Unformatted text preview: itive numbers M,a such that | f ( t ) | ≤ Me at for all t ≥ c Then b f ( s ) is deﬁned for all s > c The next result shows that Laplace transform is unique in the sense that diﬀerent continuous functions will have diﬀerent Laplace trans-form. Theorem 1.2 . If b f ( s ) = b g ( s ) for all s > c , then f ( t ) = g ( t ) at all t where both are continuous. Notice if f ( t ) and g ( t ) are piecewise continuous (continuous except at ﬁnite points where left and right limits exists,) their Laplace trans-forms can be same for all s > c even if they are diﬀerent at the isolated discontinuous point. Since solutions of ordinary equations must be continuous, so this is of no important concern. 1...
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This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.
- Spring '11