Introduction to Fourier Series; Basic Formulas for Period 2(pi)
In this lesson, we learn about Fourier series and why they are important in solving differential equations. The Fourier series allows any reasonable f(t) which is periodic with period 2(pi) to be represented as an infinite sum of sines and cosines. By using the superposition principle, the response to any periodic function of period 2(pi) can be calculated. We also learn about the orthogonality relations between sine and cosine functions, which are the basis for calculating the coefficients in the Fourier series.
Introduction to Fourier Series; Basic Formulas for Period 2(pi) -- Lecture 15. Learn about one of the foremost topics in differential equations -- Fourier Series. Learn what they are and why they are important.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 26, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
- Lecture Notes - Lecture Notes
- Supplementary Notes - Chapter 14 Supplementary Notes written by Prof. Miller
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- Fourier Coefficients Java Applet - An interactive Java applet for discovering Fourier coefficients.
- What are Fourier Series?
- Where do Fourier Series come from?
- Why are Fourier Series important?
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Staff Review
This video lecture introduces Fourier series and explains why they come about in differential equations. Trigonometric functions also come into play in this discussion. Several formulas are discussed for trigonometric functions with period 2pi.
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