# How to write absolute value as piecewise functions

Convolution Integral — In this section we giver a brief introduction to the convolution integral and how it can be used to take inverse Laplace transforms. In general, I try to work problems in class that are different from my notes.

Each cheat sheets comes in two versions. Power Series — In this section we give a brief review of some of the basics of power series.

We derive the characteristic polynomial and discuss how the Principle of Superposition is used to get the general solution. 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.

Intervals of Validity — In this section we will give an in depth look at intervals of validity as well as an answer to the existence and uniqueness question for first order differential equations.

We will also show how to sketch phase portraits associated with complex eigenvalues centers and spirals. Note that while this does not involve a series solution it is included in the series solution chapter because it illustrates how to get a solution to at least one type of differential equation at a singular point.

In addition, we give several possible boundary conditions that can be used in this situation. Here is a complete listing of all the subjects that are currently available on this site as well as brief descriptions of each.

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 give an in depth overview of the process used to solve this type of differential equation as well as a derivation of the formula needed for the integrating factor used in the solution process.

Eigenvalues and Eigenvectors — In this section we will introduce the concept of eigenvalues and eigenvectors of a matrix. Fourier Series — In this section we define the Fourier Series, i. It it still geared mostly towards Calculus students with occasional comments on how a topic will be used in a Calculus class.

Due to the nature of the mathematics on this site it is best views in landscape mode. The results of these examples will be very useful for the rest of this chapter and most of the next chapter. Not all the topics covered in an Algebra or Trig class are covered in this review.

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.

Heat Equation with Non-Zero Temperature Boundaries — In this section we take a quick look at solving the heat equation in which the boundary conditions are fixed, non-zero temperature.

However, with Differential Equation many of the problems are difficult to make up on the spur of the moment and so in this class my class work will follow these notes fairly close as far as worked problems go. The purpose of this document is go a little beyond what most people see when the first are introduced to complex numbers in say a College Algebra class.

We will solve differential equations that involve Heaviside and Dirac Delta functions. We show how to convert a system of differential equations into matrix form.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.

Algebra Cheat Sheets - This is as many common algebra facts, properties, formulas, and functions that I could think of. There is also a page of common algebra errors included. There are two versions of the cheat sheet available. One .

How to write absolute value as piecewise functions
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