(2) The function u(x) = sin(x/2) (2.1.22) is infinitely differentiable in [0, 27], but u'(0+) ‡ u'(2π¯). Its Fourier coe

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I have to build these 3 approaches in one graph in MATLAB, which
means I have to plot fig 2.3 in MATLAB. PLS HELP ME
(2) The function u(x) = sin(x/2) (2.1.22) is infinitely differentiable in [0, 27], but u'(0+) ‡ u'(2π¯). Its Fourier coeffi- cients are 2 1 ûk = π 1-4k2 -1 Pau(x) = Σ û keika _k=- (a) N=4 p2π = 21/6²5 u(r)e-ika dr, k=0, ±1, +2, ... 2TT JO 0 2πj Xj 1 N-1 x/T ük = = Σu(x;)e-ika, k=N/2,..,N/2-1. j=0 -1 INu(x) = ure¹kæ k-- N-1 (INu)' = ikuke ¹kæ k=- Fig. 2.3. Several versions of Fourier differentiation for u(x) = sin(x/2). The exact result is indicated by the solid curves and the approximate results for N = 4, These various Fourier differentiation procedures are illustrated in Fig. 2.3 for the function u(x) = sin(x/2). ük j= 0,..., N-1, 2 1- Fig. 2.3 INU' PNU' (INU)