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 :’( Next time I’ll get there! Then that will be it for complex analysis! I’ll begin discussing thinking of functions as vectors, Fourier analysis, and…other stuff!
At any rate, download my lecture notes. The rough outline is: singularities and poles, messing with the region of integration in complex variables, the residue theorem, then the Cauchy integral formulas.
I think when I get done with my next batch of notes on complex analysis, I’ll also upload a version which includes the other two notes on complex analysis.
As always…Comments Welcome!
Update
The professor has decided to replace quality with quantity. Why, just yesterday he got to second quantization! He asks the class “You’ve done this in Physics 9D right?” I turn to one of my study buddies and say “Yeah, we did this in sixth grade.” I think the professor took me seriously, so I’m gonna skip ahead to Fourier Analysis, spherical harmonics, etc. next…
