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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. e asL(f(t + a)) (s) G(s)F (s)s(t-translation)(integration. but not included in this course.f(t)1. ( ) d. s. (The function table is on the next page.) 1. Laplace Table, 18.031.

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

  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. 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.

  7. 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 ...

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