If it is not already on your hard drive, you will need to download the free DPGraph Viewer to view some of the pictures linked to on this page.

QuickTime free download.

	Table of Laplace Transforms  by Vibration Data
	Table of Laplace Transforms SOS Mathematics
	Inverse Laplace Transform applet
	Exam III Lecture Notes (incomplete)
	Here is a terrific link to Larry Green's Lake Tahoe Community College differential equations notes and examples.
	Here is a terrific set of notes for a differential equations course by Paul Dawkins at Lamar University.
	Maple Worksheet on computing Laplace and Inverse Laplace Transforms

4.6  Be able to solve a second order, constant coefficient, non-homogeneous differential equation using the method of variation of parameters to find a particular solution.  Here is variation of parameters applied to higher order equations.  An optional alternative is the reduction in order technique for finding a particular solution.  This technique sometimes leads to simpler integration but usually does not and often leads to more complex integration.  Here is another variation of parameters presentation for second order ODE's with an example.

Here are some basic definitions and results relating to the Laplace Transform  and an introduction to its use in solving differential equations from SOS Mathematics.  This link will take you to the Laplace Transform Method tutorial for students of mechanical engineering at Ohio State University who are studying system dynamics.

Here is a Fred Bass site with some nice Laplace Transform demonstrations.

7.1  Be able to find the Laplace Transform of functions similar to those in the exercises.

7.2  Be able to find the Inverse Laplace Transform of functions similar to those in the exercises.  Be able to solve second and third order constant coefficient non-homogeneous initial value problems similar to those in the exercises.

7.3  Be able to find the Laplace Transform of functions similar to those in the exercises and the Inverse Laplace Transform of functions similar to those in the exercises.  Be able to solve second order constant coefficient non-homogeneous initial value problems similar to those in the exercises.

Here is a nice Laplace Transform applet that will allow you to see the graph of a function and the graph of its Laplace Transform.

You will need to be able to show how to apply the definition of the Laplace Transform to compute a Laplace Transform of a given (simple) function.

Click here to go to a page of examples.

If there is an application problem from chapter 5 for Exam III it will again involve a spring-mass system:  Spring-mass system link 1

Spring-Mass System link 2  Here we find a group of applets by MathinSite.  Click on Mass Spring Damper Systems.

Here is a nice set of applets that includes a damped harmonic oscillator (spring).  EC  Write an explanation of what the third pane (energy vs time pane) in the damped harmonic oscillator applet is all about in a way that someone who knows nothing about the physics involved could understand.  This would include defining any terms you use.  Hint  Note that it might seem in this applet that the fundamental law of nature called conservation of energy is being contradicted.  This law refers to the fact that the total energy in any isolated system is constant.  Thus the energy represented in the graph must not be total energy.  What is it?

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        Lane Vosbury, Mathematics, Seminole State College   email:  vosburyl@seminolestate.edu

        This page was last updated on 08/21/14          Copyright 2002          webstats