Section 6.1
(Page 315)
Use the definition of the Laplace transform to find the Laplace transform of the given
functions:
# # 5 (a),
23*.
Section 6.2
Use properties of the Laplace transform and the table (see below) of Elementary Laplace
transforms to find
L
( )
[ ]
t
f
:
1.
5
3

+
t
t
2*.
t
e
t

3.
t
e
t
3
2
)
2
(
+
4.
t
e
t
3
sin
5
5*.
t
e
e
t
t
t
4
cos
3
)
1
(
2
2

+
+
6*.
t
t
β
cos
7.
t
e
t
t
β
α
sin
Pages 324 – 325
:
#
# 2, 4*, 6, 8, 10*, 12, 18, 21*, 23*
Section 6.3
Pages 333 – 334:
# # 2*, 3, 9(b), 10 *(b), 14, 15,
20*,
21*, 24.
Section 6.4
Page 340:
# # 1, 5, 10*
Section 6.5
Page 348:
# # 1, 4*, 10
Elementary Laplace Transforms
_______________________________________________________________________
( ) ( )
[ ]
s
F
L
t
f
1

=
( ) ( )
[ ]
t
f
L
s
F
=
_______________________________________________________________________
1.
1
s
1
,
0
>
s
2.
t
e
α
α

s
1
,
α
>
s
3.
,
n
t
n is positive integer
1
!
+
n
s
n
,
0
>
s
4.
t
α
sin
2
2
α
α
+
s
,
0
>
s
5.
t
α
cos
2
2
α
+
s
s
,
0
>
s
6.
( )
t
f
e
t
α
( )
α

s
F
7.
( )
t
u
c
,
s
e
s
c

0
>
s
8.
( ) ( )
c
t
f
t
u
c

( )
s
F
e
s
c

9.
( )
c
t

δ
s
c
e

10.
( )
( )
t
f
n
( ) ( ) ( )
0
0
1
1





n
n
n
f
f
s
s
F
s
K
11.
( ) ( )
t
f
t
n

( )
( )
s
F
n