Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...

Fourier series solutions are obtained for mixed boundary value problems for the Laplace equation in the plane and in the sphere. The nature of the boundary conditions presents difficulties in ...

We’ve seen many graphical and animated explainers for the Fourier series. We suppose it is because it is so much fun to create the little moving pictures, and, as a bonus, it really helps explain this ...

In this paper, we present rational approximations based on Fourier series representation. For periodic piecewise analytic functions, the well-known Gibbs phenomenon hampers the convergence of the ...

APPM 5350 Methods in Applied Mathematics: Fourier Series and Boundary Value Problems Restricted to graduate students. Same as APPM 4350. Prerequisites: Restricted to Graduate Students only.