ETL701: Engineering Mathematics Assignment: Fourier Series methods 1. Solve the following IBVP using the Fourier series method: Ut Uxx = 0,0 < x < 1,t > 0 u(x, 0) = x, 0 < x < 1, u(0,t) = 0, u(1,t) = 0, t > 0. 2. Solve the following IBVP using the Fourier series method: ― Ut Uxx = sint, 0 < x < 1, t > 0 u(x, 0) = x, 0 < x < 1, u(0,t) = 0, u(1,t) = 0, t > 0. 3. Solve the IBVP by shifting the data: - Ut Uxx u(x, 0) = 0,0 < x < 1, t > 0 = x, 0 < x < 1, u(0,t) == 0, u(1,t) = cost, t > 0. 4. Solve the IBVP using Fourier series method Ut Uxx = t,0 < x < 1, t > 0 u(x, 0) = x(1 − x), 0 < x < 1, ди Əx ди (0,t) =0, (1,t) = 0, t > 0. მე 5. Solve the IBVP using Fourier series method Ut - Uxx = }}} − x, 0 < x < 1, t > 0 - u(x, 0) = x(1 − x), 0 < x < 1, ди Əx ди (0,t) =0, (1, t) = 0, t> 0. მთ (1,t) 6. Solve the IBVP using Fourier series method Utt -c²uxx = 0, 0 < x < l,t > 0 u(x,0) = x(1 − x), 0 < x < l, au (x, 0) Ət = x, u(0,t) = u(l,t) = 0, t > 0. 7. Solve the IBVP using Fourier series method Utt C²Uxx = = 100, 0 < x <l,t > 0 - u(x, 0) = x(1 − x), 0 < x < l, (x, 0) ди = x, u(0,t) = u(l,t) = 0, t > 0.