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...Introduction fourier sine and cosine series dierentiation of method eigenfunction expansion math partial dierential equations joseph m mahay hjmahaffy mail sdsu edui department mathematics statistics dynamical systems group computational sciences research center san diego state university ca http jmahay edu spring outline denitions convergence theorem example gibbs phenomenon continuous the separation variables technique solved our various pdes provided we could write f x a cos n b sin l questions does innite converge it to is resulting really solution pde its subsidiary conditions mathematically these are all dicult problems yet solutions have worked well since early s begin by restricting class that ll consider denition piecewise smooth afunction on some interval if only nite collection sections given discontinuities allowed jump discontinuity has at point limit from right left both exist not equal allows number in function derivative...