I need help solving problems 1a & 3b

164 Chapter 5. Boundary Value Problems in Statics Exercises In Exercises 1-4, solve the BVPs using the method of Fourier series, shifting the data if necessary. If possible, produce a graph of the computed solution by plotting a partial Fourier series with enough terms to give a qualitatively correct graph. (The number of terms can be determined by trial and error; if the plot no longer changes, qualitatively, when more terms are included, it can be assumed that the partial series contains enough terms.) 1. (a) - du = 1, u(0) = u(1) = 0; dx 2 (b) - du 2 = 1, u(0) = 0, u(1) = 1. 2. (a) dx2 { = ex, u(0) = u(1) =0; ( b ) " = ex, u(0) = u(1) = 1. 3. The results of Exercises 5.2.2 and 5.2.3 will be useful for the following problems: (a) du= dx 2 = x, u(0) = 0, du (1) = 0; ( b ) - s dzu = x, dx du (0) = 0, u(1) = 1; (c) - du + 2u = 1, u(0) = u(1) =0; (d) dx2 + u = 0, u(0) = 0, u(1) = 1. 4. The results of Exercises 5.2.2 and 5.2.3 will be useful for the following problems: (a) _d'u = x2, u(0) = u(1) =0; dx 2 ( b ) - dzu+ "dx 2 + 21 = 2 - x, u(0) = 1(2) = 0; (c) - dau = x + sin (nx), u(0) = du (1) = 0; (d) _dzu = f(x), dx() , du (0) = u(1) =0, where 1, 0