I am working through Gamelin and am having trouble understanding the following:
The electric field is given by $\textbf{E} = \frac{1}{r} e_r$ where $e_r$ is the unit radial vector. Through each circle $\lbrace |z| = r \rbrace$ there is a positive outward flux given by $$\int_{|z| = r} \textbf{E} \cdot \textbf{n} \, ds = \int_{|z| = r} \textbf{E} \cdot e_r \, ds = \int_0^{2\pi} d \theta = 2 \pi.$$
I am confused on the second to last equalities. I believe Gamelin is skipping some steps and I don't quite understand how to translate between $ds$, $dr$ and $d\theta$.