ENGM 2022 Study Guide - Midterm Guide: Matlab, Horse Length, Partial Fraction Decomposition

• School: Dalhousie University
• Department: Engineering Mathematics
• Course: ENGM 2022
• Professor: All

Document Summary

Solutions of sample problems for third in-class exam. Math 246, fall 2015, professor david levermore (1) compute the laplace transform of f (t) = t e3t from its de nition. This limit diverges to + for s 3 because in that case (cid:90) t. 0 t e(3 s)t dt t dt = 2 which clearly diverges to + as t . For s > 3 an integration by parts shows that (cid:90) t. Hence, for s > 3 we have that. 1 (3 s)2 (cid:19) (cid:21) (2) consider the following matlab commands. >> syms t s y; f = ["heaviside(t)*t 2 + heaviside(t 3)*(3*t t 2)"]; >> di eqn = sym("d(d(y))(t) 6*d(y)(t) + 10*y(t) = " f); >> algeqn = subs(eqntrans, {"laplace(y(t),t,s),t,s)", "y(0)", "d(y)(0)"}, {y, 2, 3}); >> y = ilaplace(ytrans, s, t) (a) give the initial-value problem for y(t) that is being solved. (b) find the laplace transform y (s) of the solution y(t).