laplace-formulas

# laplace-formulas - = Z t f t-τ g τ dτ L f g = F s G s L...

This preview shows page 1. Sign up to view the full content.

Laplace transform information for Exam 2. L (1) = 1 s L ( t n ) = n ! s n +1 L ( e at ) = 1 s - a L (cos bt ) = s s 2 + b 2 L (sin bt ) = b s 2 + b 2 L ( u ( t - a )) = e - as s L ( δ ( t - a )) = e - as L ( f 0 ) = sF ( s ) - f (0) L ( f 00 ) = s 2 F ( s ) - sf (0) - f 0 (0) L ±Z t 0 f ( τ ) ² = 1 s L ( f ) L ( e at f ( t )) = F ( s - a ) L ( f ( t - a ) u ( t - a )) = e - as F ( s ) L ( tf ( t )) = - F 0 ( s ) L ± f ( t ) t ² = Z s F ( τ ) Deﬁne ( f * g )( t ) = Z t 0 f ( τ ) g ( t - τ )
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = Z t f ( t-τ ) g ( τ ) dτ L ( f * g ) = F ( s ) G ( s ) L ( f ) = 1 1-e-ps Z p e-st f ( t ) dt, if f is p-periodic...
View Full Document

## This note was uploaded on 04/03/2012 for the course MA 527 taught by Professor Weitsman during the Spring '08 term at Purdue.

Ask a homework question - tutors are online