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Note for Applied Mathematics - 2 - M-2 by Bhubanjit Sahu

  • Applied Mathematics - 2 - M-2
  • Note
  • Biju Patnaik University of Technology BPUT - BPUT
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INVERSE LAPLACE TRANSFORMS FORMULAS S.No F  s   L f t  f t  1 s 1 s2 1 1 2 3 1 sn t 4 1 s 1 5 s 6 1 sa 7 8 10 t 1 sa 1 eat 1 12 13 a te at 2  n  1, 2,... n  s  a 11 1 t n1eat n  1 !   1  k  0 k k  15 16 17  a  b 1 eat  ebt    a  b s  a  b 1 aeat  bebt    a  b  s  a  s  b   s  a  s  b  1 1 s  2 s 2 s  2 1 2 s  a2 s 2 s  a2 1  s  a   2 18 t k 1eat 1 sin t  cost 2 14  a 1  a  0 1  s  a t 2 3 2 s  a 9 t n1  n 1! 1 t  n  1, 2,... 1 sinh at a cosh at 1 2  sa e at sin t eat cos t  s  a  2 2 19 1 s  s  2  2 Dr. K. Kameswaran. Peri, Department of Mathematics 1 2 1  cos t 

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INVERSE LAPLACE TRANSFORMS FORMULAS 20 21 22 1 s 2 s 2   s s  a 2  s 25 2 b 2 3 t sin t 2  1  sin t  t cos t  2  2 2 2  a 2  b2  1 s  4k 4 4 26 s s  4k 4 1 4 s  k4 s 4 s  k4 s a  s b 4 27 28 29 30 1 sa s b 31 1 32 s2  a2 s s  a 33 34 35 36 s 1 2  a2  k t  sin t   sin t  t cos t  2 2 s 2 1  s2 2 3 2 2 s 23 24 1 1 s2  s2   2  3 2  k  0 e as s e  as 1 ln s s Dr. K. Kameswaran. Peri, Department of Mathematics 1  cos at  cos bt  b  a2 2 1  sin kt cos kt  cos kt sinh kt  4k 3 1 sin kt sinh kt 2k 2 1  sinh kt  sin kt  2k 3 1  cosh kt  cos kt  2k 2 1 ebt  eat 3 2 t  e    a  b t 2 1 t  a b  I0  t  2  J 0  at  eat 1  2at    t    k 1 2 I  k   2a  k  2 u t  a   t  a   ln t   1  at 

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