The University of Zambia
Department of Mathematics and Statistics
Mat 3110-Engineering Mathematics II
Assignment 2A- Submit by Friday, 29th July, 2022 at 12.00hrs during the
Friday Lecture.
1. (a) The graph of f (t) is given below. Write f (t) in terms of unit step functions and
find its Laplace transform.
y
1
x
0
1
2
3
4
5
(b) The graph of g(t) is given below. Write g(t) in terms of unit step functions and
find its Laplace transform.
y
2
1
x
0
1
2
3
4
5
2. Find the inverse Laplace transform of the following functions.
(a)
F (s) =
s3 − 1
(s2 + 1)2 (s + 4)2
(b)
G(s) =
s4 + 5s2 + 2s − 9
(s2 + 8s + 17)(s − 2)2
3. Use Laplace transform to solve the initial value problem
y ′′ + 3y ′ + 2y = 6e−t , (0) = 1, y ′ (0) = 2.
1