Project #5 is due Thursday 13 Feb 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. 

This is mostly more of the same Maple from last week. The only new
twisted is to make the angles `RIGHT'. By default, Maple has different
scales in the x and y directions and this makes angles incorrect.
For example plot(x,x=-1..1) plots the line y=x which makes a Pi/4
angle with the x and y axis, but the angle between the line and 
x axis looks less than Pi/4. The option scaling=constrained used like
plot(x,x=-1..1,scaling=constrained); will make the x and y scales
the same and so angles will be `RIGHT'.

1&2 Use the function sin(x)+sin(y) over the range 0..2Pi in both
variables (one period).

1. Like #2 from last week for the function and ranges above. To make
the contours smooth we need to avoid the z=zero contour. Do this by
adding the option contours=[1.8,1.4,1.0,0.6,0.2,-0.2,-0.6,-1.0,-1.4,-1.8]
together with the shading=zhue,style=patchcontour. Don't forget
the title or the axis.

2. Like #5 from last week use display to combine the contourplot
and gradplot (with arrows=thick) for the function sin(x)+sin(y)
over the range 0..2Pi in both variables (one period). Use the option,
scaling=constrained to make the angles correct.) Don't forget the title.
[A neat trick is to use contours=15, or any odd number, so that 
the z=0 contour is not plotted. No amount of numpoints will make
the zero contour `RIGHT' because of round off errors.]

3 Uses the function (x^2+y^2-25)(3x+4y)(3x-4y) over the range -5..5 in
both variables.

3. Like #2 above. Remember a title, adjust the contours, make angles correct.

4 Uses the function xy(10-x-y)(10-x)(10-y) over the range -1..11 in
both variables.

4. Like #2 above. Remember a title, adjust the contours, make angles correct.


5 Uses the matlab function given below for the same range as last
week.
 
[Remember, either define e:=exp(1) or replace e^x with exp(x). A common
error is to replace e^x with exp^x, and unfortunately Maple doesn't
notice the error, and does something dumb.]

The MATLAB function is given below, it has missing *'s and e's don't work
in Maple

matlab:= 3(1-x)^2 e^(-x^2-(y+1)^2)
    - 10(x/5-x^3-y^5)e^(-x^2-y^2) -(1/3)e^(-(x+1)^2-y^2).

5. Display four graphs together. The first is a contourplot3d of the 
matlab function with the same -3..3 range as last week. The other 3
are spacecurve plots. The
spacecurves are determined by the cross-sections x=1 and y=2
and x-y=-1. Use thickness=3 and color=red (x=1), green (y=2) and
blue (x-y=-1). Don't forget the axes or a title.

As a shortcut the curves you want are (maple commands almost)
curve:=[x,y,matlab];
a:=spacecurve(eval(curve,x=1),y=-3..3,color=red, ... ):
b:=spacecurve(eval(curve,y=2),x=-3..3,color=green, ... ):
c:=spacecurve(eval(curve,y=1+x),x=-3..2,color=blue, ... ):
                                      ^             ^^^
                                      |             other options
                                      2 instead of 3 so that y=1+x <= 3.