A first look at the definition and concept of Fourier series as a global expansion in a finite interval, compared with a Taylor series as a local expansion. More in upcoming videos!
A quick look at the derivation of Euler’s formula and its uses and connections to trigonometric and hyperbolic sine and cosine functions of complex variables.
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.
A quick look at the adjoint of a linear operator (aka the hermitian conjugate). An example with a differential operator and how to prove properties using the definition based on the inner product.
How do you represent a function on a computer with discrete memory? What about its derivatives? A first look at stuff on a lattice, the matrix form of the first-derivative operator (forward, with periodic boundary conditions), and its eigenvectors and eigenvalues (Fourier modes).
