Page 484 - Applied Numerical Methods Using MATLAB

APPENDIX D

LAPLACE TRANSFORM

Table D.1 Laplace Transforms of Basic Functions

x(t) X(s) x(t) X(s) x(t) X(s)
1 ω
(1) δ(t) 1 (5) e −at u s (t) (9) e −at sin ωt u s (t)
2
s + a (s + a) + ω 2
m! s + a
m −at
(2) δ(t − t 1 ) e −t 1 s (6) t e u s (t) (10) e −at cos ωt u s (t)
2
(s + a) m+1 (s + a) + ω 2
1 ω
(3) u s (t) (7) sin ωt u s (t)
2
s s + ω 2
m! s
m
(4) t u s (t) (8) cos ωt u s (t)
2
s m+1 s + ω 2


Applied Numerical Methods Using MATLAB , by Yang, Cao, Chung, and Morris
Copyright  2005 John Wiley & Sons, I nc., ISBN 0-471-69833-4

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