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Fourier Series : Expansions and Differentiation

Let f (x) = |x| for x greater or equal to -1, less than or equal to +1

a) Write the Fourier series for f (x) on [-1,1].

b) Show that this series can be differentiated term by term to yield the Fourier expansion of f'(x) on [-1,1]

c) Determine f'(x) and write it's Fourier series on [-1,1]

d) Compare b and c.

keywords: derivatives

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http://www.sosmath.com/fourier/fourier3/gibbs.html

Let f (x) = |x| for x greater or equal to -1, less than or equal to +1

a) Write the Fourier series for f (x) on [-1,1].

b) Show that this series can be differentiated term by term to yield the Fourier expansion of f'(x) on [-1,1]

c) Determine f'(x) and write it's Fourier ...

Solution Summary

Expansion and Differentiation of a Fourier Series is invesitgated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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