EE 200 Laplace Transformation

a₁f₁(t)+a₂f₂(t)

a₁F₁(s)+a₂F₂(s)

f(at)

(1/a)F(s/a)

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

e^-atF(s)

e^-atf(t)

F(s+a)

df/dt

sF(s)-f(0)

(d²f)/(dt²)

s²F(s)-sf(0)-f’(0)

Integration of f(x) from s to 0

(1/s)F(s)

f(0)

limit of sF(s) as s goes to infinity

f(infinity)

limit of sF(s) as s goes to infinity

delta(t)

1

u(t)

1/s

e^-at

1/(s+a)

te^-at

1/(s+a)²

sinωt

ω/(s²+ω²)

cosωt

s/(s²+ω²)

sin(ωt+θ)

(s*sinθ +ωcosθ)/(s²+ω²)

cos(ωt+θ)

(s*cosθ -ωsinθ)/(s²+ω²)

e^-atsin(ωt)

ω/((s+a)²+ω²)

e^-atcos(ωt)

(s+a)/((s+a)²+ω²)