Paul's Online Math Notes
Differential Equations (Notes) / Boundary Value Problems & Fourier Series   [Notes]
Differential Equations - Notes

Internet Explorer 10 & 11 Users : If you have been using Internet Explorer 10 or 11 to view the site (or did at one point anyway) then you know that the equations were not properly placed on the pages unless you put IE into "Compatibility Mode". I beleive that I have partially figured out a way around that and have implimented the "fix" in the Algebra notes (not the practice/assignment problems yet). It's not perfect as some equations that are "inline" (i.e. equations that are in sentences as opposed to those on lines by themselves) are now shifted upwards or downwards slightly but it is better than it was.

If you wish to test this out please make sure the IE is not in Compatibility Mode and give it a test run in the Algebra notes. If you run into any problems please let me know. If things go well over the next week or two then I'll push the fix the full site. I'll also continue to see if I can get the inline equations to display properly.
Higher Order Differential Equations Previous Chapter   Next Chapter Partial Differential Equations
Series Solutions Previous Section   Next Section Boundary Value Problems

 Boundary Value Problems & Fourier Series

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.

Series Solutions Previous Section   Next Section Boundary Value Problems
Higher Order Differential Equations Previous Chapter   Next Chapter Partial Differential Equations

Differential Equations (Notes) / Boundary Value Problems & Fourier Series    [Notes]

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