In this video lesson, Math Instructor Donny Lee uses the even property of a function, to find the Fourier Series of x^2 on [-3, 3] which serves as an example of why certain functions do not need to agree with its Fourier Series. A Convergence Theorem is needed.

1. Definition of the Fourier Series
2. Fourier Series of a 'Broken' Function
3. Fourier Series of Function on [-L, L]
4. Example of Fourier Series on [-L, L]
5. Fourier Series On Odd and Even Functions
6. Fourier Series of x^2 [may not = f(x)]
7. Recap On Piecewise Continuous Functions
8. Convergence Theorem of a Fourier Series
9. Convergence of Fourier Series of f(x)=2x
10. Convergence of a 'broken' Function
11. Graphs of Various Fourier Series
12. Contrasting Power and Fourier Series
13. Fourier Cosine Series
14. Fourier Sine Series
15. Half Range Expansions of f(x)=e^2x
16. Periodic Functions
17. Phase Angle Form of a Function

In this course, GMath Instructor Donny Lee gives 17 video lessons on Fourier Analysis. Some of the topics covered are: Convergence Theorem, Contrasting Power, Fourier Cosine Series, Fourier Sine Series, Periodic Functions, Phase Angle form of a Function, and many more.