More on the Fourier series

Let extended periodically.

1. Compute the Fourier series for $f(t)$.
2. Write out the series explicitly up to the $3^{\text{rd}}$ harmonic.

Let extended periodically.

1. Compute the Fourier series for $f(t)$.
2. Write out the series explicitly up to the $3^{\text{rd}}$ harmonic.

Let Compute $f'(t)$.

Let

1. Find the antiderivative.
2. Is the antiderivative periodic?

Let extended periodically.

1. Compute the Fourier series for $f(t)$.
2. Plug in $t=\nicefrac{\pi}{2}$ to find a series representation for $\nicefrac{\pi}{4}$.
3. Using the first 4 terms of the result from part b) approximate $\nicefrac{\pi}{4}$.

Let extended periodically. Suppose $F(t)$ is the function given by the Fourier series of $f$. Without computing the Fourier series evaluate

1. $F(0)$
2. $F(-1)$
3. $F(1)$
4. $F(-2)$
5. $F(4)$
6. $F(-9)$