Lectures in course PHYS-216: Mathematical methods (for SPH)

Fourier Transforms: Properties and Applications

Explores Fourier transforms, including properties, convolution, Parseval's theorem, and energy spectral density for non-periodic functions.

Solving unbounded PDE's using Fourier Transforms and Convolution: Obtaining the d'Alembert solution of the wave equation

Explores elementary properties of Fourier Transforms, convolution, Parseval's Theorem, and the d'Alembert solution of the wave equation using Fourier Transforms and convolution.

Dispersion and Schrödinger Equation Solution

Explores the solution of the 1D Schrödinger equation using Fourier transforms and convolution techniques.