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.
	PurelyGeometry:  Extra Credit:  Prove that if you connect the midpoints of the four sides of any quadrilateral you will form a parallelogram.  Follow the link and grab any corner of the blue quadrilateral with your mouse and move it.  You will see that the red parallelogram remains a parallelogram.
	You will complete Practice Problem 8 using Maple in the classroom (S219) with my help.

4.7  You will need to be able to solve a Cauchy-Euler equation.

6.1  You will need to be able to generate the power series solution to second order, linear, homogeneous differential equations including initial value problems.  The first example at the end of this link is like my series solution example 1.  Here is the SOS introduction to series solutions. You need to know how to differentiate a power series and, when necessary, shift the index.  

You will need to be able to use the power series method on a non-homogeneous equation by finding the power series solution to the complementary (corresponding homogeneous) equation and a particular solution to the non-homogeneous equation.  You will need to know how to find a power series solution when the initial conditions are not prescribed at zero.  You will need to be able to quickly figure out the minimum radius of convergence of a power series solution.  Here are two excellent introductory SOS examples where the power series method is applied to constant coefficient equations whose solution could be obtained by other methods (like in take-home test problem 1 below).  You will need to be able to solve Airy's Equation and Hermite's Equation.  Here is more information on Airy's Equation, an Airy's Equation applet, and more on Hermite's Equation.

Pendulum applet Click here for a small angle deformation pendulum problem example and a bit on the nonlinear model including the first few terms in a series solution.

Click here to see a page of worked out series solution examples.

HAPPY HOLIDAYS  (if it is December)

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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