The Fourier transform and its applications to partial differential equations.

In this master’s thesis I will introduce a way to solve partial differential equations and boundary value problems by transforming signals from a time domain to a frequency domain, and back. This algorithm is called the Fourier transform and is widely used in signal-processing and wave studies, quantum mechanics and in spectropy, for example nuclear magnetic resonance. The Fourier transform is, as we will see, defined as an improper Riemann-integral. Even though it may seem as a detour to transform a problem back and forth, my goal is to show that the Fourier transform helps to decompose an ”insoluble” mathematical problem into smaller steps that are easier to solve