MIT18_03S10_lt

MIT18_03S10_lt - LT. Laplace Transform 1. Translation...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: LT. Laplace Transform 1. Translation formula. The usual L.T. formula for translation on the t-axis is (1) L u ( t a ) f ( t a ) = e as F ( s ) , where F ( s ) = L f ( t ) , a > . This formula is useful for computing the inverse Laplace transform of e as F ( s ), for example. On the other hand, as written above it is not immediately applicable to computing the L.T. of functions having the form u ( t a ) f ( t ). For this you should use instead this form of (1): (2) L u ( t a ) f ( t ) = e as L f ( t + a ) , a > . Example 1. Calculate the Laplace transform of u ( t 1)( t 2 + 2 t ). Solution. Here f ( t ) = t 2 + 2 t , so (check this!) f ( t + 1) = t 2 + 4 t + 3. So by (2), 2 4 3 s s L u ( t 1)( t 2 + 2 t ) = e L ( t 2 + 4 t + 3) = e 3 + 2 + . s s s Example 2. Find L u ( t 2 ) sin t . Solution. L u ( t = e s/ 2 L sin( t + 2 2 ) sin t = e s/ 2 L (cos t ) = e s/ 2 s ....
View Full Document

This note was uploaded on 10/21/2011 for the course MATH 18.03 taught by Professor Vogan during the Fall '09 term at MIT.

Page1 / 3

MIT18_03S10_lt - LT. Laplace Transform 1. Translation...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online