Fourier Series in Differential Equations

What I saw in my class today
What I saw in my class today

We’ve been seeing some really interesting stuff in my Differential Equations class. This week, we started seeing Fourier series, which, in some cases, are great to approximate functions. If the function is smooth enough, adding up the series actually equals the function.

Exams and Fevers

Not a good day today. I caught a cold last week, probably because of the lack of sleep. I’ve been putting together graduate school applications and there is a lot of stuff to take care of. Luckily, one of them is ready to go and will arrive by Friday in Taiwan, thanks to FedEx.

I had an Differential Equations exam today. It didn’t go that well. I was glad to find out that others had trouble with it as well. You can tell that an exam is challenging when no one leaves after two hours. The Prof extended the exam time by 15 minutes. That didn’t help much.

There were the Picard iterations which I couldn’t remember how to do and how to prove a point was a regular singularity. In retrospect, I should have just used some complex analysis to prove that. It would have been straightforward.

There was a differential equation system that had to be resolved. I calculated eigenvalues and eigenvectors to come up with the solution. However, the eigenvectors and eigenvalues that I found, the real one at least, as well as the complex ones, didn’t work. I came to understand that even though the matrix was a 3×3, the dimension of the kernel was only 2. Meaning that I could simply disregard the last column and line.

I slept about two hours last night and I’m going to bed soon. Maybe I’ll play a bit of Gears of War 2 to relieve some stress. Haven’t played that game much ever since I bought it last week on special.