% 16.1: Line Integrals.
\item
Section 16.1: Problems 15, 23, 25, 29.

% 16.2: Vector Fields and Line Integrals, Work, Circulation and Flux.
\item
Section 16.2: Problems 19, 23, 25, 27, 29, 35, 47.

% 16.3: Path Independence, Conservative Fields and Potential Functions.
\item
Section 16.3: Problems 1, 3, 5, 9, 11, 19, 21, 26, 29, 33.

\item
Let 
$\vF = { x \over \sqrt{x^2+y^2}} \vi + { y \over \sqrt{ x^2+y^2}} \vj + 0 \vk$
and
$\vG = {-y \over x^2+y^2} \vi + { x \over x^2+y^2} \vj + 0 \vk$.
\begin{enumerate}
\item
Show that both $\vF$ and $\vG$ satisfy the component test.
\item
The natural domain for both $\vF$ and
$\vG$ is $\{(x,y,z), \, x^2+y^2 \neq 0 \}$
(that is where $\vF$ and $\vG$ are defined).
Show that $\vF$ is conservative in this domain by finding
its potential function.
\item
Show that $\vG$ is NOT conservative in this domain (read example 5).
\item
If given another $\vH$ satisfying the component test in this
domain, how do you determine whether $\vH$ is conservative?
\end{enumerate}

\item
Let $\vF = { x \over \sqrt{x^2+y^2+z^2}} \vi +
         + { y \over \sqrt{x^2+y^2+z^2}} \vj +
         + { z \over \sqrt{x^2+y^2+z^2}} \vk$.
What is the natural domain for $\vF$? 
Show that $\vF$ satisfies the component test in this domain.
Is this domain simply connected?
Is $\vF$ conservative in this domain? 

% 16.4: Green's Theorem in the Plane.
\item
Section 16.4: Problems 10, 17, 19, 23, 27, 29, 38, 39.

% 16.5: Surface and Area.
\item
Section 16.5: 5, 6, 11, 13, 15, 19, 23, 25, 31, 33, 45, 49, 51, 55, 56. 

% 16.6: Surface Integrals.
\item
Section 16.6: Problems 17, 19, 21, 25, 35, 37.

% 16.7: Stokes's Theorem.
% 16.8: The Divergence Theorem and a Unified Theory.