Gibbs Phenomenon Resolution in 2&3 Dimensional Space via Mupad Micro Models

Abstract

This paper aims to reconstruct Mupad models to treat & resolve the overshoots & tautologically undershoots that usually appears while approximating continuous or piecewise continuous function through by Fourier series, i.e. inexperienced resolution for Gibbs phenomenon.  These   models have to go from harmonic to square wave as well as triangle wave ones in 2D,3D planes & vice versa. The author will come across advantages & disadvantages of Fourier series as well as a new reformulation for Dirchlet’s Theorem; in addition to that an extended accuracy for Gibbs Constant will find itself among the lines of this work.

Keywords: Gibbs Phenomenon, Gibbs Constant, Fourier series, overshoots, undershoots, square wave,

Triangle wave, Dirchlet’s Theorem.