Repeated Eigenvalues — In this section we will solve systems of two linear differential equations in which the eigenvalues are real repeated double in this case numbers.

We work a wide variety of examples illustrating the many guidelines for making the initial guess of the form of the particular solution that is needed for the method. Modeling with First Order Differential Equations — In this section we will use first order differential equations to model physical situations.

We will also compute a couple Laplace transforms using the definition. We will concentrate mostly on constant coefficient second order differential equations.

With that being said I will, on occasion, work problems off the top of my head when I can to provide more examples than just those in my notes.

We will solve differential equations that involve Heaviside and Dirac Delta functions. We apply the method to several partial differential equations. Nonhomogeneous Systems — In this section we will work quick examples illustrating the use of undetermined coefficients and variation of parameters to solve nonhomogeneous systems of differential equations.

This section will also introduce the idea of using a substitution to help us solve differential equations.

Systems of Equations — In this section we will give a review of the traditional starting point for a linear algebra class. In addition we model some physical situations with first order differential equations.

We will also take a look at direction fields and how they can be used to determine some of the behavior of solutions to differential equations.

Final Thoughts — In this section we give a couple of final thoughts on what we will be looking at throughout this course. Series Solutions to Differential Equations - In this chapter we are going to take a quick look at how to represent the solution to a differential equation with a power series.

We will also give brief overview on using Laplace transforms to solve nonconstant coefficient differential equations. We will also show how to sketch phase portraits associated with complex eigenvalues centers and spirals.

Vibrating String — In this section we solve the one dimensional wave equation to get the displacement of a vibrating string.

If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width.

Undetermined Coefficients — In this section we introduce the method of undetermined coefficients to find particular solutions to nonhomogeneous differential equation.Differential Equations Here are my notes for my differential equations course that I teach here at Lamar University.

Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher on differential equations. x + y = 0 y + z = 3 z – x = 2.

I first need to rearrange the system as: x + y = 0 y + z = 3 –x + z = 2 Then I can write the associated matrix as: When forming the augmented matrix, use a zero for any entry where the corresponding spot in the system of linear equations .

DownloadWrite an augmented matrix for the system of equations

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