# 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

Â© BrainMass Inc. brainmass.com December 24, 2021, 6:26 pm ad1c9bdddfhttps://brainmass.com/math/fourier-analysis/fourier-series-expansions-differentiation-114264

#### Solution Preview

Hi there and thank you again for posting your questions to BrainMass.

Please see attached file.

Check out:

http://mathworld.wolfram.com/FourierSeries.html

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.