Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.