Thu Mar 25 15:25:08 EST 1999
This project is ready construction
The due date for project 8 is 1 Apr

General Rules for Maple projects.

1. Your name must appear on all printed pages as Maple input.
2. Assignments must be stabled (not paper clipped).
3. Maple output can be confusing if the worksheet is not executed
from top to bottom. Make sure you to execute the the worksheet
from top to bottom before printing.
4. Some Maple programs use too big font for printing. Be sure the
font size is reasonable.
5. The student version of Maple has a "smartplot", do NOT use this.
6. Include your name in the title of any plot.

Hints:
Maple can plot more than just functions. It can plot implicit functions
like F(x,y) = 0, using the implicitplot command (like animate, this is
part of the "with(plots);" package.

All equations can be turned into the form F(x,y) = 0. For example y=f(x),
can be re-written y-f(x)=0 so F(x,y) = y-f(x). The circle x^2+y^2=25
can be written x^2+y^2-25=0, so F(x,y)=x^2+y^2-25.

To plot the circle above, one has to give both the xrange and the yrange
for example 
implicitplot(x^2+y^2-25=0,x=-10..10,y=0..10);
This plot looks, well it looks wrong. The ranges are not the ones given
and the different x and y scale make the picture look like a parabola
and not a semi-circle. The option "scaling=CONSTRAINED" fixes the later
problem, and the option "view=[-10..10,0..10]" fixes the former.

Multiple implicit functions can be done on the same graph and different
plots can be combined by the "display" command.

Project 8. (This project can be done individually or in groups of 2)
If you do it as a group, I need each member of a group to make a statement
saying roughly what percentage each person contributed. (If everyone
agrees on the relative percentages, this can be one page with everyones
signature.)

#1-10 Use implicitplot to draw: (Select "good" ranges.)
#1 the hyperbola  x^2-y^2=1 
#2 the parabola x=y^2
#3 x^3-x*y^2 = 1
#4 the ellipse x^2/25+y^2/9=1, make sure the plot looks "good"
#5 Compare the implicitplot of x^2-y^2=0 and the equivalent functions
one gets from noting 0=x^2-y^2=(x-y)(x+y)=0 <=> y=x or y=-x.
#6 Combine x^2-y^2=1 and its asympotes into one plot.
#7 The equation from problem 20 in section 4.7 (page 227).
#8 The equation from problem 10 in section 4.7 (page 226) with a=10.
Be careful how you write x^2/3. x^2/3=(x^2)/3, x^(2/3) is not correct
either because it does not look for negative x. The plot is 
symmetric about the x-axis, the y-axis and the origin.
#9 F(x.y)= 4*x^6*y^2+x^8-48*x^2*y^2+8*x^4+6*x^4*y^4+y^8+4*x^2*y^6+8*y^4 = 0
Again this is symmetric about the both the x-axis and y-axis and
the origin. Start with x,y going -5..5 and play with the ranges and
numpoints to get a nicer picture.
#10 Use implicitplot to reproduce Figure 4.29 on page 225. Both the
curve and the tangent line should look the same. The 2, 7, the dash
lines, the arrow and the text "Curve has slope 2/5 here" are optional
but they can be done. Make sure the plot looks "smooth".