6.3 - Math 334 Lecture #25 6.3: Step Functions (and other...

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: Math 334 Lecture #25 6.3: Step Functions (and other Piecewise Continuous Functions) A Prototype. The unit step function with an upward step of 1 at c 0 is u c ( t ) = if 0 t < c, 1 if t c. [Sketch graph of the unit step function.] The Laplace transform of the unit step function is L{ u c ( t ) } = lim A Z A e- st u c ( t ) dt [ u c ( t ) is zero for t < c ] = lim A Z A c e- st dt = lim A e- st- s A c = lim A e- sA- s- e- sc- s = e- cs s when s > 0. Example. Can the piecewise defined function h ( t ) = 1 if 0 t < 1 , t if 1 t < 2 , if t 2 , be written as a linear combination of unit step functions? Yes, it can: h ( t ) = 1 u ( t )- 1 u 1 ( t ) + tu 1 ( t )- tu 2 ( t ) + 0 u 2 ( t ) = 1 + ( t- 1) u 1 ( t )- tu 2 ( t ) . [Use appropriate unit step functions to switch on or switch off pieces of the function.] What is the Laplace transform of a function like h ( t )?...
View Full Document

This note was uploaded on 03/08/2011 for the course MATH 334 taught by Professor Smith during the Spring '11 term at Vanderbilt.

Page1 / 3

6.3 - Math 334 Lecture #25 6.3: Step Functions (and other...

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