Convergence Patterns in Fourier Series
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Explore the convergence properties of piecewise continuous functions in the context of Fourier series. Understand the concept of period and its relation to function behavior. Dive into the intricacies of function continuity and its implications for convergence analysis.
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http://tutorial.math.lamar.edu/Classes/DE/FourierSeries.aspx
Recall: If f(x + 6) = f(x), then period = , let L =
Recall: If f(x + 6) = f(x), then period = 6, so let L = 6 2 = 3
Recall: If f(x + 6) = f(x), then period = 6, so let L = 6 2 = 3
fis piecewise continuous d c p 10.3 Convergence
Gibbs phenomenon: Larger error near discontinuities. Overshot.
10.4 Even and Odd Functions: A function is said to be even if f( x) = f(x) A function is said to be oddif f( x) = f(x) http://tutorial.math.lamar.edu/Classes/DE/PeriodicOrthogonal.aspx
A function is said to be even if f(x) = f(x) A function is said to be oddif f( x) = f(x)
A function is said to be even if f(x) = f(x) A function is said to be oddif f( x) = f(x)
10.4 If f(x) is an odd function: Fourier sine series
10.4 If f(x) is an even function: Fourier cosine series
http://tutorial.math.lamar.edu/Classes/DE/FourierSeries.aspx
Periodic extension: Extend function f(x) = x, -3 < x < 3, via a periodic function.
http://tutorial.math.lamar.edu/Classes/DE/FourierSeries.aspx 10.2
