Teaching The Wave Equation Through The Use Of Fourier's Theory

The teaching of differential equations is a fundamental part of the education of engineering students as a tool for use in a wide variety of applications. A remarkable role in the study of differential equations is occupied by the Wave equation due to the variety of phenomena that it allows to model. The present research aims to describe the teaching of the wave equation from the point of view of its mathematical development and the use of Fourier's theory as a solution method. In the first part of the article the mathematical framework that defines the wave equation is defined, then by the use of case studies the analytical solution of the mathematical model is developed step by step and finally by the application of the computational simulation the behavior of the solution in different circumstances is developed.