Thu Mar 18 16:34:51 EST 1999
This project is now ready
The due date for project 7 is 25 Mar

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.
7. Since it is hard to print an animation, a better solution is to
save the project as a Maple worksheet and then send it as an email
attachment.

The hints this time are on a Maple worksheet. which you can obtain
A. if you are on taylor:
cp ~bellenot/cal1/animation.mws .
B. Over the internet
http://www.math.fsu.edu/~bellenot/class/s99/cal1/animation.mws

Project 7. (This project can be done individually or in groups of 2 or 3)
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.)

#1-2. Animate the tangent line moving on a curve. Hint if the curve is
f:=x->x^2; or any other function, then tangent line is given by
tangent:=(x,t)->D(f)(t)*(x-t)+f(t). This looks wrong, think of it this
way, for fixed t, this is the equation of the tangent line at x=t.
[That is x is the independent variable for the line.] So "to animate"
requires that both x and t have the same range [ie x=a..b,t=a..b].
You should use the Maple command "animate" for this.

[Helpful options: change the color with color=your favorite color. limit
the "y" with the view=ymin..ymax. Reminber to plot both f(x) and the
tangent line.

1. For the function sin(x), x=0..2*Pi.
2. For the function (x-2)(x-1)(x+1)(x+2), x=-2.5..2.5 (limit the view=-10..10)

#3 Using display to "glue" pictures together.
Make separate plots for a green sin(x) x=0..2*Pi and a blue cos(x)
x = Pi/2..5*Pi/2 and combine the two plots using the display command.

#4-5 The second way to create an animation is to draw all the plots and
then glue them together. Let us re-do the tangent line example. This
with the tangent lines in green, the curves in blue and a moving red
dot tracing the "curve".

4. For the function sin(x), x=0..2*Pi.
5. For the function (x-2)(x-1)(x+1)(x+2), x=-2.5..2.5 (limit the view=-10..10)

#6 Make maple print out the product quotient and chain rules. [ie
diff(F(x)*G(x),x); etc.]

#7-10 Use maple to do the last problem of Test2. The Maple commands used
to draw the curve in the test were
f:=x->piecewise(x<40,15*x*(80-x)/1600,x<58,35*(60-x)^3/8000-20,10*x-600);
and
plot(f(x),x=0..60,y=-20..20, labelfont=[HELVETICA,18], font=[HELVETICA, 18],titlefont=[HELVETICA,18],labels=['t','v'], color=black, xtickmarks=[10,20,30,40,50,60],ytickmarks=[-20,-10,0,10,20],title=`V (ft/min)`);

[The font size was increased because the graph is "reduced" in the test.]

7. Plot the acceleration, and find the intervals where the acceleration is 
positive and negative.
8. Find the time between 40 and 50 seconds where the velocity was zero
9. Plot the altitude, and find the x and y co-ordiantes of the maximum
altitude.
10. Find the height of the hill they landed on.