A quick reminder of the derivation of the geometric sum and its limit as a series. Video. Notes.
Category Archives: Other fun stuff
The binomial theorem
A simple proof, by induction, of the binomial theorem. Video. Notes.
More about Gaussian integrals
I show how to calculate a Gaussian integral in arbitrary dimensions in the presence of a linear source term, as a first step toward applications in quantum field theory and statistical mechanics. Video. Notes.
A 1d Green’s function example two ways
A closer look at how to calculate a Green’s function in a 1D example, using a direct solution and a spectral representation. Video. Notes.
The Dirac delta
A first look at the Dirac delta and an application with Green’s functions. Video. Notes.
Eigensystems and Inverses. Part 2.
Recap of Part 1. Orthogonality and completeness relations. What do they look like in the infinite-dimensional case of part 1? Video. Notes.
Eigensystems and Inverses
Spectral representation of the inverse of a matrix. An example in infinite dimensions and… a first appearance of a Green’s function! Video. Notes.
Gaussian integrals and Feynman’s trick
We go over how to calculate the basic Gaussian integral and then other integrals using Feynman’s parameter differentiation approach. There will be more videos coming up on multidimensional Gaussians!Video. Notes.