Laplacetable - Laplace table PDF

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Laplace table...

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ME209 Mathematical Modelling and Analysis & MM217 Mathematics 2M Table of Some Laplace Transforms L{f (t)} =

Z ∞

f (t)e−stdt = f (s)

0

f (t)

f (s)

1.

1

2.

t

3.

tn

4.

eat

5.

sinh ωt

6.

cosh ωt

7.

sin ωt

8.

cos ωt

9.

(sin ωt − ωt cos ωt)/2ω 3

10.

(t sin ωt)/2ω

11.

teat

1 s 1 s2 n!/sn+1 1 ( s − a) ω 2 (s − ω 2 ) s 2 (s − ω 2 ) ω (s2 + ω 2 ) s 2 (s + ω 2 ) 1 (s2 + ω 2 )2 s 2 (s + ω 2 )2 1 ( s − a) 2

Some properties of the Laplace Transform 1.

L{f (t) + g (t)} = L{f (t)} + L{g (t)}

2.

L{e−atf (t)} = f (s + a) d L{tf (t)} = − (f (s)) ds ′ L{f (t)} = sf (s) − f (0)

3. 4.

L{f ′′(t)} = s2 f (s) − sf (0) − f ′ (0)

1. 2. 3.

Some useful identities f ′ (x) dx = ln |f (x)| + C f (x) Z 1 cos θ sinn θ dθ = sinn+1 θ + C (n 6= −1) (n + 1) Z 1 sin θ cosn θ dθ = − cosn+1 θ + C (n 6= −1) (n + 1) Z...