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.

	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 example--multiply, factor polynomials
	Click here to see a Maple worksheet showing commands for some of the steps necessary in solving a higher order non-homogeneous differential equation (same worksheet with audio using Flash).
	Click here to see a Maple worksheet showing commands for computing the Wronskian of three functions.
	Here is a PowerPoint presentation on finding the form for a particular solution (same presentation with audio using Flash).
	Here are audio/videos on  Solving Linear Systems on a TI-84 (matrix method) or TI-89  Solving Linear Systems on a TI-84 Using Simult Eqn Solver
	Maple DE Example

I have started to write up some admittedly sketchy lecture notes.  These notes will not be complete and will not include all the examples or all the theory I go over in class.  Nevertheless, take a look at them and see if they are helpful.  Chapter Four Notes  

Here is a nice summary of solving second order linear differential equations.  There are some things here we did not go over in class and there is a lot here that is similar to what we did in class and you might find it helpful.  Here is a nice little applet that will show you the graph of a variety of differential equations encountered in applications.     

4.1  Be able to prove a set of functions to be linearly independent using the Wronskian.  Be able to prove a set of functions to be linearly dependent based on definition 4.1.1 in your textbook.

4.2  Be able to use the reduction in order method to find a second linearly independent solution to a homogeneous second order linear differential equation if one solution to the equation is given.

4.3  Be able to solve constant coefficient, homogeneous, second order and higher order differential equations including initial value problems and boundary value problems (when they can be solved).

4.5  Be able to solve constant coefficient, non-homogeneous, second order and higher order differential equations including ones with conditions attached using the second order undetermined coefficients and higher order undetermined coefficients--annihilator approach to find a particular solution.

5.1  Be able to solve a vibrating spring problem.  MyPhysicsLab includes some terrific spring simulations.

Simple Harmonic Motion--The vibrating spring with no damping and no forcing function.

Find the position function for a 32 pound object attached to the end of a spring with a spring constant of 1 with no forcing function acting on the system and neglecting damping (k₂ = 0).  The object is pulled down until the spring is stretched to 5 feet below its equilibrium position and then the object is released from rest (i.e., the initial velocity is 0).  Click here to see an animation of the motion.  Take y = 0 to be the equilibrium position of the bottom of the object and y positive to indicate below the equilibrium position (contrary to the labeling in the animation).  Use the differential equation given below with F(t) = 0.

(W/g)y" + k₂y' + k₁y = F(t)    where W represents the weight of the object attached to the end of the spring, k₂ is the damping factor, k₁ is the spring constant, F(t) is an external force acting on the system, y gives the position of the bottom of the object as a function of time with y = 0 the equilibrium position and y positive indicates below the equilibrium position (contrary to the labeling in the animation).

Pendulum Phase Plane Applet Spring-Mass System  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) and a simple plane pendulum. Click here for a small angle deformation pendulum problem example.

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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