MTHE 281 Lecture : Week 9-9

(1 point) Find the inverse Laplace transform f(t)-L-I {F(s)) of the function F(s) = You may use h(t) for the Heaviside step function. 2s (2 -a(2s-98) s2 +81 -(2-8) 82 +81 f(t) = L-1 help (formulas)

(2) with the (generalized) function f(t)-Σ0016(t - n), Consider the IVP [24 pts] y" + 3y' + 2,-, y(0) = 0, y'(0) = 1 . (iii) Find a 1-periodic function y*-y'(t) with lim,-.+ y (t)-y.(t)l-o.

(1 point) For the functions f (t)-e and g(t)-e, defined on O So.compute f*g in two different ways: a. By directly evaluating the integral in the definition of f g. (f * g)(t) = dw = b. By computing L-1(F(s)G(s)) where F(s)-E(f(t)) and G(s) = C {g(t)). help (formulas)