Formulario 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