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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 f(t)e st dt (De nition) af(t) + bg(t) aF(s) + bG(s) (Linearity) eatf(t) F(s a) (s-shift) f0(t) sF(s) f(0 ) f00(t) s2F(s) sf(0 ) f0(0 ) f(n)(t) snF(s) sn 1f(0 ) f(n 1)(0 ) tf(t) F0(s) t nf(t) ( 1)nF( )(s) u(t a)f(t a) e asF(s) (t-translation or t-shift)
Laplace transforms table Function Laplace transform eat 1 s−a tn n! sn+1 sin(at) a s 2+a cos(at) s s2 +a2 δ 0(t) 1 y0 sY(s)−y(0) y00 s2Y(s)−sy(0)−y0(0) eatf(t) F(s−a) tnf(t) (−1)nF(n)(s) H(t−c)f(t−c) e−csF(s) (f ∗g)(t) F(s)·G(s) ecttn n! (s−c)n+1 ect sin(at) a (s−c)2 +a2 ect cos(at) s−c
Table of Laplace transforms f(t) L(f(t)) or F(s) 1. 1 1 s 2. eat 1 s−a 3. tn n! sn+1 n≥0 integer 4. eattn n! (s−a)n+1 n≥0 integer 5. sinkt k s2 +k2 6. coskt s s2 +k2 7. eatsinkt k (s−a)2 +k2 8. eatcoskt s−a (s−a)2 +k2 9. 1 √ t r π s 10. u(t−a) e−as s a≥0 11. δ(t−a) e−as a≥0
Table of Laplace Transforms. In the table below c is a constant. The functions f and g are piecewise continuous functions of exponential type; F and G denote their Laplace transforms respectively. The Heavyside function u0(t) is defined to be equal to 1 for t > 0 and equal to 0 for t < 0, and δ0 denotes the δ-“function” at 0.
Table of Laplace transforms. f(t) F(s) 1. sin at. cos at. ectf(t) tnf(t) f(t − c)uc(t)
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) Created Date: 12/6/2016 10:45:20 PM ...
