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\noindent{\bf Math 3335\hfill Formula Sheet for Test 1\hfill\today}\bigskip\\
\begin{description}
\item{\textbf{Integrals.}} Let $\vc{r}(t)=(x(t),y(t),z(t)):[a,b]\to\real^3$ parametrize a curve $C$.
\begin{description}
\item{\textbf{Arclength. }} $\int_C ds=\int_a^b \|\vc{r'}(t)\|\,dt=\int_a^b \sqrt{(x'(t))^2+(y'(t))^2+(z'(t))^2}\,dt$.
\item{\textbf{Line integral with respect to arclength. }} For a scalar-valued function $f:\real^3\to\real$, \[\int_C f\, ds=\int_a^b f(\vc{r}(t))  \|\vc{r'}(t)\|\,dt.\]
\item{\textbf{Line integral. }} For a vector field $\vc{F}=(F_1,F_2,F_3):\real^3\to\real^3$, \[\int_C \vc{F}\cdot d\vc{r}=\int_C F_1\,dx+F_2\, dy+F_3\, dz=\int_a^b \vc{F}(\vc{r}(t))\cdot \vc{r'}(t)\,dt.\]
\end{description}

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