Table of Laplace Transforms | University of Michigan - Edubirdie

University:
University of Michigan
Course:
MATH 105 | Data, Functions, and Graphs
Academic year:

2023
Views:

314

Pages:

1
Author:

Jameson Hunt

Table of Laplace Transforms Here a and b are real numbers, and the transforms will exist for sufficiently large s. Function → Transform f (t) ′ f (t) f ′′ (t) → → sF (s) − f (0) s2 F (s) − sf (0) − f ′ (0) → 1 tn ta → Γ(a + 1)/sa+1 → e 1/s n!/sn+1 → at tn eat F (s) → 1/(s − a) n!/(s − a)n+1 → cos bt → s/(s2 + b2 ) sin bt → b/(s2 + b2 ) cosh bt sinh bt eat cos bt s/(s2 − b2 ) → b/(s2 − b2 ) (s − a)/((s − a)2 + b2 ) → eat sin bt → b/((s − a)2 + b2 ) → u(t − a) δ(t − a) at e f (t) e−as/s → → u(t − a)f (t − a) → e−as F (s − a) → e−asF (s)

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