Happy Monday! I must say, it is wonderfully pleasant to have a busy Monday doing things that I actually care about to look forward to. Also apparently, when left to my natural rhythm, I need about 9 hours of sleep. Zzzz. Perhaps this will decrease as I become fully rested, but perhaps not.
Today I set for myself three chapters to study: Oscillations, Traveling Waves, and Superposition and Standing Waves. This was pretty ambitious, honestly. It’s the entire Part II of this book! But I got through it all, and it makes sense. I hit this pretty hard when studying for the pGRE, so I feel relatively comfortable with the material presented. There are a lot of interesting practical examples regarding music and musical instruments that are very interesting. Amazing how people came up with this stuff intuitively/through trial and error long before we could show the principles behind what is happening in even a relatively simple instrument!
I returned to Mathematical Methods today, and luckily this chapter went more smoothly than the last one. This was a re-introduction to calculus, covering derivatives and integrals. Weird that I find this easier to follow than the algebra chapter, but this is (as stated in the book) the kind of math most frequently found in physical sciences, so perhaps that is not surprising.
And I even had time to take a long midday break to go see Wonder Woman and buy exorbitant amounts of junk food at Sam’s Club with my boyfriend! What a nice Monday. =)
Today’s fun “new” fact: Okay, so this has mostly been about physics so far, but today I’m giving the honors to math. While I’ve always known in the back of my mind what a derivative is and how to derive one (hehe), if yesterday you’d asked me to do it, I might have flailed a little. But it’s really actually simple to show, for example, the derivative of a simple power function. For f(x)=x2, take the limit as ∆x approaches zero of [f(x+∆x)-f(x)]/∆x.
And as ∆x goes to zero: f'(x)=2x.