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Unformatted text preview: ﬁmﬁcew “EV/2766’??? Mdﬂémaf/‘kr, fA’myszf'f, oofézzfd _ 296 ’ Laplace Transforms 50,8 Laplace Transformzﬁmerai Formulas an m) = $30)} = f ammo? Deﬁnition of Transform 0 ﬂ!) = 3'1{F(S)} ' Inverse Transform Elam) +~ bgm} = aEBUtO} + wow} ${e°"f(r)} = F0 — a) .r—Shifting
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Compared to the usual method, what are the advantages of the Laplace transform in solving
differential equations? ‘ ‘ ,
2.. What is the crucial property of the Laplace transform that makes it suitable for solving
differential equations?
3. What do we mean by saying that the Laplace transfprm is a linear operation? Why is this I
practically important?
4. For what problems would you prefer the Laplace transform over the usual method? Give a
reason.
5. What is the subsidiary equation? How is it used?
6. Does every continuous function have a Laplace transform? Give a reason or a counterexample.
7. What is the unit step function? Why is it important?
8. What is Dirac's delta function? How did we use it?
412(0‘} 9. State the Laplace transforms of a few simple functions from memory. ‘
10. State the formula for the Laplace transform of the nth derivative of a functiOn ﬁt) from memory.
11. Can a discontinuous function have a Laplace transform? (Give a reason for your answer.)
12. Does tan 1' have a Laplace transform? Is it piecewise continuous?
13. If you know ﬁr) m 2'1[F(s)}, how would you ﬁnd EE"I[F(3)IS2}?
14. Is §£{f(r)g(r)} W ${f(t)}$[g{r)}‘? Or what?
15. What is the difference in the shifting by the ﬁrst shifting theorem and by the second shifting
theorem?
Laplace Transform. Find the Laplace transform of the given. function. (Show the details of your
work.)
16. e"sio art 17. c0532: 18. Sin2(7rI/2)
19. 3‘14: — 2) 20. t2u(t ~ a) 21. t* e'3‘
22. a” at cos 4; 23. cosh 1%: 24. rcosr + sin!
Inverse Laplace Transform. In Probs. 25m33 find the inverse Laplace transform of the given
.5772) function. (Show your work.) 3+3 1 s+1 25..—— 2. ..
s2+9 ﬁszmhufi s ...
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 Summer '08
 OLORTEGUI
 Derivative, Laplace, Continuous function

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