Laplace2 - The Laplace Transform We again consider the...

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

View Full Document Right Arrow Icon
The Laplace Transform We again consider the nonhomogeneous IVP ˙ y = A y + g y ( x 0 ) = y 0 . In class, following Braun pp. 368-369, we showed that the Laplace transform applied to both sides of this equation gave the new matrix equation ( sI - A ) Y ( s ) = y 0 + G ( s ) where we defined Y ( s ) = Y 1 ( s ) Y 2 ( s ) . . . Y n ( s ) = L [ y 1 ( x )] L [ y 2 ( x )] . . . L [ y n ( x )] = L ± y ( x ) ² and similarly G ( s ) = G 1 ( s ) G 2 ( s ) . . . G n ( s ) = L [ g 1 ( x )] L [ g 2 ( x )] . . . L [ g n ( x )] = L ± g ( x ) ² . Then to solve this nonhomogeneous IVP we can just (1) Apply the Laplace transform to both sides of the nonhomogeneous equation to get the new matrix equation ( sI - A ) Y ( s ) = y 0 + G ( s ) . (2) Solve for Y , the Laplace transform of the solution, by any method from linear algebra. The easiest perhaps being to multiply both sides by the inverse of
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/03/2012 for the course MATH 4430 at Colorado.

Page1 / 3

Laplace2 - The Laplace Transform We again consider the...

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