Operational Methods - Test 1 Review | MATH 4564, Quizzes of Production and Operations Management

Download Operational Methods - Test 1 Review | MATH 4564 and more Quizzes Production and Operations Management in PDF only on Docsity! MATH4564 - Review for Test No1 - Fall 03 - Konaté Notice: Show your work. A right answer with a bad reasoning will be considered as wrong. . ——————————————————– PROBLEM 1 • Find the Laplace Transform of the function:) f1(t) = t 4 cos (t) f2(t) = (4t + 1)Uπ(t) f3(t) = (1 + t) 2 PROBLEM 2 • Find the Laplace Transform of the function: g1(t) =   0 for 0 < t < 4 t for 4 < t < 6 2 for 6 < t < +∞ g2(t) = { 1 for 0 < t < π t for π < t < +∞ PROBLEM 3 • Find the Inverse Laplace Transform of the function: F1(s) = − 3ss2 − 4s + 8 F2(s) = e −πs 3s2 + 1 2s3 + 8s PROBLEM 4 • Find the Inverse Laplace Transform of the function: F1(s) = − s(s + 2)2 F2(s) = 4s s2 − 2s − 3 PROBLEM 5 • Use the Laplace Transform method to solve the differential equation: Equation 1   2y′ + 3y = 1 y(0) = 1 Equation 2   y′′ + y′ − 2y = 0 y(0) = 1 y′(0) = 1 ——————————————————– 1