Formulario de Laplace

Laplace
0) {f(t)} =
• {1} =
•(t}=
• { tn } =
4) { eat } =
5) {Sen at } =
6) { Cos at } =
7) { Senh at } =
8) { Cosh at } =
Laplace Inversa
9) −1{
}=1
10) −1{
}=t
11) −1{
} = tn
12) −1{
} = eat
1
13) −1{
} = Sen at
14) −1{
} = Cos at
15) −1{
} = Senh at
16) −1{
} = Cosh at
Propiedades
17) { eat f(t) } = F(s − a)
18) { tn f(t) } = (−1) n F(n) (s)
19) { Y' ) = s{ Y} − Y(0)
20) { Y ) = s2{Y} −sY(0) − Y'(0)
21) {
}=
= F(s)
• f( t) =
−1 {F'(s) }
• −1 {
}=
= f( t)
•{
}=
• {F(t)} =
2
Si F(t) es periodica
Función Unitaria y Impulso
• ( (t) } = 1
• { (t − a)} = e−as
• { '(t) } = s
• ( n(t) } = sn
• {u(t)} =
• { u (t − a) } =
• r(t) =
r(t)=Rampa
• 44) (t) =
(t)=Impulso
• { f(t −a)u(t − a) } = e−as{ f(t) }
• −1 {e−as F(s) } = f(t − a)u(t − a)
Función Gamma
• (n+1) = n (n) para Fracciones
• (n+1) = n! Para enteros
• (½)=" {tn}=
n=Fracc.
• ( −½ ) = −2"
Convolución
• f(t) g(t) =
Circuitos
• VL = L
=L
• IL =
• VC =
=
3
• Ic =
=C
4