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 [...]
Above is a picture of Joseph Fourier, the French mathematician after whom the next phase of our course is named. Since our current textbook does not cover Fourier series and Fourier transforms, we will temporarily be switching references. Our new reference for the next three weeks will be a set of lecture notes by Brad [...]
Above is a picture of Leo Frobenius, an archaeologist not to be confused with Ferdinand Frobenius, the mathematician after which one of our recent methods is named. And here is the flowchart that was handed out in class on Thursday, which helps us keep track of what types of solutions to expect for second-order linear [...]
