Unit v laplace transform(formula)

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Unit v laplace transform(formula)

  1. 1. FORMULA FOR LAPLACE TRANSFORM and its inversesS.NO f(t) L[f(t)] L-1 (L[f(t)])= f(t)1 1 L[1] = 1/s 1/s =12 t L[t] = 1/s2 1/s2 = t3 tn L[tn] = n!/sn+1 1/sn = tn-1/(n-1)!4 tn L[tn] = Ғ(n+1)/sn+1,n- non integer5. L[ ] = 1/s-a 1/s-a =6 L[ ] = 1/s+a 1/s+a =7 Sinat L[Sinat] = a/ a/ , 1/ = sinat/a8 Cosat L[Cosat] == s/ s/ = Cosat9 Sinhat L[Sinhat] == a/ a/ = sinhat10 Coshat L[Coshat] == s/ s/ = coshat
  2. 2. Properties of LAPLACE TRANSFORMS.NO PROPERTY f(t) L[f(t)]1 scale f(at) 1/a F(s/a)2 derivative (t) sL[f(t)]-f(0) (0)3 Division by t 1/t f(t)4 Multiple by t tn f(t) (-1)n dn/dsn L[f(t)]5 Initial value theorem6 Final value theorem7 First shifting F[s-a] theorem F[s+a]
  3. 3. Properties of inverses LAPLACE TRANSFORMS.NO PROPERTY1 First shifting L-1[F(s+a)] [F(s)]2 derivatives L-1[ ] (identification : -t L-1 F(s) :3 Division by s L-1 (identification : :4 Multiple by s L-1[s F(s)] (identification : d/dt L-1F(s) :5 L-1[Log, cot ,tan functions] -1/t L-16 Convolution L[(f*g)] = L[f(t)]L[g(t)] theorem

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