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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. The formula L(f0) = sF (s) ¡ f(0¡) must be interpreted very carefully when f has a discon-tinuity at t = 0. We'll give two examples of the correct interpretation. First, suppose that f is the constant 1, and has no discontinuity at t = 0. In other words, f is the constant function with value 1.

  5. 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.

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

  7. 24 Μαΐ 2013 · 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 ...

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