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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 ...
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
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)
State the Laplace transforms of a few simple functions from memory. What are the steps of solving an ODE by the Laplace transform? In what cases of solving ODEs is the present method preferable to that in Chap. 2? What property of the Laplace transform is crucial in solving ODEs? = Explain. When and how do you use the unit step function and
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.Boyd EE102 Table of Laplace Transforms Rememberthatweconsiderallfunctions(signals)asdeflnedonlyont‚0. General f(t) F(s)= Z 1 0 f(t)e¡st dt f+g F+G fif(fi2R) fiF
Table Notes. This list is not a complete listing of Laplace transforms and only contains some of the more commonly used Laplace transforms and formulas. Recall the definition of hyperbolic functions. et + e t et e t. cosh (t) = sinh (t) =. 2. 2. Be careful when using “normal” trig function vs. hyperbolic functions.
