Paul's Online Math Notes
     
 
Online Notes / Differential Equations (Notes) / Second Order DE's
Notice
I've been notified that Lamar University will be doing some network maintenance on August 9 during the hours of 8:00 AM through Midnight Central Daylight Time. During this time the site will either be completely unavailable or you will receive an error when trying to access any of the notes and/or problem pages. I realize this is probably a bad time for many of you but I have no control over this kind of thing and there are really no good times for this to happen and they picked the time that would cause the least disruptions for the fewest people. I apologize for the inconvenience!

Paul.



Internet Explorer 10 & 11 Users : If you are using Internet Explorer 10 or Internet Explorer 11 then, in all likelihood, the equations on the pages are all shifted downward. To fix this you need to put your browser in Compatibility View for my site. Click here for instructions on how to do that. Alternatively, you can also view the pages in Chrome or Firefox as they should display properly in the latest versions of those browsers without any additional steps on your part.

Euler's Method Differential Equations - Notes Basic Concepts

In the previous chapter we looked at first order differential equations.  In this chapter we will move on to second order differential equations.  Just as we did in the last chapter we will look at some special cases of second order differential equations that we can solve.  Unlike the previous chapter however, we are going to have to be even more restrictive as to the kinds of differential equations that we’ll look at.  This will be required in order for us to actually be able to solve them.

 

Here is a list of topics that will be covered in this chapter.

 

Basic Concepts  Some of the basic concepts and ideas that are involved in solving second order differential equations.

 

Real Roots  Solving differential equations whose characteristic equation has real roots.

 

Complex Roots  Solving differential equations whose characteristic equation complex real roots.

 

Repeated Roots  Solving differential equations whose characteristic equation has repeated roots.

 

Reduction of Order  A brief look at the topic of reduction of order.  This will be one of the few times in this chapter that non-constant coefficient differential equation will be looked at.

 

Fundamental Sets of Solutions  A look at some of the theory behind the solution to second order differential equations, including looks at the Wronskian and fundamental sets of solutions.

 

More on the Wronskian  An application of the Wronskian and an alternate method for finding it.

 

Nonhomogeneous Differential Equations  A quick look into how to solve nonhomogeneous differential equations in general.

 

Undetermined Coefficients  The first method for solving nonhomogeneous differential equations that we’ll be looking at in this section.

 

Variation of Parameters  Another method for solving nonhomogeneous differential equations.

 

Mechanical Vibrations  An application of second order differential equations.  This section focuses on mechanical vibrations, yet a simple change of notation can move this into almost any other engineering field.

Euler's Method Differential Equations - Notes Basic Concepts

Online Notes / Differential Equations (Notes) / Second Order DE's

[Contact Me] [Links] [Privacy Statement] [Site Map] [Terms of Use] [Menus by Milonic]

© 2003 - 2014 Paul Dawkins