I didn’t go to my Diff Eq class on Wednesday, which is always dangerous, because we have a quiz every Friday, and I am shooting myself in the foot if I don’t go to class. I tell myself that I can catch up by going over the teachers notes and teaching myself. Of course, I also tell myself that I am good enough, smart enough, and doggone it, people like me. Lately I seem to be wrong a lot.
The quiz was over the Volter Integral or some such, and I had never seen it at all. It looked about 75% like a standard inverse Laplace transform problem, with initial values for y and y prime, but for some reason one of my convoluted inverse Laplace transforms functions, my f(t), was showing up, not as a function I could transform from F(s) into f(t) and then solve for the initial values, but just as f(t-(tau)), which I had no idea what to do with, because it was already in the form I wanted to get it. I can’t transform one side without transforming the other, and I didn’t know how to take the second transform, if that was even possible. And, yes, I buy my commas at Costco cause they are cheaper in bulk.
(oh, and if any of that makes no sense whatsoever, you are not real far from where I stand. I struggle hard to keep up. Math is one of the many things I call ‘not my strong suit.’ I have a lot of those but I wear mostly jeans)
So, anyway, I decided to treat F(s) as if it equalled the variable of integration, t, which transformed into 1/s^2, but then with the rest of the inverse transforms that i calculated it left me with a horrendous partial fraction algebraic problem before I could solve for the final solution using the initial values. And I had ten minutes total for the quiz. Five were spent figuring out my strategy.
I did my best, but still barely got the partial fraction decomposition done before the ten minutes was up. And wasn’t close to solving the initial value problem. I figured I had done something wrong with the erroneous F(s); I thought it had been covered when I was skipping and so I humbled myself after class to ask the teacher what I had done wrong.
Turns out that he had made the mistake. The F(s) was not supposed to be there, so it was no wonder I had no idea how to transform it properly. So I got full credit for the quiz, even though it is not certain I would have known how to do it even if he had not made a mistake. I was still clueless about that particular integral. Just don’t seem like it should work out that way. I got off easy.
My favorite show in the world is Bing Bang Theory. I laugh and laugh and it makes everything better.