LAPLACE
TRANSFORMS
CHAPTER I
, ↳ Used
to safe differential equations when 1st
year
methods and D -
operator methods fail .
PROCESS ( basic ) :
[ Diffwennntneigeeafquoteign
) I
Algebra
,
igeayahiau ]
L
I tf
[
-
solution gets
] C
K
'←E
inverse Laplace )
( Solve above ]
.
Make t →
s
assuming t④ always
•
The laplace transform of a function is defined as an
"
Integral
"
Improper .
, -1mA
{ .
Improper Integral }
Integral is
infinitely tall integral is infinitely wide
→ →
asymptote)
an
( onieaamit )
.
%
g.
f. Kyat 4µm
ftp.tdt#....
e. "
9.
0 2
vertical asymptote at * =o
=p .
tadt
COMBINATION
Kim
"
fsteyttttdt
, Examples :
-
.
Evaluate
fgitdt
T
ftp.f.etat
=
*
cnhoafafsien
ftp.fe.tt
=
.
ftp.fet H )]
=
-
=
1
Evaluate
f.lttfdt aluatefttttsdt
laimoflattttdt
=
ifdsnafstttydt
=akm.o[ ztty ;
[ ]I
's
[
za
] entti
=
2
=
hang fins
-
. .
]
o
.a[enH
2
-
=
-
o
-
njm
-
=
2
&
diverges
=
test
integral
*
Same as
.
TRANSFORMS
CHAPTER I
, ↳ Used
to safe differential equations when 1st
year
methods and D -
operator methods fail .
PROCESS ( basic ) :
[ Diffwennntneigeeafquoteign
) I
Algebra
,
igeayahiau ]
L
I tf
[
-
solution gets
] C
K
'←E
inverse Laplace )
( Solve above ]
.
Make t →
s
assuming t④ always
•
The laplace transform of a function is defined as an
"
Integral
"
Improper .
, -1mA
{ .
Improper Integral }
Integral is
infinitely tall integral is infinitely wide
→ →
asymptote)
an
( onieaamit )
.
%
g.
f. Kyat 4µm
ftp.tdt#....
e. "
9.
0 2
vertical asymptote at * =o
=p .
tadt
COMBINATION
Kim
"
fsteyttttdt
, Examples :
-
.
Evaluate
fgitdt
T
ftp.f.etat
=
*
cnhoafafsien
ftp.fe.tt
=
.
ftp.fet H )]
=
-
=
1
Evaluate
f.lttfdt aluatefttttsdt
laimoflattttdt
=
ifdsnafstttydt
=akm.o[ ztty ;
[ ]I
's
[
za
] entti
=
2
=
hang fins
-
. .
]
o
.a[enH
2
-
=
-
o
-
njm
-
=
2
&
diverges
=
test
integral
*
Same as
.
