MATH 406 Final: MATH406_COHEN-J_SUMMER II2009_0101_FINAL_EXAM

• School: University of Maryland
• Department: Mathematics
• Course: MATH 406
• Professor: All

Document Summary

Put a box around your nal answer to each problem!! Write down any for- mula that you use but don"t derive. Show all your work on these pages, using the backs for scratch paper. Check your answers: (25 points) find the function y(t) whose laplace transform is (a) e s /4(cid:18) 1 s2 + 1 s2 + 16(cid:19) (b) s + 5 s2 + 4s + 13: (25 points) find the laplace transform, l(y)(s) = f (s), of y. y is a linear combination of three functions. State what are they without solving for y. y + 4y + 5y = e t where y(0) = 1, y (0) = 2. Math 246: (30 points) for each of the following matrices a, nd the eigenvalues and the corresponding eigenvectors. (a) (cid:18) 3. 3(a)): x = 3x + 3y y = 5x + y where x(0) = 2, y(0) = 2. 3(cid:19) ; r = 3, v = (cid:18) 3.