Maple #5 is due Thursday 24 Oct 2002

For FULL credit STAPLE your sheets together.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Actually unstapled assignments will not be accepted.

You are to plot the five functions below. 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. 

1. Find the quadratic Taylor polynomial (call it T) about (Pi/2,Pi/2) to
f=sin(x)sin(y) plot the two graphs together in a fashion
you can tell which is which. Make sure your title also makes it clear
which is which (for example, it could say which is on the bottom).
Use the range 0 <= x, y <= Pi (both x & y 0..Pi). [Hint: mtaylor] [one plot]

2. Find the quadratic Taylor polynomial (call it T) about (Pi,Pi) to
f=sin(x)sin(y) plot the two graphs together in a fashion
you can tell which is which. Make sure your title also makes it clear
which is which (for example, it could say which is on the bottom.
Or one could be wireframe and the other contour.)
Use the range Pi/2 <= x, y <= 3Pi/2 (both x & y P/2..3Pi/2). [Hint: mtaylor]
[one plot]

3. Using Fieldplot. Look at the vector field F=<y, -x> (Maple wants [y, -x))
and note that F is not the gradient of a function f(x,y). (If it was, then
grad F = <f_x, f_y> = <y, -x>. So f_x = y and f_xy = 1, but f_y = -x so
f_xy = -1.) Display two fieldplots together, both use -3..3 for x and y
ranges, both use scaling=contrained to get angles correct. One uses the
default arrows and grid, but the other uses arrows=think,grid=[5,5].
[hint with(plots);][one plot] 

4. Repeat #3 with the vector field <y,x>. [one plot]

5. Repeat #3 with the vector field <x,y>. [one plot]

Maple help for fieldplot has examples like:
fieldplot([x/(x^2+y^2+4)^(1/2),-y/(x^2+y^2+4)^(1/2)],x=-2..2,y=-2..2);