Unformatted text preview: 2 − k 2 , L{ cosh kt } = s s 2 − k 2 . 1 3. Su ﬃ cient Conditions for Existence of L{ f ( t ) } . Def: A function f is said to be of exponential order c if there exist constants c, M > , and T > 0 such that  f ( t )  ≤ Me ct for all t ≥ T. Theorem: If f is piecewise continuous on [0 , ∞ ) and of exponential order c , then L{ f ( t ) } exists for s > c. Theorem: If f is piecewise continuous on [0 , ∞ ) and of exponential order and F ( s ) = L{ f ( t ) } , then lim s →∞ F ( s ) = 0 . 2...
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 Fall '08
 DR.DU
 Differential Equations, Equations, Derivative, Laplace, Limit, Existence, Continuous function

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