Fourier_2020_forelas Ningar.pdf

Fourier analysis is a collection of techniques for solving partial differential equations (PDEs) in physics and chemistry. PDEs involve unknown functions of multiple independent real variables and their partial derivatives. Examples of PDEs include the Laplace equation, wave equation, and heat equation. The wave equation is sensitive to the geometry of the space and has no general solution, requiring individual analysis for each problem. One method for solving PDEs is separation of variables, which involves assuming the unknown function is a product of two functions, each depending on one variable. This technique is demonstrated using a vibrating string example, where the wave equation is separated into two ordinary differential equations, one for the spatial variable and one for time. The spatial equation is solved using boundary conditions, and the solution is found to be a sinusoidal function.