Question
Transcribed Text
HW 7
1. (a) Starting from the Fourier series for x2, compute the Fourier series for x3, -II <x<t.
(b) What values of x does it converge for?
2. (a) Suppose {ak, bk} are Fourier coefficients of f which is piecewise C1 and periodic of period
2. If {ak,bk} are Fourier coefficients of f', find the relationship between {ak,bk} and {ak,b'k}
(b) Conclude that {ak, bk} satisfy a strong convergence condition.
(c) What if f is piecewise-C'??
3.Find the Fourier series for f(x) = |sin(x)|. Use the double-angle formula to show that:
</x<t.
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