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  1. 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 ...

  2. 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

  3. 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

  4. Table of Laplace transforms. f(t) F(s) 1. sin at. cos at. ectf(t) tnf(t) f(t − c)uc(t)

  5. 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) ... Function Table Function Transform Region of convergence 1 1=s Re(s) >0 eat 1=(s a) Re(s) >Re(a) t 1=s2 Re(s) >0 tn n!=sn+1 Re(s) >0 cos(!t) s=(s2 + !2) Re(s) >0

  6. Table of Laplace Transforms f(t) L[f(t)] = F(s) 1 1 s (1) eatf(t) F(sa) (2) U(ta) e as s (3) f(ta)U(ta) 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 for integral-table.com. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Revised with ...

  7. 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