LAPLACE/ Simple Fourier / Simple Z table Flashcards by Bryx William Garcia | Brainscape

Q

LAPLACE TRANSFORM OF:

1

A

1 / s

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Q

LAPLACE TRANSFORM OF:

t^n

A

n! / ( s^[n+1] )

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Q

LAPLACE TRANSFORM OF:

√ t

A

(√π) / (2*s^0.5 )

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Q

LAPLACE TRANSFORM OF:

e^at

A

1 / (s - a)

SHIFTING THEOREM

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Q

LAPLACE TRANSFORM OF:

sin (at)

A

a / (s² + a²)

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Q

LAPLACE TRANSFORM OF:

cos (at)

A

s / (s² + a²)

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Q

LAPLACE TRANSFORM OF:

t*sin (at)

A

2as / (s² + a²)²

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Q

LAPLACE TRANSFORM OF:

t*cos (at)

A

(s² - a²) / (s² + a²)²

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Q

LAPLACE TRANSFORM OF:

sin (at + b)

A

[ssin(b) + acos(b)] / (s² + a²)

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Q

LAPLACE TRANSFORM OF:

cos (at + b)

A

[scos(b) - asin(b)] / (s² + a²)

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Q

LAPLACE TRANSFORM OF:

sinh (at)

A

a / (s² - a²)

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Q

LAPLACE TRANSFORM OF:

cosh (at)

A

s / (s² - a²)

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Q

LAPLACE TRANSFORM OF:

e^at) * sin (ωt

A

ω / ((s - a)² + ω²)

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Q

LAPLACE TRANSFORM OF:

e^at) * cos (ωt

A

(s - a) / ((s - a)² + ω²)

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Q

LAPLACE TRANSFORM OF:

e^at) * sinh (ωt

A

ω / ((s - a)² -ω²)

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Q

LAPLACE TRANSFORM OF:

e^at) * cosh (ωt

A

(s - a) / ((s - a)² - ω²)

Q

LAPLACE TRANSFORM OF:

t^n ) * (e^at

A

n! / ( {s - a}^[n+1] )

Q

LAPLACE TRANSFORM OF:

UNIT STEP
u(t - c)

A

[ e^(-cs) ] / s

Q

LAPLACE TRANSFORM OF:

DIRAC DELTA
δ(t - c)

A

e^(-cs)

Q

LAPLACE TRANSFORM OF:

f’(t)

A

s*F(s) - f(0)

Q

LAPLACE TRANSFORM OF:

f’‘(t)

A

(s² * F(s)) - (s * f(0)) - (f’(0))

Q

LAPLACE TRANSFORM OF:

∫ f(t) dt

A

F(s) / s

Q

LAPLACE TRANSFORM OF:

f(t - a)

A

if laplace of f(t) is F(s),

Laplace of f(t - a)
e^(-a*s) * F(s)

TIME SHIFTING

Q

Z TRANSFORM OF:

DIRAC DELTA
δ(n)

A

1

Q

Z TRANSFORM OF:

UNIT STEP
u(n)

A

z / (z - 1)

Q

Z TRANSFORM OF:

b^n

A

z / (z - b)

Q

Z TRANSFORM OF:

n

A

z / (z - 1)²

Q

FOURIER TRANSFORM OF:

DIRAC DELTA
δ(t)

A

1

Q

FOURIER TRANSFORM OF:

DIRAC DELTA
δ(t - c)

A

e^(-iω*c)