Map 2302 Differential Equations Worksheet
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1
2MAP 2302
Differential Equations
1. Express the function as a linear combination of unit step functions. Find the Laplace
Transform
a)
4!if!0 < t < 1
"
$
2!if!1 < t < 5
$
f(t) =
#
!3!if!5 < t < 7
$
$
0!if!t > 7
%
b)
1!if!0 < t < 2
!
#
0!if!2 < t < 4
#
f(t) =
"
1!if!4 < t < 7
#
#
0!if!t > 7
$
2. Using the Shifting Property find the Laplace Transform
a)
0!if!0 < t < 1
"
$
f(t) =
#
! 2t + 2!if!t > 1
2
% $
t
b)
0!if!0 < t < 3
!
#
f(t) =
"
!if!t > 3
t
$ #
e
c)
!
!if!0 < t < 4
2
#
t
f(t) =
"
(t + 1)
!if!t > 4
2
$ #
d)
1!if!0 < t < 4
!
#
f(t) =
"
if!t > 4!
2
$ #
t
e)
3!if!0 < t < 1
!
f(t) =
"
t!if!t > 1
#
f)
!
!if!0 < t < 1
2
t
#
f(t) =
3!if!1 < t < 2
"
#
0!if!t > 2
$
g)
3!if!0 < t < 4
"
f(t) =
#
2t ! 5!if!t > 4
$
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