(4) Determine the dominant modes in the function of space x and time t f (x,t) = e -2sin (x + 3t) cos (x t) considering the interval 2 (-5,5), t e [0, 10). (a) Plot the singular values in uniform as well as semilog scales. (b) Plot the solution in the x-t plane over the given interval. (c) How much "energy of the solution is contained in mode 1 and in modes 1+2? (d) Plot the first two columns of U and V in the SVD of matrix F obtained by cal- culating f (x, t) over a grid with 100 points in x and 50 points in t. Explain their meaning (4) Determine the dominant modes in the function of space x and time t f (x,t) = e -2sin (x + 3t) cos (x t) considering the interval 2 (-5,5), t e [0, 10). (a) Plot the singular values in uniform as well as semilog scales. (b) Plot the solution in the x-t plane over the given interval. (c) How much "energy of the solution is contained in mode 1 and in modes 1+2? (d) Plot the first two columns of U and V in the SVD of matrix F obtained by cal- culating f (x, t) over a grid with 100 points in x and 50 points in t. Explain their meaning