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...Science journal of applied mathematics and statistics http www sciencepublishinggroup com j sjams doi issn print online approximation functions using fourier series its application to the solution partial differential equations desta sodano sheiso department college natural computational sciences wolkite university ethiopia email address cite this article vol no pp received june accepted september published abstract are a powerful tool in indeed their importance is twofold since used represent both periodic real as well solutions admitted by linear with assigned initial boundary conditions idea inspiring introduction approximate regular function period t via superposition trigonometric same thus polynomials constructed they play case role analogue that one taylor when smooth considered thesis we will study fs method make an attempt square wave line exponential polynomial dft also be values from data set compare accuracy error actual find very close d heat equation laplace obtained btcs...