You can navigate through this E-Book using the menu to the left. For E-Books that have a Chapter/Section organization each option in the menu to the left indicates a chapter and will open a menu showing the sections in that chapter. Alternatively, you can navigate to the next/previous section or chapter by clicking the links in the boxes at the very top and bottom of the material.
Also, depending upon the E-Book, it will be possible to download the complete E-Book, the chapter containing the current section and/or the current section. You can do this be clicking on the E-Book, Chapter, and/or the Section link provided below.
For those pages with mathematics on them you can, in most cases, enlarge the mathematics portion by clicking on the equation. Click the enlarged version to hide it.
In this chapter we’ll be taking a quick and very brief look
at a couple of topics. The two main
topics in this chapter are Boundary Value Problems and Fourier Series. We’ll also take a look at a couple of other
topics in this chapter. The main point
of this chapter is to get some of the basics out of the way that we’ll need in
the next chapter where we’ll take a look at one of the more common solution
methods for partial differential equations.
It should be pointed out that both of these topics are far
more in depth than what we’ll be covering here.
In fact you can do whole courses on each of these topics. What we’ll be covering here are simply the
basics of these topics that well need in order to do the work in the next
chapter. There are whole areas of both
of these topics that we’ll not be even touching on.
Here is a brief listing of the topics in this chapter.
Boundary Value Problems 
In this section we’ll define the boundary
value problems as well as work some basic examples.
Eigenvalues and Eigenfunctions Here we’ll take a look at the eigenvalues and
eigenfunctions for boundary value problems.
Periodic Functions and Orthogonal Functions
We’ll take a look at periodic functions and
orthogonal functions in section.
Fourier Sine Series In this section we’ll start looking at Fourier
Series by looking at a special case : Fourier Sine Series.
Fourier Cosine Series We’ll continue looking at Fourier Series by
taking a look at another special case : Fourier Cosine Series.
Fourier Series Here we will look at the full Fourier series.
Convergence
of Fourier Series Here we’ll take a look at some ideas involved
in the just what functions the Fourier series converge to as well as
differentiation and integration of a Fourier series.