%% Name: 

%% Problem 1
% Plot the portion of $$ x^2 + y^2 = 16 $$ above the xy-plane and between $$ y = -3 $$ and $$ y = 3 $$.

%% Problem 2
% Plot the vector field $$ \vec{F}(x, y) = \frac{1}{2} (x^2 + y^2) \hat{i} + \frac{1}{2} (x - y) \hat{j} $$ using meshgrid(-5:1:5, -5:1:5).

%% Problem 3
% Evaluate the line integral $$ \int_C x + y \, ds $$ where $$ C $$ is the straight line segment from $$ (1, 1, 1) $$ to $$ (2, 2, 2) $$.

%% Problem 4
% Evaluate the line integral $$ \int_C yz \, dx + yz \, dy + y \, dz $$ where $$ C $$ is the top half of the circle $$ y^2 + z^2 = 9 $$ in the yz-plane traveling from left to right.

%% Problem 5
% Evaluate the line integral of $$ f(x, y, z) = x^2 + y - 2z $$ along the curve $$ \vec{r}(t) = -3t \, \hat{i} + t \, \hat{j} + 2t \, \hat{k} $$ from $$ 0 \leq t \leq 1 $$.

%% Problem 6
% Integrate the function $$ f(x, y, z) = y^2 + z^2 $$ over the surface $$ \vec{r}(\phi, \theta) = 2 \sin(\phi) \, \hat{i} + 2 \cos(\phi)\sin(\theta) \, \hat{j} + 2 \cos(\phi) \cos(\theta) \, \hat{k} $$ for $$0 \leq \phi \leq \pi/2$$ and $$0\leq \theta \leq 3\pi/2 $$.

%% Problem 7
% Integrate the vector field $$ \vec{F}(x, y, z) = x^2 \, \hat{i} + y^2 \, \hat{j} + z^2 \, \hat{k} $$ over the surface $$ \vec{r}(\phi, y) = 2 \cos(\phi) \, \hat{i} + y \, \hat{j} + \cos(\phi) \, \hat{k} $$ from $$ 0 \leq \phi \leq 2\pi $$ and $$ -2 \leq y \leq 2 $$.