Chapter 6 Laplace Transform

Introduction To solve differential equation Convert to algebraic form Include Initial Condition

Laplace Transform

Initial value problem

Shifting Theorem Example

The Inverse Transformation Example

Invert using Partial Fraction Case I Distinct linear factor in the denominator

Case II Linear factor in the denominator, some repeat Case III Quadratic factors in the denominator

Application Solve 16 15 19

Differential respect to s

Integral of Transform Integration by part

Diameter of Column = ?

input Output BV Problem

Integrating Factor 55,1

MATLAB Safety

The Step Function Unit Step Function

Unit Impulse Function L’Hopital’s Rule, diff respect to c

Example Steady State Unsteady State

8, 12, 61 with shifting

Convolution Example

23

Inversion by elementary Integration 8

Inversion by Contour Integral IF THEN

Example