In Tuesday's class we started but didn't finish an example of maximizing a three-variable function subject to one constraint. For reference, here is the full solution to that example. The problem was the following: Suppose we are trying to maximize the volume of an open rectangular box using a fixed amount of material. In [...]
3Blue1Brown is a YouTube channel that produces terrific computer-animated explanations of various mathematical concepts. If you have twenty minutes free some time, I highly encourage you to take a look at some of the videos, especially those on Fourier series and the Fourier transform. Below is a link to the the video on Fourier series [...]
The following is a summary of the relationships between the three equivalent forms of Fourier series. First Form: Sines Only The first type of form we began with could be described as a "sines only" form: \[ \sum_{n=0}^{\infty} A_n\sin(2\pi nt+\phi_n). \] Here I'm including $n=0$, which gives a constant term $A_0\sin(\phi_0)$. Second [...]
