Introduction to Electric Circuits

Chapter 14 The Laplace TransformPart 1

Laplace Transform

Inverse Laplace Transform

Linearity

Laplace Transform of Derivative

Integration by parts

d du dv dv d duuv v u u uv vdt dt dt dt dt dt

dv duu uv vdt dt

00 0

, ,

( ) (0 )

st st

st st st

dv df duu e v f sedt dt dt

df e dt e f s fe dt sF s fdt

Pulse Inputs

Unit step function

Impulse Function

Impulse Function

Time-shifted Function

Inverse Laplace Transform

Simple Complex Conjugate Poles

Repeated Poles