1. (25 points) A waveform $v(t)$ is periodic and has the sawtooth shape illustrated in Fig. 1.
Figure 1 Sawtooth waveform $v(t)$ of Problem 1
Use the Laplace transform to find the Fourier series of $v(t)$. Specifically:
(a) Write an expression for the first period $v_1(t)$ of $v(t)$:
$v_1(t) = \begin{cases} v(t), & 0 < t < T \\ 0, & t < 0 \text{ or } t > T \end{cases}$
(b) Find the Laplace transform $V_1(s)$
(c) Use your result from part (b) to find the complex Fourier series coefficients $c_n$.
(d) Use your result from part (c) to find the rectangular Fourier series coefficients $a_n$ and $b_n$.
