Maple #7 is due Thursday 4 April 2002 

For FULL credit STAPLE your sheets together.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Actually unstapled assignments will not be accepted.
	Draft mode of web maple is not acceptable, use PDF mode.

Each plot must be rotated to a "nice" position and "look good (smooth)".
Each plot must have include axes and the title must include your name
and what was plotted. Note that the expressions below are not
necessarily in a form that Maple likes.

To plot the surface <x(u, v), y(u, v), z(u, v)> a <= u <= b, c <= v <= d
with Maple use plot3d([x(u, v), y(u, v), z(u, v)], u=a..b, v=c..d)

1&2 Plot the following surfaces from u=0..2, v=0..4 (from test 3 fall 98)
Each plot is separate.
  1a. <cos v, sin v, u>
  1b. <(2+u)cos 2v, (2+u)sin 2v, v>
  2a. <u cos v, u sin v, u>
  2b. <sin u cos v, sin u sin v, cos u>

3.  Line integrals. Use maple to draw  curtain plots like in the
maple worksheet of March 21 (or see below).
Eventually each line integral over a curve C reduces to integrating a
function like int(g(t),t=a..b). What we want is a `curtain' of height
g(t) over the curve C. If C is given by <x(t), y(t)>, t=a..b then
we want to plot the surface <x(t), y(t), s*g(t)> t=a..b, s=0..1.
We can do this with plot3d as follows
plot3d([x(t),y(t),s*g(t)],t=a..b,s=0..1,title=`line curtain`,axes=BOXED);
#3. Draw the curtain for #4 in 18.2 of the text

4. Plot a torus as a surface. It is the circle in the xz-plane
given by (x-2)^2+z^2=1 rotated about the z-axis. Be sure to give
the parametric equations of the surface.

5.  Plot a Klein bottle. The following should help. The handle and
bulb `fit together' to make one smooth surface.
c:=.6;a:=.2;
plot1 the handle:
Range u=Pi/2..5*Pi/2,v=Pi/4..5*Pi/4
A:=c*(cos(v)*sin(v) -0.5 + a*sin(u)*sin(v)/sqrt(sin(v)^2+cos(2*v)^2));
B:=a*c*cos(u);
C:=cos(v)+a*c*sin(u)*cos(2*v)/sqrt(sin(v)^2+cos(2*v)^2);
parametric equations of this part of the surface [A, B, C]

plot2 the bulb: v=5*Pi/4..9*Pi/4
Range u=Pi/2..5*Pi/2,v=5*Pi/4..9*Pi/4
r:=sin(v)*cos(v) - (a+1/2);
A:=c* sin(u) * r;
B:= -c * cos(u) * r;
C:=cos(v);
parametric equations of this part of the surface [A, B, C]