I only got through differential calculus in college before I lost interest and while I passed the second quarter of my calculus class, technically completing first-year calculus, I did it by cramming hard for a few days before the exam and then doing a lot of operations by rote. When I decided that I was going to try for a Master's in Engineering, rather than doing a second bachelor's, I bought the text book for calculus at NSCC and started reviewing, starting with algebra (seriously.) Trig I remembered better but still spent some time reviewing.

Differential calculus was a lot easier than I remembered it when I did it at my own pace, and before I started solidifying my schedule and figured out I didn't have time, I also did a lot of proofs, which I think was good. Incidentally, I suspect "my own pace" was still faster than when I did it at UCSC. Of course, the holidays interfered with my study of integral calculus and I didn't get as far as I'd hoped, so I felt a little lost looking at the first few differential equations this quarter and the entrance exam scared me a lot - there are several approaches to integration, starting with taking anti-derivatives, basically the opposite of differential calculus, and then taking a hard left turn into Weird. I'd already studied substitution, but the entrance exam also included differentiation by parts and partial fractions, which I'd never heard of.

Differentiation by parts is tricky and used quite a lot in differential equations so far. For those who remember their differential calculus, it's basically the converse of the Product Law. For those who don't... I'm not going to restate the entire body of calculus here.

Partial Fractions are difficult, but not all that weird. The commutative property applies to integration, which means that if I want to integrate a ratio of two polynomials and I can't apply a simpler rule, I can separate the equation into bite-sized pieces which are hopefully easier to solve. In order to do that, I need to factor the denominator, not necessarily an easy task, and then express the numerator as the sum of multiples of factors of the denominator. The really difficult part is figuring out the coefficients for the new, smaller pieces of numerator. To do that, I need to set up a system of equations and solve for each power of the independent variable. Yeow. The process looks pretty obvious doing it in the opposite direction (adding together the different pieces) and anyone who took algebra in high school has probably done that more times than they care to remember, but nothing in integral calculus is done the easy way.

Anyway, I've survived, my brain hasn't melted, I've handed in my entrance exam, and I've even done the reading and some of the problems due next week. I've also ordered my text books, which I found at substantially lower prices than list on, and I'm feeling pretty positive. Math will be my redheaded stepchild. Or at least my familiar.

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