Harmonic analysis and partial differential equations. Brief walk through these domains

In this walk we are going to walk through some domains of harmonic analysis and partial differential equations (PDE). The objective of this article is to motivate students and colleagues to study these beautiful areas of analysis and therefore we emphasize the ideas, some mathematical results and some historical data. In this “ tourist” tour we will see a panorama of such areas in the 19th and 20 th centuries, a panorama of the Fourier series; we give a vision of the theory of distributions, of the theory of linear partial differential operators and we culminate by given a vision of harmonic analysis and its relationship we the PDE.