Lecture Notes Four: A Panicked Introduction to Fourier Series and the Fourier Transform

Readme first! I am still in the process of revising these notes, and I have posted my first version, and the vastly updated revision.
Alrighty, in this epic tome I introduced the Fourier series. I reviewed the Gibbs phenomena, when we have discontinuities the partial sums appear to sort of “overshoot” the function near the discontinuities; [...]

Lecture Notes Three: A different Approach to the Residue Theorem

I’ve been so unsatisfied with every proof of the residue theorem, it really does just look like magic! So I tried doing it slightly differently, in a way that is to me straightforward and logical.
Unfortunately, however, I didn’t get to evaluating definite integrals or infinite sums using residues so I had me a good cry [...]

Lecture Notes Two: An Introduction to Complex Analysis

I’ve been quickly writing up notes on complex analysis, and here is the first batch of notes on complex analysis. I cover analytic functions and basic contour integration. I haven’t gotten to meremorphic functions yet, nor the Residue theorem, so you’ll have to wait until next time to see them…
Here are the lecture notes, and [...]

Lecture Notes One: An Introduction to Matrix Groups

Since the mathematical methods of physics course is thus far entirely complex analysis and not really geared towards undergrads, I wrote up some ancient lecture notes. So here are my lecture notes, comments are welcome.
Download my lecture notes.
I will probably be covering complex analysis, followed by differential equations and (“God willing”) differential geometry from there! [...]