# lt2 - Boise State University Department of Electrical and...

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

Department of Electrical and Computer Engineering ECE225 – Circuit Analysis and Design The Laplace Transform II Reading Assignment : Read Sec. 15.4 Lecture Objectives : 1. To derive the Laplace transforms of the derivative and integral of a time function. 2. To apply the partial-fraction technique in the solution of linear diﬀerential equations. Property 5: Derivative of a Time Function L{ f ( t ) } = Z 0 f ( t ) e - st dt = F ( s ) L ' f 0 ( t ) = L df dt ± = sF ( s ) - f (0 - ) Proof : L ' f 0 ( t ) = L df dt ± = Z 0 - df dt e - st dt = Z 0 - e - st df = [ f ( t ) e - st ] 0 - - Z 0 - f ( t ) d ( e - st ) = [ f ( ) e - s - f (0 - ) e - s 0 - ] + s Z 0 - f ( t ) e - st dt = sF ( s ) - f (0 - ) Higher Derivatives of a Time Function : L ' f 00 ( t ) = L d dt £ f 0 ( t ) / ± = s L ' f 0 ( t ) - f 0 (0 - ) = s [ sF ( s ) - f (0 - )] - f 0 (0 - ) = s 2 F ( s ) - sf (0 - ) - f 0 (0 - ) L ' f 000 ( t ) = L d dt £ f 00 ( t ) / ± = s L ' f 00 ( t ) - f 00 (0 - ) = s [ s 2 F ( s ) - sf (0 - ) - f 0 (0 - )] - f 00 (0 - ) = s 3 F

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## lt2 - Boise State University Department of Electrical and...

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

View Full Document
Ask a homework question - tutors are online