Laplace Transform review. MAP PDF

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Summary

Review of the different Laplace Transform and their applications...

Description

 Laplace Transform definition o o

L { f } (s) =

Common Laplace Transforms: f (t)

L { f } (s)

Limits

f (t)

L { f } (s)

C

C/s

s>0

eat tn

tn

n! sn+1 1 s-a b 2 s + b2 s 2 s + b2

s>0

eat sin(bt)

s>a

eat cos(bt)

s>0

u (t-a)

s>0

f (t-a) u (t-a)

eat sin (bt) cos (bt)

o

F (s) =

n! (s – a) n + 1 b (s – a)2 + b2 s-a (s – a)2 + b2 e-as s -as e F (s)

Limits

s>a s>a s>a s > 0, a >= 0 a >=0

Discontinuities h (t) 0 < a

L { f } (s) = g (t) a < b

o

Exponential Order  | f (t) | =< M e α t 

o

L { f } (s) =

Unit Step Function  Π a, b (t) = u (t – a) – u (t – b) =

0 t...