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  3. University Of The Witwatersrand (wits)
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  5. Mathematics II (MATH2014)

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Transforms Chapter 1
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  • Course
  • Mathematics II (MATH2014)
  • Institution
  • University Of The Witwatersrand (wits)

This chapter includes notes on Laplace Transforms, Inverse Laplace Transforms and solving Differential Equations using Laplace. Each section includes multiple worked examples. Notes were taken on an iPad

Last document update: 5 year ago

Preview 4 out of 42  pages

Document information

  • August 18, 2019
  • August 20, 2019
  • 42
  • 2018/2019
  • Study guide

Subjects

  • maths
  • mathematics
  • engineering
  • laplace
  • laplace transforms
  • transforms

Written for

  • University of the Witwatersrand (wits)
  • Mathematics II (MATH2014)
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Content preview

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




.

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