I think it is ready now 4:30pm 26 Jan
The due date for project 2 is 4 Feb

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:

Project 2. (This is not a group project)
This project is about "Tables" in Maple. Table 1.17 on page 30 of the
text has a table for 3 functions one is g(t) below. 
t	h(t)
1.0	3.00
1.2	5.18
1.4	8.23
1.6	12.29
1.8	17.50
2.0	24.00

Maple has a `table' operator, but it is too limited, instead we will
use its `lists'. To enter the above table into a list "h" one
types
h:=[[1, 3], [1.2, 5.18], [1.4, 8.23], [1.6, 12.29], [1.8, 17.5], [2, 24]];

The variable h is a list of lists. We can think of the two element sub-lists
as [x-coordiate, y-coordinate] pairs. One can "plot" h with the plot
command like 
plot(h, x=1.5..3);

The x=1.5..3 determines the x-range of the plot. h is truncated to this
range. Note that the points of h are connected by lines which might or
might not be "correct" for the function values. (One can modify this
behavoir by using the "style=point" option to plot.)

Given a list like h, one can access the 3rd element of the list by
h[3] which is [1.4, 8.23] (Maple lists start with the first element and
not the zeroth element as some computer languages. One can get the
y-coordinate of this point by using h[3][2].

If one has a function of the form y = f(x) and one wants to construct
a table for f(x), one can use the Maple "seq" command. For example
f:=x->x^2+x+1;
g:=x->0.9+x/10;
h2:=[seq([g(i), f(g(i))],i=1..10)];

will construct a table of values for f(x) for the x-values 1.0, 1.1, .... 2.0.
One can plot f(x) and h2 on the same graph using plot({h2,f(x)},<xrange>);

When you command Maple to plot a function with "plot(f(x),x=a..b);" Maple
will (sometimes) just divide the range a..b into 50 equal points create
a list of list table and just plot these points. One can "see" the list
of list table that Maple constructed using the "lprint" command. For example
lprint(plot(x,x=0..1,numpoints=5); outputs:
PLOT(CURVES([[0, 0], [.6539146250000000e-1, .6539146250000000e-1], [.1307829250000000, .1307829250000000], [.1961743875000000, .1961743875000000], [.2615658500000000, .2615658500000000], [.3184626118750000, .3184626118750000], [.3753593737500000, .3753593737500000], [.4322561356250000, .4322561356250000], [.4891528975000000, .4891528975000000], [.5531392568750000, .5531392568750000], [.6171256162500001, .6171256162500001], [.6811119756250000, .6811119756250000], [.7450983350000000, .7450983350000000], [.8088237512500001, .8088237512500001], [.8725491675000000, .8725491675000000], [.9362745837499999, .9362745837499999], [1., 1.]],COLOUR(RGB,1.0,0,0)),AXESLABELS("x",``),VIEW(0 .. 1.,DEFAULT))

The "table of values" is easy to pick out. (The numpoints option makes the
table "start" with 5 values, but Maple will not do 5, we have about 17. The
default for numpoints is 50.)

One can use the lprint output in cut and paste to get a table containing
the data to plot.

If f is a list of list table with n points/items (n is  nops(f)) then
A. seq( f[i+1][1]-f[i][1], i=1..n-1 ) is the list of delta x's
B. seq( f[i+1][2]-f[i][2], i=1..n-1 ) is the list of delta y's
C. seq( f[i+1][2]/f[i][2], i=1..n-1 ) is the list of y - ratios.
D. seq( (f[i+1][2]-f[i][2])/(f[i+1][1]-f[i][1]), i=1..n-1 ) is the list of
slope's.
E. [seq( [f[i][2], f[i][1]], i=1..n )] is the list of the inverse function

Getting data from external files. An external file is a file created
(possibly) outside of Maple. Suppose there is a data file foo which
contains data in the text format
x1 y1
x2 y2
x3 y3
x4 y4
You want to read this data in without retyping it. Here are the commands
file:=fopen(foo,READ); data:=readdata(file,[float,float]); fclose(file);

Problems:
#1 Using Maple text write a sentence explaining the difference in the
Maple notations [1,2,3] and {1,2,3}.
#2 Directly create a list of list table for Table 1.1 of the text (page 2).
#3 Plot your table in #2 with "style=point" to produce the left graph in
figure 1.1 of the text (page 2). "symbol=circle" might has be needed.
#4 Use seq to create a list of lists table for f(x)=x^2 evaluated at
the integers -2, -1, 0, 1, 2.
#5 Plot your table in #4 together with f(x) over the range -2..2 using
the default style and note how two graphs are not prefect matches.
#6 Use Maple and #C above to answer problem #25 in 1.3. In particular
enter the tables for the functions f, g, h in Table 1.14.
#7 Use the tables for f, g and h and #E above to construct tables for
inverse functions. Plot all six functions together.
#8 Use lprint and cut and paste and nops to determine how many data points
Maple uses to plot(sin(x),x=0..2*Pi);
#9 Copy http://www.math.fsu.edu/~bellenot/class/s99/cal1/data2 to your
system. And use this external file to read this data into Maple and plot
the data.
#10 Sort the delta x's of the external data, using sort and #A above. Use
the help system to figure out how to sort.