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Table of Laplace Transforms f(t) L[f(t)] = F(s) 1 1 s (1) eatf(t) F(s a) (2) U(t a) e as s (3) f(t a)U(t a) e asF(s) (4) (t) 1 (5) (t stt 0) e 0 (6) tnf(t) ( 1)n dnF(s) dsn (7) ... « 2011 B.E.Shapiro forintegral-table.com. This work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Revised with ...
18.031 Laplace Transform Table Properties and Rules Function Transform f(t) F(s) = Z 1 0 ... (integration rule) Interesting, but not included in this course. f(t) t Z 1 s F(˙)d˙ (The function table is on the next page.) 1. Laplace Table, 18.031 2 Function Table Function Transform Region of convergence 1 1=s Re(s) >0
Table of Laplace transforms. f(t) F(s) 1. sin at. cos at. ectf(t) tnf(t) f(t − c)uc(t)
Integration and Laplace Transform Tables! xn dx = xn+1 n+1, n ∕= −1;! 1 x dx = ln|x|! eax dx = eax a,! ax dx = ax! lna ln(ax)dx = x(ln(ax)−1)! xn ln(ax)dx = x(n+1) (n+1)2 " (n+1)ln(ax)−1 #! xeax dx = eax a2 (ax−1)! x2 eax dx = eax a3 (a2x2 −2ax+2)! sin(ax)dx = − 1 a cos(ax)! cos(ax)dx = 1 a sin(ax)! xsin(ax)dx = − x a cos(ax)+ 1 ...
Table of Laplace Transforms f(t) L{f(t)} =F(s) 1. 1 1 s 2. t 1 s2 3. tn n! sn+1, n apositiveinteger 4. sinkt k s2 +k2 5. coskt s s2 +k2 6. sin2kt 2k2 s(s2 +4k2) 7. cos2kt s2 +2k2 s(s2 +4k2) 8. eat 1 s−a 9. sinhkt k s2 −k2 10. coshkt s s2 −k2 11. eatt 1 (s−a)2 f(t) L{f(t)} =F(s) 12. eattn n! (s−a)n+1, n apositiveinteger 13. eatsinkt k ...
Table of Laplace transforms f(t) = L 1fF(s)g F(s) = Lff(t)g 1 1 s; s > 0 e at 1 s+a; s > a tn, n positive integer n! sn+1; s > 0 sin(at) a s2 +a2, s > 0 cos(at) s s2 +a2, s > 0 u(t a) e as s, s > 0 u(t a)f(t a) e asF(s) e atf(t) F(s+a) f0(t) sF(s) f(0) f00(t) s2F(s) sf(0) f0(0)
Table of Laplace Transforms f(x) F(s) = L[f(x)] c c s, s > 0 erx 1 s−r, s > r cos βx s s2 + ...
