Continuation: More General Periods; Even and Odd Functions; Periodic Extension
In this lesson, the instructor discusses Fourier series and the Fourier expansion for f of t, emphasizing that f of t should be periodic with a periodic of 2 pi. The lesson covers even and odd functions and how to use them to simplify the calculations for the Fourier series. The instructor also shows how to remove various restrictions on functions and extend the range of Fourier series. Using a simple periodic even function as an example, the instructor demonstrates how to calculate the Fourier series using the better formulas derived earlier to simplify the work.
Continuation: More General Periods; Even and Odd Functions; Periodic Extension -- Lecture 16. More info about trig functions and their periods.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 27, 2008). License: Creative Commons BY-NC-SA.
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- Recitation Problems - Recitation Problems and classwork exercises
- Lecture Notes - Lecture Notes
- Recitation Solutions - Recitation problem solutions
- More Lecture Notes - Driving through the dashpot additional lecture notes
- How do you use even and odd function in ODEs?
- What is a periodic extension?
- How can you shorten calculations with even and odd functions?
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Staff Review
This video talks some more about Fourier series and their use in trigonometric and even and odd functions. Much of the talk is on the period of a function and how calculations can be simplified. A great explanation of how the period of a function determines a lot about it and can help with calculations.
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