Tabla de Transformadas Laplace y Fourier

Serie de Fourier Funci´ on f (t) −π < t < π f (t) = t Serie 2 ∞ X (−1)n+1 n=1 f (t) = |t| −π < t < π n sen nt ∞

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Serie de Fourier Funci´ on f (t) −π < t < π

f (t) = t

Serie 2

∞ X (−1)n+1 n=1

f (t) = |t|

−π < t < π

n

sen nt

∞ π 4 X cos (2n − 1)t − 2 π (2n − 1)2 n=1

f (t) = π − t

0 < t < 2π

2

∞ X sen nt n=1

( f (t) =

0

−π < t < 0

t

0 | Im(z) | Re(s + ω) > | Im(z) |

f 0 (t)

sF (s) − f (0)

f (n (t)

sn F (s) − sn−1 f (0) − sn−2 f 0 (0) − · · · − f (n−1 (0)

tn f (t)

(−1)n F (n (s)

eat f (t)

F (s − a)

a∈C

f (t − a)

e−as F (s)

a≥0

f (at) f (t) sen ωt f (t) cos ωt

  1 s F a>0 a a   1 F (s − iω) − F (s + iω) 2i   1 F (s − iω) + F (s + iω) 2