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WTW256: LU 3.2: TRANSFORMATION OF INITIAL VALUE PROBLEMS Lecture notes R80,00   Add to cart
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WTW256: LU 3.2: TRANSFORMATION OF INITIAL VALUE PROBLEMS Lecture notes
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Lecture notes were made while watching the recorded lectures assigned to watch. These notes include theory (theorems) and worked out examples from the lecturer. These specific notes cover Transformation of initial value problems.

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  • July 11, 2022
  • 6
  • 2021/2022
  • Class notes
  • Ms l mostert
  • All classes

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3. 2. Transformation of / UP

* when is continuous function but a
glx ) not a

piece wise function
-

.




Derivatives of Laplace transforms
first derivative
L { 1-41-1 }=gf( s) -

f / a)

L { ] S2 Fcs) s f- (e) f / c)
'

f- ( t)
-
" -
- -




second derivative

I { eat fits } =


Fcs -




d)
I{ fit d) -



yet a) } - =
e-
as
Fcs)

L{ get yet a) ] -
-

-




e-
"
L { gotra ) }


Theorem 7.2.2 .
P2 89

I{ f' " } snL{ f }
=
-

Sn flat
-

' -


Sn
-
'
f
'

lo ) -


. . .
f-
'" "
(a)

If A- 1 PROOF


L{ f / SL { f)
'
= -




fed
* Need to be able to prove !*
'

① Apply definition of Laplace transform -


to t that is

L{ f) =


5. e-" 1- '


( Hot

② use integration by parts
③ To fÑÉÉÑthe fact that tis of exp order .
t
Squee • a
Tthheeoreemm

, lim b
/
"
b →8 e- t ( Hdt
a




f!
"
d) e- f 't Hdt
b Int




st-fitijbj.es/obfitse-stdl:ie-i b- i b-ji -i. i.s :titie-stdt
=




- -
- -
- -
-




b) Iim
☆→ • (e- ¥1b ) -
f (a) asf:b fit )e stdt )
-




limb
=




→ • e-sbflb )
-


flat is L{ f)

/ e-sbfcb ) / / e-sb / / fib) / e-sbmecb
≤
◦ ≤ =
b≥ 7

proof continued in appendix

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