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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.
We are learning Rolle, Lagrange, Fermat, Taylor Theorems in our Real Analysis class. We just finished continuity and are now studying differentiation.
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