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imes" 1 12 128 0 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 3 0 3 0 2 2 0
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{SECT 0 {SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "Introduction to Maple" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 279 "In order to make much use of Mapl
e when creating homework sets, you need a modest knowledge of the app
lication to start, and have a way to expand your knowledge as the need
dictates. In this activity, you will get a small dose of what Maple \+
is, and what it can be used for. " }}{PARA 257 "" 0 "" {TEXT 256 0
"" }{TEXT 295 0 "" }{TEXT 296 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1
280 "You can go a long way with Maple if you just think of it as a fan
cy graphing calculator. You can make calculations, plot functions, an
d solve equations with Maple. First, however, you can save yourself t
ime later by going through the basic editing features of a Maple works
heet." }}}{SECT 1 {PARA 258 "" 0 "" {TEXT -1 15 "Catechism on B" }
{TEXT 299 0 "" }{TEXT -1 14 "asic Editing. " }}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 69 "The answers below are not unique, but are the most conven
ient for me." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT
-1 49 "How do you open an input cell below the cursor? " }{TEXT 300
6 "Answer" }{TEXT -1 9 ": Press " }{TEXT 298 9 "control J" }{TEXT -1
56 ", that is, hold the control key down and press the j key" }}{PARA
0 "" 0 "" {TEXT -1 49 "How do you open an input cell above the cursor?
" }{TEXT 301 7 "Answer:" }{TEXT -1 8 " Press " }{TEXT 309 9 "contro
l K" }}{PARA 0 "" 0 "" {TEXT -1 58 "How do you change an empty input c
ell into a text cell? " }{TEXT 304 6 "Answer" }{TEXT -1 11 ": Press
F5" }}{PARA 0 "" 0 "" {TEXT -1 155 "How do you typeset a mathematical
expression in a text cell? Answer: Press control M, then type it in,
then toggle the X and Maple leaf at the upper left." }{MPLTEXT 1 0 0
"" }{TEXT -1 31 "\nHow do you join two cells? " }{TEXT 303 6 "Answe
r" }{TEXT -1 46 ": Put the cursor in the top cell and press F4" }}
{PARA 0 "" 0 "" {TEXT -1 26 "How do you split a cell? " }{TEXT 302 6
"Answer" }{TEXT -1 83 ": Put the cursor at the front of the line just \+
below the desired split and press F3" }}{PARA 0 "" 0 "" {TEXT -1 33 "H
ow do you copy and paste text? " }{TEXT 306 6 "Answer" }{TEXT -1 99 "
: Use the cursor select the text, then press control C. Then place th
e cursor and press control V." }}{PARA 0 "" 0 "" {TEXT -1 68 "How do y
ou put a new line in an input cell with out executing it? " }{TEXT
307 6 "Answer" }{TEXT -1 8 ": Do a " }{TEXT 297 12 "shift return" }
{TEXT -1 53 ", that is, hold the shift key down and press enter. " }}
{PARA 0 "" 0 "" {TEXT -1 34 "How do you create a new section? " }
{TEXT 308 6 "Answer" }{TEXT -1 95 ": Hold the alt key down and press
I and S ( or U depending on desires indent) in succession " }}{PARA
0 "" 0 "" {TEXT -1 38 "How do you copy and paste a section? " }{TEXT
305 6 "Answer" }{TEXT -1 81 " Close the section and select it. Contr
ol C and control V to copy and paste it." }}{PARA 0 "" 0 "" {TEXT -1
0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 81 "Exercise: Practice eac
h of these basic editing operations until you know them. " }}}}{SECT
1 {PARA 5 "" 0 "" {TEXT 284 11 "1. Entering" }{TEXT 282 38 " arithmeti
c and algebraic expressions " }{TEXT 281 5 "using" }{TEXT 283 19 " cal
culator syntax " }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 257 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 183 "It is important to be able to look a
t a mathematical expressioin, and decide how to type that into Maple. \+
The syntax is almost the same as typing it into a TI-83. Some examp
les: " }{XPPEDIT 18 0 "4*(5+8)" "6#*&\"\"%\"\"\",&\"\"&F%\"\")F%F%"
}{TEXT -1 28 " is entered as 4*(5+8), " }{XPPEDIT 18 0 "x^2 + 3*x
" "6#,&*$%\"xG\"\"#\"\"\"*&\"\"$F'F%F'F'" }{TEXT -1 42 " is x^2 + 3*
x, sqrt(3)/(1+sqrt(2)) is " }{XPPEDIT 18 0 "sqrt(3)/(1+sqrt(2))" "6#
*&-%%sqrtG6#\"\"$\"\"\",&F(F(-F%6#\"\"#F(!\"\"" }{TEXT -1 6 " and " }
{XPPEDIT 18 0 "sin(4/3*Pi)-1;" "6#,&-%$sinG6#*(\"\"%\"\"\"\"\"$!\"\"%#
PiGF)F)F)F+" }{TEXT -1 328 " is sin(4/3*Pi)-1. When you type the ex
pression into an input cell (starts with a prompt '>' and has red text
), you need to end it with a semicolon ';'. Then when you press ente
r (with the cursor anywhere in that input cell), Maple will evaluate t
he expression and format the result in a following output cell. Examp
les: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "4^(5+9);" }}{PARA
11 "" 1 "" {XPPMATH 20 "6#\"*caVo#" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 10 "x^2 + 3*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%
\"xG\"\"#\"\"\"F(*&\"\"$F(F&F(F(" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 14 "sin(7/5*Pi)-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-
%$sinG6#,$%#PiG#\"\"#\"\"&!\"\"\"\"\"F," }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 88 "To convert a number expressed symbolically to decimal for
m, we would use the maple word " }{TEXT 259 6 "evalf." }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "sin(4/3*Pi)-1 = evalf(sin(4/3*Pi)-1
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*$-%%sqrtG6#\"\"$\"\"\"#!\"\"
\"\"#F*F,$!+/a-m=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT 294 4 "Hint" }{TEXT -1 346 ": Use contr
ol J to open an input cell below the cursor and control K to open one \+
above the cursor. It is usually a good idea to have an input cell dir
ectly under (or nearly so) a cell you execute. This is because the \+
cursor will jump down to the next input cell, and if that is way down \+
the worksheet you can lose your place in the worksheet." }}}{EXCHG
{PARA 256 "" 0 "" {TEXT 260 9 "Exercise:" }{TEXT -1 20 " Type the nu
mber " }{XPPEDIT 18 0 "sin(5/7*Pi) + sqrt(2)" "6#,&-%$sinG6#*(\"\"&\"
\"\"\"\"(!\"\"%#PiGF)F)-%%sqrtG6#\"\"#F)" }{TEXT -1 145 " into an inpu
t cell. End the line with a semicolon. Put the cursor anywhere in th
e line and press return. Then convert it to a decimal number." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 285 11 "2. Plott
ing" }{TEXT 286 11 " functions:" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0
"" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 258 "The original popular
ity of the graphing calculator as an educational tool was based to a l
arge extent on its capability to plot functions. Maple gives much bet
ter resolution graphs than any calculator. For example, suppose we \+
want to plot the functions " }{XPPEDIT 18 0 "x^3 -x + 1" "6#,(*$%\"xG
\"\"$\"\"\"F%!\"\"F'F'" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "x^2 - 1" "
6#,&*$%\"xG\"\"#\"\"\"F'!\"\"" }{TEXT -1 25 " to solve the equation \+
" }{XPPEDIT 18 0 "x^3-x +1=x^2-1" "6#/,(*$%\"xG\"\"$\"\"\"F&!\"\"F(F(,
&*$F&\"\"#F(F(F)" }{TEXT -1 20 ". . The maple word " }{TEXT 258 4 "pl
ot" }{TEXT -1 215 " is used. In the plot below, we have plotted both \+
sides of the equation, specifying the range to be from x= -2 to x = 3,
and the view window to be the rectangle with x range from -2 to 3 and
y range from -2 to 2.5." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51
"plot(\{x^3-x-1,x^2-1\},x=-2..3,view=[-2..3,-2..2.5]);" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT
-1 73 "By looking at the graphs, we can see that the solutions to the \+
equation " }{XPPEDIT 18 0 "x^3-x-1 = x^2-1;" "6#/,(*$%\"xG\"\"$\"\"\"
F&!\"\"F(F),&*$F&\"\"#F(F(F)" }{TEXT -1 13 " are about " }{XPPEDIT
18 0 "x =.6, x = 0" "6$/%\"xG-%&FloatG6$\"\"'!\"\"/F$\"\"!" }{TEXT
-1 6 ", and " }{XPPEDIT 18 0 "x = 1.6" "6#/%\"xG-%&FloatG6$\"#;!\"\""
}{TEXT -1 5 ". " }}{PARA 0 "" 0 "" {TEXT 264 5 "Note:" }{TEXT -1
58 " If we raised the left hand side of the equation by 1 to " }
{XPPEDIT 18 0 "x^3-x" "6#,&*$%\"xG\"\"$\"\"\"F%!\"\"" }{TEXT -1 95 ", \+
we can see that two of the solutions disappear. (Actually, they beco
me complex. See below)" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 261 9 "Exer
cise:" }{TEXT -1 24 " Solve the equation " }{XPPEDIT 18 0 "2*x + 1
" "6#,&*&\"\"#\"\"\"%\"xGF&F&F&F&" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "x
^3 - 1" "6#,&*$%\"xG\"\"$\"\"\"F'!\"\"" }{TEXT -1 58 " by plotting bo
th sides of the equation on the same axes." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "
" {TEXT -1 0 "" }{TEXT 287 10 "3. Solving" }{TEXT -1 24 " equations al
gebraically" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 356 "With a graphing ca
lculator, you can solve equations graphically. For more accuracy, yo
u can use the algera you know to try and get x by itself on one side o
f the equation. (This particular equation is easily solved by hand wi
th pencil and paper.) These kinds of manipulations of the equations ca
n be carried out in a Maple worksheet. A word to use is " }{TEXT
262 5 "solve" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 29 "sol :=solve(x^3-x-1=x^2-1,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT
-1 128 "So, we see that there are three solutions to the equation. W
e can convert the third one to a decimal approximation with evalf " }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(sol[3]);" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT
-1 44 "Note that if we were to lower the parabola " }{XPPEDIT 18 0 "x
^2-1" "6#,&*$%\"xG\"\"#\"\"\"F'!\"\"" }{TEXT -1 18 " down one unit to \+
" }{XPPEDIT 18 0 "x^2-2;" "6#,&*$%\"xG\"\"#\"\"\"F&!\"\"" }{TEXT -1
117 ", we can see the resulting equation would only have one real solu
tion. The other two solutions are complex numbers." }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 25 "solve(x^3-x-11=x^2-.2,x);" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT
263 9 "Exercise." }{TEXT -1 24 " Solve the equation " }{XPPEDIT
18 0 "2*x + 1" "6#,&*&\"\"#\"\"\"%\"xGF&F&F&F&" }{TEXT -1 3 " = " }
{XPPEDIT 18 0 "x^3 - 1" "6#,&*$%\"xG\"\"$\"\"\"F'!\"\"" }{TEXT -1 119
" by using the Maple word solve. (To get the solutions in decimal fo
rm, make at least one of the coefficients decimal." }}}{EXCHG {PARA 0
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 288 19 "4. Naming and Using" }
{TEXT 289 39 " expression sequences, sets, and lists." }{TEXT -1 0 ""
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 113 " It is important to distinguish
between three ways to input data into a Maple input line. Each way h
as its uses." }}{PARA 0 "" 0 "" {TEXT -1 3 "An " }{TEXT 265 19 "expres
sion sequence" }{TEXT -1 63 " is a comma separated sequence of express
ions. So for example " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "(
a+b)^2, 2*x^2-2, 4^10, 2*(x^2-1) ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT
-1 202 "is an expression sequence. It has four things in it. We ca
n give a name to the expression sequence so that we can refer to it la
ter without having to type it in again. We'll call our sequence bill.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "bill :=(a+b)^2, 2*x^2-2
, 4^10, 2*(x^2-1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "We can ref
er to terms in the sequence by using indices, so bill[2] refers to th
e second term in the sequence." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 8 "bill[2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 56 "If
you want to treat it as a single object, you can put " }{TEXT 267 15
"square brackets" }{TEXT -1 29 " around it. This is called a " }{TEXT
266 4 "list" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
36 "[(a+b)^2, 2*x^2-2, 4^10, 2*(x^2-1)];" }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 41 "If you enclose an expression sequence in " }{TEXT 268 17
"curley brackets, " }{TEXT -1 125 " the result is called a set. Dupli
cates are removed from a set and the order of the terms in a set may g
et changed by Maple." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "\{(
a+b)^2, 2*x^2-2, 4^10, 2*(x^2-1)\};" }}}{EXCHG {PARA 0 "" 0 "" {TEXT
-1 179 "You can name lists and sets, just like you can an expression s
equence. In fact, you can give a name to almost any Maple output and \+
use that to refer to it later in the worksheet." }}{PARA 0 "" 0 ""
{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 112 "Exercise: Give a nam
e to list above and then multiply the first term in the list by the la
st term in the list." }{TEXT 277 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 290 8 "5. Using" }{TEXT 291
20 " online Maple help. " }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 152 "There is extensive online help available in Maple, which
you can use to expand and refresh your knowledge. For example, if yo
u forget the syntax for a " }}{PARA 0 "" 0 "" {TEXT -1 226 "Maple word
, like plot, you can highlight the word plot and click on Help at the
top of Maple. Then click on Help for plot. A page will come up. Do
wn at the bottom are examples of how plot is used. Often that is enou
gh. " }}{PARA 0 "" 0 "" {TEXT -1 179 "To make a systematic investiga
tion of Maple, you can use the help glossary. This gives you access t
o an orgainization tree of the various words and packages of words in \+
Maple. " }}{PARA 256 "" 0 "" {TEXT -1 33 "Exercise: How is the Mapl
e word " }{TEXT 269 6 "expand" }{TEXT -1 7 " used?." }}}{EXCHG {PARA
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 52 "Exerc
ise: What is a package and how do you use one?" }}}{EXCHG {PARA 0 ""
0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 292 8 "6. Using"
}{TEXT 293 42 " the plots, plottools and MCtools packages" }{TEXT -1
0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 288 "The plots, plottools, and \+
MCtools packages all contain Maple words which are used to draw diagra
ms containing lines, circles, polygons, spheres, etc. Anytime we want
to include a diagram in the statement of a WHS problem, we will use o
ne or more words from one or more of these packages." }}{PARA 0 "" 0 "
" {TEXT 276 7 "Example" }{TEXT -1 55 ": Make a diagram of a square wi
th an inscribed circle." }}{PARA 0 "" 0 "" {TEXT -1 221 "Solution. Th
ere are many ways to do this in Maple. Here is one. We draw (using t
he word polygon in plottools) the square with vertices [0,0], [1,0], \+
[1,1], and [0,1]. Give it a name so that we can refer to it later. "
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "sq := plottools[polygon](
[[0,0],[1,0],[1,1],[0,1]],color=grey);" }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 57 "Then draw the inscribed circle (using disk in plottools).
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "circ := plottools[disk]
([.5,.5],.5,color=yellow):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 204 "No
w use plots[display] to put both of these objects on the same graph. \+
Note the choice of options scaling = contained (that means draw to sc
ale) and axes = none (that means don't show the x and y axes)." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plots[display](circ,sq,scali
ng=constrained,axes=none);" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 131 "
Exercise. Using the help page for plots[textplot], put a label in th
e center of the circle saying \"yellow circle in grey square\"." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 362 "The plots and plottools packages \+
come with Maple. The MCtools package was written at UK specifically t
o help create WHS homework. It has several words to aid in drawing an
d labelling diagrams, plus some words to aid with formatting a problem
for WHS. You will usually find a version at the top of any Maple wo
rksheet which is the source of a WHS homework. " }}{PARA 0 "" 0 ""
{TEXT -1 230 "The procedure to use MCtools is to open the section whic
h contains it and execute the cell containing MCtools, then close the \+
section. MCtools help is different too. A list of the word in the \+
package is available by executing " }{TEXT 278 12 " mctools(); " }
{TEXT -1 18 " in an input cell." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "mctools();" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 259 "
Several of the graphing word in MCtools are written to simplify the us
e of some corresponding word in plots or plottools. For example, PT m
eans Put Text and replaces plots[textplot]. So we could add the labe
l in the above exercise with PT. Get the syntax." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 12 "mctools(PT);" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "plots[d
isplay](circ,sq,PT([.5,.5],\"yellow circle in gray square\"),\n scalin
g=constrained,axes=none);" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 279 9 "Ex
ercise:" }{TEXT -1 165 " Subdivide the square into 4 subsquares and p
ut inscribed circles into each of those squares. Use PC, Put Circle
, from the MCtools package to draw the circles. " }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0
"" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 20 "Answers to exercises" }}
{EXCHG {PARA 256 "" 0 "" {TEXT 270 9 "Exercise:" }{TEXT -1 20 " Type
the number " }{XPPEDIT 18 0 "sin(5/7*Pi) + sqrt(2)" "6#,&-%$sinG6#*(
\"\"&\"\"\"\"\"(!\"\"%#PiGF)F)-%%sqrtG6#\"\"#F)" }{TEXT -1 145 " into \+
an input cell. End the line with a semicolon. Put the cursor anywher
e in the line and press return. Then convert it to a decimal number.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "sin(5/7*Pi)+sqrt(2);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalf(sin(5/7*Pi)+sqrt(2))
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "
" 0 "" {TEXT 271 9 "Exercise." }{TEXT -1 24 " Solve the equation \+
" }{XPPEDIT 18 0 "2*x + 1" "6#,&*&\"\"#\"\"\"%\"xGF&F&F&F&" }{TEXT -1
3 " = " }{XPPEDIT 18 0 "x^3 - 1" "6#,&*$%\"xG\"\"$\"\"\"F'!\"\"" }
{TEXT -1 58 " by plotting both sides of the equation on the same axes
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(\{2*x+1,x^3-1\},x
=-2..2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 317 "By inspection, we se
e that the equation only has one real solution, approximately x = 1.78
(See this by putting your curson on the crossing point on the graph,
clicking the left mouse button, and reading the approximate coordinat
es of the crossing point in the line just above the upper left corner \+
of the worksheet." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(2*x+1=x^3-1,x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "" 0 "
" {TEXT 272 9 "Exercise." }{TEXT -1 24 " Solve the equation " }
{XPPEDIT 18 0 "2*x + 1" "6#,&*&\"\"#\"\"\"%\"xGF&F&F&F&" }{TEXT -1 3 "
= " }{XPPEDIT 18 0 "x^3 - 1" "6#,&*$%\"xG\"\"$\"\"\"F'!\"\"" }{TEXT
-1 119 " by using the Maple word solve. (To get the solutions in dec
imal form, make at least one of the coefficients decimal." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solv
e(2*x+1 = x^3-1.,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "So, we se
e one real solution at x=1.77 approximately, and two complex solutions
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "
" 0 "" {TEXT -1 112 "Exercise: Give a name to list above and then mu
ltiply the first term in the list by the last term in the list." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 43 "sam := [(a+b)^2, 2*x^2-2, 4^10, 2*(x^2-1)];" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 14 "sam[1]*sam[4];" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 22 "expand(sam[1]*sam[4]);" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 33 "Exercise: \+
How is the Maple word " }{TEXT 273 6 "expand" }{TEXT -1 7 " used?." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 323 "Highligh
t the word and click on Help. Then click Help on expand. A page come
s up. Go to the bottom and skim the examples to see the usage. If y
ou have any further questions, you can read the descriptive text at th
e top of the help sheet. We see that expand can be used to multiply o
ut polynomials, among other things." }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 37 " p := x^2 + 3; q := 3*x^4 -x +1; p*q;" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "expand(p*q);" }}}{EXCHG {PARA 256 "
" 0 "" {TEXT -1 52 "Exercise: What is a package and how do you use on
e?" }}{PARA 0 "" 0 "" {TEXT -1 139 "Highlight the word and click on He
lp, then on Help on package. You are given two choice. Choose the in
dex of packages. Then click on the " }{TEXT 275 13 "plots package" }
{TEXT -1 71 ". There are lots of words in this package. One you will
use later is " }{TEXT 274 10 "display. " }{TEXT -1 169 " This is us
ed to display several drawings in the same picture. Another word word
in plots is textplot, which is used to put labels on drawings. See \+
the next section." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 15 "?plots[display]" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1
0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 131 "Exercise. Using the h
elp page for plots[textplot], put a label in the center of the circle \+
saying \"yellow circle in grey square\"." }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 106 "Using the syntax as desc
ribed in the examples, create the label, name it, and add the name to \+
the display." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "labl := plo
ts[textplot]([.5,.5,\"yellow circle in grey square\"]):" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "sq := plottools[polygon]([[0,0],[1,
0],[1,1],[0,1]],color=grey);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 49 "circ := plottools[disk]([.5,.5],.5,color=yellow):" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plots[display](labl,circ,sq,scaling
=constrained,axes=none);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256
"" 0 "" {TEXT 280 9 "Exercise:" }{TEXT -1 164 " Subdivide the square \+
into 4 subsquares and put inscribed circles into each of those squares
. Use PC, Put Circle, from the MCtools package to draw the circles
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 291 "sq1 := plottools[poly
gon]([[0,0],[1/2,0],[1/2,1/2],[0,1/2]],color=grey):\nsq2 := plottools[
polygon]([[0,1/2],[1/2,1/2],[1/2,1],[0,1]],color=red):\nsq3 := plottoo
ls[polygon]([[1/2,0],[1,0],[1,1/2],[1/2,1/2]],color=blue):\nsq4 := plo
ttools[polygon]([[1/2,1/2],[1,1/2],[1,1],[1/2,1]],color=green):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "circ1 := PC([.25,.25],.25,c
olor=yellow):\ncirc2 := PC([.25,.75],.25,color=magenta):\ncirc3 := PC(
[.75,.25],.25,color=turquoise):\ncirc4 := PC([.75,.75],.25,color=pink)
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 76 "plots[display](circ1,circ2,circ3,circ4,sq1,sq2
,sq3,sq4,scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 91
"Now if we were to use the disk word from plottools, we could color th
e inside of the circle" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 217 "
circ1 := plottools[disk]([.25,.25],.25,color=yellow):\ncirc2 := plotto
ols[disk]([.25,.75],.25,color=magenta):\ncirc3 := plottools[disk]([.75
,.25],.25,color=turquoise):\ncirc4 := plottools[disk]([.75,.75],.25,co
lor=pink):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "plots[display
](circ1,circ2,circ3,circ4,sq1,sq2,sq3,sq4,scaling=constrained);" }}}}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 49 "Using Maple while making up and s
olving problems " }}{EXCHG {PARA 0 "" 0 "" {TEXT 315 0 "" }{TEXT -1
502 "We are all acustomed to writing, thinking, and working on paper, \+
and will continue to do that. Being teachers, we can also add the bla
ckboard work to the list of media we feel comfortable working and thin
king with. Increasingly, we adding the monitor screen and keyboard t
o this list. The Maple worksheet provides a 'paper-like' place to wor
k on mathematics problems, make calculations, draw diagrams, and write
textual materials in a way that can be saved and retrieved later for \+
further work. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 ""
{TEXT 310 8 "Starting" }{TEXT 316 25 " with a familiar problem." }
{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 113 "To illustrate how you m
ight use Maple to work on mathematics, lets take a familiar problem as
the starting point." }}{PARA 256 "" 0 "" {TEXT 321 8 "Problem." }
{TEXT -1 187 " Bill mows a yard in 3 hours. Jim can mow the same ya
rd in 2 hours. How long does it take them to mow it together? (Assum
e they do not slow each other down, when they work together.)" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 311 7 "Setting"
}{TEXT 317 33 " up the equation for the problem." }{TEXT -1 2 " " }}
{PARA 0 "" 0 "" {TEXT -1 89 "Let x be the length of time it takes when
they mow together. Then in 1 hour, they mow " }{XPPEDIT 18 0 "1/x \+
" "6#*&\"\"\"F$%\"xG!\"\"" }{TEXT -1 28 " of the yard. Now Bill mows \+
" }{XPPEDIT 18 0 " 1/3 " "6#*&\"\"\"F$\"\"$!\"\"" }{TEXT -1 37 " of th
e yard in an hour and Jim mows " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"
\"#!\"\"" }{TEXT -1 36 " of the yard. So the equation is " }
{XPPEDIT 18 0 "1/x = 1/3 + 1/2" "6#/*&\"\"\"F%%\"xG!\"\",&*&F%F%\"\"$F
'F%*&F%F%\"\"#F'F%" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "5/6" "6#*&\"\"&
\"\"\"\"\"'!\"\"" }{TEXT -1 47 " Taking reciprocals of both sides
, we get " }{XPPEDIT 18 0 "x = 6/5" "6#/%\"xG*&\"\"'\"\"\"\"\"&!\"\""
}{TEXT -1 20 " = 1.2 hours log(3)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 256 "" 0 "" {TEXT 329 30 "Exercise on inline formatting." }
{TEXT -1 221 " When you type a mathematical expression into a text \+
cell, you use calculator syntax. You can convert this to a typeset e
xpression by painting the expression with your mouse cursor, then usi
ng the mouse to open the " }{TEXT 326 6 "Format" }{TEXT -1 51 " menu o
n the top line of Maple, then selecting the " }{TEXT 327 11 "Convert t
o " }{TEXT -1 53 "item (at the bottom of the menu), then selecting the
" }{TEXT 328 13 "Standard Math" }{TEXT -1 204 " item in the menu that
opens up. It sounds a little involved, and it is tedious, but it is \+
important to be able to do it. Use the procedure to format the mathem
atical expressions in the next two lines." }}{PARA 0 "" 0 "" {TEXT
-1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 110 "1 Pythagoras' theorem says \+
that in a right triangle with legs a and b, and hypotenuse c, c^2 = a
^2 + b^2. " }}{PARA 256 "" 0 "" {TEXT -1 113 "2 The sum of the recip
rocals of x and y would be written 1/x + 1/y, the reciprocal of t
hat is 1/(1/x +1/y)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 312 5 "Using" }
{TEXT 318 72 " the algebraic manipulation vocabulary in Maple to solve
your equations." }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 45 " We \+
can also use Maple to solve the equation." }}{PARA 0 "" 0 "" {TEXT -1
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "eq := 1/x = 1/3+1/2;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/*&\"\"\"F'%\"xG!\"\"#\"\"&
\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "solve(eq" }{TEXT
-1 0 "" }{MPLTEXT 1 0 4 ",x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"
'\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 313 5 "Using" }{TEXT
319 62 " text cells to record your notes and comments on the solution.
" }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 240 "It is very handy fe
ature to have. To be able to record notes and comments in the same pl
ace you make computations works well. You can turn an empty input ce
ll into a text cell by placing the cursor in it and pressing the F5 fu
nction key " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT
314 9 "Modifying" }{TEXT 320 63 " the problem to a parameterized probl
em or to a related problem" }{TEXT -1 3 ". " }}{PARA 0 "" 0 "" {TEXT
-1 2 "A " }{TEXT 335 9 "parameter" }{TEXT -1 72 " is a quantity which \+
is regarded as known but unspecified in a problem. " }}{PARA 0 "" 0 "
" {TEXT -1 135 "We can parameterize this problem by replacing the numb
ers in the problem with parameters and then solving in terms of the pa
rameters. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 ""
{TEXT 322 22 "Parameterized Problem." }{TEXT -1 118 " Bill mows a ya
rd in A hours. Jim can mow the same yard in B hours. How long does i
t take them to mow it together?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 323 9 "Solution." }{TEXT -1 93 " As before let
x be the time needed when both are working together. In one hour, Bil
l mows " }{XPPEDIT 18 0 "1/A" "6#*&\"\"\"F$%\"AG!\"\"" }{TEXT -1 26 " \+
of the yard and Jim mows " }{XPPEDIT 18 0 "1/B" "6#*&\"\"\"F$%\"BG!\"
\"" }{TEXT -1 39 " of the yard. Together, they would mow " }{XPPEDIT
18 0 "1/x = 1/A + 1/B" "6#/*&\"\"\"F%%\"xG!\"\",&*&F%F%%\"AGF'F%*&F%F%
%\"BGF'F%" }{TEXT -1 38 " of the yard. Solving for x, we get " }
{XPPEDIT 18 0 "x = 1/(1/A+1/B)" "6#/%\"xG*&\"\"\"F&,&*&F&F&%\"AG!\"\"F
&*&F&F&%\"BGF*F&F*" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "(A*B)/(A+B)" "6#
*(%\"AG\"\"\"%\"BGF%,&F$F%F&F%!\"\"" }}{PARA 0 "" 0 "" {TEXT -1 33 "Ch
ecking the solution with Maple," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 22 "eq := 1/x = 1/A + 1/B;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e
qG/*&\"\"\"F'%\"xG!\"\",&*&F'F'%\"AGF)F'*&F'F'%\"BGF)F'" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "solve(eq,x);" }}{PARA 11 "" 1 ""
{XPPMATH 20 "6#*(%\"AG\"\"\"%\"BGF%,&F&F%F$F%!\"\"" }}}{EXCHG {PARA
256 "" 0 "" {TEXT -1 209 "Exercise. Work this related problem. \"Bi
ll mows a yard in 5 hours. Together Bill and Jim can mow the yard in \+
2 hours. How long does it take Jim to mow it?\" Then parameterize t
he problem and rework it. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 364 "We nee
d to develop strategies for checking our work. For example, one good
check is to work the problem using a different tool. So doing the pr
oblem with pencil and paper, and then using Maple to resolve the equat
ion will sometimes expose errors. In geometric problems, drawing a s
cale picture can serve as a visual check to a computation. Here's an \+
example." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT
-1 104 "Problem. Find the area of the circle inscribed in an isoscel
es right triangle with a hypotenuse of 10." }}{PARA 0 "" 0 "" {TEXT
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 324 17 "Solution outline." }{TEXT -1
98 " We need to find the radius of the inscribed circle. Call it R. \+
The the area of the circle is " }{XPPEDIT 18 0 "Pi*R^2" "6#*&%#PiG\"
\"\"*$%\"RG\"\"#F%" }{TEXT -1 45 ". So lets find an equation in R to s
olve. " }{TEXT 325 35 "We can make a rough sketch on paper" }{TEXT
-1 263 " of the triangle and its inscribed circle to help us with our \+
thoughts. The circle touches the hypotenuse at the midpoint (why?). \+
Using this fact and two congruent triangles (which ones?), we can writ
e two expression for the length of a leg of the triangle: " }
{XPPEDIT 18 0 "sqrt(50)=R+5" "6#/-%%sqrtG6#\"#],&%\"RG\"\"\"\"\"&F*" }
{TEXT -1 22 ". Solve for R to get " }{XPPEDIT 18 0 "R = sqrt(50)-5" "
6#/%\"RG,&-%%sqrtG6#\"#]\"\"\"\"\"&!\"\"" }{TEXT -1 20 " . So the are
a is " }{XPPEDIT 18 0 "Pi*(sqrt(50)-5);" "6#*&%#PiG\"\"\",&-%%sqrtG6#
\"#]F%\"\"&!\"\"F%" }{TEXT -1 44 ". We can this to a decimal approxi
mation, " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "R:=evalf(sqrt(5
0)-5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG$\"+5y1r?!\"*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Area := evalf(Pi*R^2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%AreaG$\"+4-`Z8!\")" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 223 "Now, we can draw a scale diagram to che
ck our work. First draw the triangle. We can situate it in the coordi
nate plane so that the vertex opposite the hypotenuse is at the origin
[0,0], and the other two vertices are at [" }{XPPEDIT 18 0 "sqrt(50)
" "6#-%%sqrtG6#\"#]" }{TEXT -1 11 ",0] and [0," }{XPPEDIT 18 0 "sqrt(5
0)" "6#-%%sqrtG6#\"#]" }{TEXT -1 132 "]. So, now we use the plottoo
ls and plots package words to draw and name the triangle and the circl
e, then display them together." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 75 "tri := plottools[polygon]([[0,0],[sqrt(50),0],[0,sqrt(50)]],co
lor=yellow): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "circ := pl
ottools[disk]([R,R],R,color=turquoise):" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 45 "plots[display](circ,tri,scaling=constrained);" }}
{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%)POLYGONSG6$7U
7$$\"+?c8UT!\"*$\"+5y1r?F*7$$\"+KY!e7%F*$\"+O9kIBF*7$$\"+;#pq2%F*$\"+I
97'e#F*7$$\"+gzp'*RF*$\"+@(yM$GF*7$$\"+n$ef)QF*$\"+PB\")oIF*7$$\"+lofY
PF*$\"+D4T)G$F*7$$\"+p7\"3e$F*$\"+'G6))[$F*7$$\"+;h@\"R$F*$\"+&)H&om$F
*7$$\"+P9!3=$F*$\"+(>G(>QF*7$$\"+&f&)G&HF*$\"+#*f-XRF*7$$\"+fH16FF*$\"
+Z.xSSF*7$$\"+=s9fCF*$\"+:8X0TF*7$$\"+L76,AF*$\"+T)[!QTF*7$$\"+'QC5%>F
*Fao7$$\"+,%))Ho\"F*F\\o7$$\"+hE2J9F*$\"+Y.xSSF*7$$\"+E+D*=\"F*FX7$$\"
*%=M8'*F*$\"+)>G(>QF*7$$\"*/&>4vF*FN7$$\"*\\VKh&F*$\"+%G6))[$F*7$$\"*a
(QbRF*$\"+B4T)G$F*7$$\"*_s9gb\"F*7$$\"*gwVX\"F*$\"+**ol38F*7
$$\"*`s4vF*$\"*MEGv%F*7$$\"*&=M8'*F*$\"*@uSA$F*7$$\"+F+D*=\"F*$
\"*F'4r>F*7$$\"+iE2J9F*$\"*t_O,\"F*7$$\"+.%))Ho\"F*$\")/VoOF*7$$\"+)QC
5%>F*$\"(zn3%F*7$$\"+N76,AF*Fdv7$$\"+?s9fCF*$\")0VoOF*7$$\"+gH16FF*$\"
*u_O,\"F*7$FV$\"*G'4r>F*7$FQ$\"*AuSA$F*7$FL$\"*NEGv%F*7$$\"+r7\"3e$F*$
\"*PVK`'F*7$$\"+nofYPF*$\"*(pCP&)F*7$$\"+o$ef)QF*$\"+'GBL2\"F*7$$\"+hz
p'*RF*$\"+,pl38F*7$$\"+<#pq2%F*$\"+#>9gb\"F*7$F.$\"+'=%\\6=F*7$F($\"+7
y1r?F*-%'COLOURG6&%$RGBG$\")PJ%y'!\")$\")1Zw\"*FazFbz-F$6$7%7$FhrFhr7$
$\"+5y1rqF*Fhr7$FhrFiz-F\\z6&F^z$\"*++++\"FazF^[lFhr-%(SCALINGG6#%,CON
STRAINEDG" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Cu
rve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "The visual ev
idence is sufficient to convince me of the correctness of my method."
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 12 "Exerc
ises. " }}{PARA 256 "" 0 "" {TEXT -1 37 "1 Change the colors of the
diagram." }}{PARA 256 "" 0 "" {TEXT -1 64 "2. Change the location of
the triangle in the coordinate plane." }}{PARA 256 "" 0 "" {TEXT -1
83 "3. Interchange the order of tri and circ in the display line. Wh
at is the effect?" }}{PARA 256 "" 0 "" {TEXT -1 86 "4. In the display
line, remove the option scaling = constrained. What is the effect?"
}}{PARA 256 "" 0 "" {TEXT -1 128 "5. Get the help page on plot[option
s] and find out how to remove the axes from the diagram. (Hint: look \+
at the second option.)" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 20 "answer
s to exercises" }}{EXCHG {PARA 256 "" 0 "" {TEXT 333 30 "Exercise on i
nline formatting." }{TEXT -1 221 " When you type a mathematical exp
ression into a text cell, you use calculator syntax. You can convert
this to a typeset expression by painting the expression with your mo
use cursor, then using the mouse to open the " }{TEXT 330 6 "Format" }
{TEXT -1 51 " menu on the top line of Maple, then selecting the " }
{TEXT 331 11 "Convert to " }{TEXT -1 53 "item (at the bottom of the me
nu), then selecting the " }{TEXT 332 13 "Standard Math" }{TEXT -1 204
" item in the menu that opens up. It sounds a little involved, and it
is tedious, but it is important to be able to do it. Use the procedu
re to format the mathematical expressions in the next two lines." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 92 "1 Pytha
ngoras' theorem says that in a right triangle with legs a and b, and \+
hypotenuse c, " }{XPPEDIT 18 0 "c^2 = a^2 + b^2" "6#/*$%\"cG\"\"#,&*$
%\"aGF&\"\"\"*$%\"bGF&F*" }{TEXT -1 4 ". " }}{PARA 256 "" 0 ""
{TEXT -1 61 "2 The sum of the reciprocals of x and y would be writte
n " }{XPPEDIT 18 0 "1/x + 1/y" "6#,&*&\"\"\"F%%\"xG!\"\"F%*&F%F%%\"y
GF'F%" }{TEXT -1 30 ", the reciprocal of that is " }{XPPEDIT 18 0 "1
/(1/x +1/y)" "6#*&\"\"\"F$,&*&F$F$%\"xG!\"\"F$*&F$F$%\"yGF(F$F(" }
{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 ""
{TEXT -1 209 "Exercise. Work this similar problem. \"Bill mows a ya
rd in 5 hours. Together Bill and Jim can mow the yard in 2 hours. Ho
w long does it take Jim to mow it?\" Then parameterize the problem a
nd rework it. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 ""
{TEXT 334 8 "Solution" }{TEXT -1 116 ". Here in the parameterized p
robleme problem we could replace 5 with A and 2 with B. Then the equa
tion would be " }{XPPEDIT 18 0 "1/x = 1/B-1/A;" "6#/*&\"\"\"F%%\"xG!\"
\",&*&F%F%%\"BGF'F%*&F%F%%\"AGF'F'" }{TEXT -1 24 ". Solve for x to g
et " }{XPPEDIT 18 0 "x = 1/(1/B-1/A);" "6#/%\"xG*&\"\"\"F&,&*&F&F&%\"
BG!\"\"F&*&F&F&%\"AGF*F*F*" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "A*B/(A-B
);" "6#*(%\"AG\"\"\"%\"BGF%,&F$F%F&!\"\"F(" }{TEXT -1 110 ". So now,
the solution to the specific instance of the problem with A = 5 and B
= 2 is 10/3 =3.33 hours " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 15 "We can make an " }{TEXT 337 5 "arrow" }
{TEXT -1 1 " " }{TEXT 336 8 "function" }{TEXT -1 57 " here. (Get the \+
help page for -> to see more examples) " }}{PARA 0 "" 0 "" {TEXT -1
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f := (A,B) -> A*B/(A
-B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"AG%\"BG6\"6$%)ope
ratorG%&arrowGF)*(9$\"\"\"9%F/,&F.F/F0!\"\"F2F)F)F)" }}}{EXCHG {PARA
0 "" 0 "" {TEXT -1 111 "Now to get the value of x for any values of A \+
and B (with A > B > 0), just call the function with those values " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "f(5.,2);" }}{PARA 11 "" 1 ""
{XPPMATH 20 "6#$\"+LLLLL!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 ""
{TEXT -1 12 "Exercises. " }}{PARA 256 "" 0 "" {TEXT -1 37 "1 Change
the colors of the diagram." }}{PARA 0 "" 0 "" {TEXT -1 62 " I like
magenta and grey. (You may have other preferences)" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "tri := pl
ottools[polygon]([[0,0],[sqrt(50),0],[0,sqrt(50)]],color=magenta): " }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "circ := plottools[disk]([R
,R],R,color=grey):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "plots
[display](circ,tri,scaling=constrained);" }}{PARA 13 "" 1 ""
{GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%)POLYGONSG6$7U7$$\"+?c8UT!\"*$
\"+5y1r?F*7$$\"+KY!e7%F*$\"+O9kIBF*7$$\"+;#pq2%F*$\"+I97'e#F*7$$\"+gzp
'*RF*$\"+@(yM$GF*7$$\"+n$ef)QF*$\"+PB\")oIF*7$$\"+lofYPF*$\"+D4T)G$F*7
$$\"+p7\"3e$F*$\"+'G6))[$F*7$$\"+;h@\"R$F*$\"+&)H&om$F*7$$\"+P9!3=$F*$
\"+(>G(>QF*7$$\"+&f&)G&HF*$\"+#*f-XRF*7$$\"+fH16FF*$\"+Z.xSSF*7$$\"+=s
9fCF*$\"+:8X0TF*7$$\"+L76,AF*$\"+T)[!QTF*7$$\"+'QC5%>F*Fao7$$\"+,%))Ho
\"F*F\\o7$$\"+hE2J9F*$\"+Y.xSSF*7$$\"+E+D*=\"F*FX7$$\"*%=M8'*F*$\"+)>G
(>QF*7$$\"*/&>4vF*FN7$$\"*\\VKh&F*$\"+%G6))[$F*7$$\"*a(QbRF*$\"+B4T)G$
F*7$$\"*_s9gb\"F*7$$\"*gwVX\"F*$\"+**ol38F*7$$\"*`s4vF
*$\"*MEGv%F*7$$\"*&=M8'*F*$\"*@uSA$F*7$$\"+F+D*=\"F*$\"*F'4r>F*7$$\"+i
E2J9F*$\"*t_O,\"F*7$$\"+.%))Ho\"F*$\")/VoOF*7$$\"+)QC5%>F*$\"(zn3%F*7$
$\"+N76,AF*Fdv7$$\"+?s9fCF*$\")0VoOF*7$$\"+gH16FF*$\"*u_O,\"F*7$FV$\"*
G'4r>F*7$FQ$\"*AuSA$F*7$FL$\"*NEGv%F*7$$\"+r7\"3e$F*$\"*PVK`'F*7$$\"+n
ofYPF*$\"*(pCP&)F*7$$\"+o$ef)QF*$\"+'GBL2\"F*7$$\"+hzp'*RF*$\"+,pl38F*
7$$\"+<#pq2%F*$\"+#>9gb\"F*7$F.$\"+'=%\\6=F*7$F($\"+7y1r?F*-%'COLOURG6
&%$RGBG$\")=THv!\")F_zF_z-F$6$7%7$FhrFhr7$$\"+5y1rqF*Fhr7$FhrFgz-F\\z6
&F^z$\"*++++\"FazFhrF\\[l-%(SCALINGG6#%,CONSTRAINEDG" 1 2 0 1 10 0 2
9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 130 "You can make a function here too.
This is a more complicated function, so we would use the word proc \+
to define the function. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
207 "pic := proc(clr1,clr2)\nlocal tri,circ;\ntri := plottools[polygon
]([[0,0],[sqrt(50),0],[0,sqrt(50)]],color=clr1): circ := plottools[dis
k]([R,R],R,color=clr2):\nplots[display](circ,tri,scaling=constrained);
\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "pic(blue,red); "
}}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%)POLYGONSG6$
7U7$$\"+?c8UT!\"*$\"+5y1r?F*7$$\"+KY!e7%F*$\"+O9kIBF*7$$\"+;#pq2%F*$\"
+I97'e#F*7$$\"+gzp'*RF*$\"+@(yM$GF*7$$\"+n$ef)QF*$\"+PB\")oIF*7$$\"+lo
fYPF*$\"+D4T)G$F*7$$\"+p7\"3e$F*$\"+'G6))[$F*7$$\"+;h@\"R$F*$\"+&)H&om
$F*7$$\"+P9!3=$F*$\"+(>G(>QF*7$$\"+&f&)G&HF*$\"+#*f-XRF*7$$\"+fH16FF*$
\"+Z.xSSF*7$$\"+=s9fCF*$\"+:8X0TF*7$$\"+L76,AF*$\"+T)[!QTF*7$$\"+'QC5%
>F*Fao7$$\"+,%))Ho\"F*F\\o7$$\"+hE2J9F*$\"+Y.xSSF*7$$\"+E+D*=\"F*FX7$$
\"*%=M8'*F*$\"+)>G(>QF*7$$\"*/&>4vF*FN7$$\"*\\VKh&F*$\"+%G6))[$F*7$$\"
*a(QbRF*$\"+B4T)G$F*7$$\"*_s9gb\"F*7$$\"*gwVX\"F*$\"+**ol38F
*7$$\"*`s4vF*$\"*MEGv%F*7$$\"*&=M8'*F*$\"*@uSA$F*7$$\"+F+D*=\"F*
$\"*F'4r>F*7$$\"+iE2J9F*$\"*t_O,\"F*7$$\"+.%))Ho\"F*$\")/VoOF*7$$\"+)Q
C5%>F*$\"(zn3%F*7$$\"+N76,AF*Fdv7$$\"+?s9fCF*$\")0VoOF*7$$\"+gH16FF*$
\"*u_O,\"F*7$FV$\"*G'4r>F*7$FQ$\"*AuSA$F*7$FL$\"*NEGv%F*7$$\"+r7\"3e$F
*$\"*PVK`'F*7$$\"+nofYPF*$\"*(pCP&)F*7$$\"+o$ef)QF*$\"+'GBL2\"F*7$$\"+
hzp'*RF*$\"+,pl38F*7$$\"+<#pq2%F*$\"+#>9gb\"F*7$F.$\"+'=%\\6=F*7$F($\"
+7y1r?F*-%'COLOURG6&%$RGBG$\"*++++\"!\")FhrFhr-F$6$7%7$FhrFhr7$$\"+5y1
rqF*Fhr7$FhrFgz-F\\z6&F^zFhrFhrF_z-%(SCALINGG6#%,CONSTRAINEDG" 1 2 0
1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2"
}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0
"" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 64 "2. Change the locat
ion of the triangle in the coordinate plane." }}{PARA 0 "" 0 "" {TEXT
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 267 "This is a matter of changing t
he coordinates of the vertices of the triangle and the center of the d
isk. So, if we wanted to flip it about the x axis, the only change wo
uld be to move the point [0,sqrt(50)] to [0,-sqrt(50)], and the cente
r of the circle to [R, -R]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
77 "tri := plottools[polygon]([[0,0],[sqrt(50),0],[0,-sqrt(50)]],color
=magenta): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "circ := plot
tools[disk]([R,-R],R,color=grey):" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 45 "plots[display](circ,tri,scaling=constrained);" }}
{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%)POLYGONSG6$7U
7$$\"+?c8UT!\"*$!+5y1r?F*7$$\"+KY!e7%F*$!+%=%\\6=F*7$$\"+;#pq2%F*$!+!>
9gb\"F*7$$\"+gzp'*RF*$!+**ol38F*7$$\"+n$ef)QF*$!+$GBL2\"F*7$$\"+lofYPF
*$!*&pCP&)F*7$$\"+p7\"3e$F*$!*MVK`'F*7$$\"+;h@\"R$F*$!*NEGv%F*7$$\"+P9
!3=$F*$!*BuSA$F*7$$\"+&f&)G&HF*$!*G'4r>F*7$$\"+fH16FF*$!*t_O,\"F*7$$\"
+=s9fCF*$!)0VoOF*7$$\"+L76,AF*$!(zn3%F*7$$\"+'QC5%>F*Fao7$$\"+,%))Ho\"
F*F\\o7$$\"+hE2J9F*$!*u_O,\"F*7$$\"+E+D*=\"F*FX7$$\"*%=M8'*F*$!*AuSA$F
*7$$\"*/&>4vF*FN7$$\"*\\VKh&F*$!*OVK`'F*7$$\"*a(QbRF*$!*(pCP&)F*7$$\"*
_s9gb\"F*7$
$\")))4L;F*$!+'=%\\6=F*7$$\"\"!Fir$!+6y1r?F*7$Fcr$!+O9kIBF*7$$\")/k1lF
*$!+I97'e#F*7$$\"*gwVX\"F*$!+@(yM$GF*7$$\"*`s4vF*$!+')H&om$F*7$$
\"*&=M8'*F*$!+*>G(>QF*7$$\"+F+D*=\"F*$!+$*f-XRF*7$$\"+iE2J9F*$!+Z.xSSF
*7$$\"+.%))Ho\"F*$!+;8X0TF*7$$\"+)QC5%>F*$!+T)[!QTF*7$$\"+N76,AF*Fdv7$
$\"+?s9fCF*$!+:8X0TF*7$$\"+gH16FF*$!+Y.xSSF*7$FV$!+#*f-XRF*7$FQ$!+)>G(
>QF*7$FL$!+&)H&om$F*7$$\"+r7\"3e$F*$!+$G6))[$F*7$$\"+nofYPF*$!+B4T)G$F
*7$$\"+o$ef)QF*$!+MB\")oIF*7$$\"+hzp'*RF*$!+>(yM$GF*7$$\"+<#pq2%F*$!+G
97'e#F*7$F.$!+M9kIBF*7$F($!+3y1r?F*-%'COLOURG6&%$RGBG$\")=THv!\")F_zF_
z-F$6$7%7$FhrFhr7$$\"+5y1rqF*Fhr7$Fhr$!+5y1rqF*-F\\z6&F^z$\"*++++\"Faz
FhrF^[l-%(SCALINGG6#%,CONSTRAINEDG" 1 2 0 1 10 0 2 9 1 4 1 1.000000
45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 83 "3. Inte
rchange the order of tri and circ in the display line. What is the ef
fect?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 228
"The effect is that you don't see the color of the disk. What display
does is lay down the parts of the picture from right to left. If you
want to see the color of a part, lay it down after you lay down anyth
ing that covers it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0
"" {TEXT -1 86 "4. In the display line, remove the option scaling = c
onstrained. What is the effect?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 319 "The effect is that the circle becomes an
ellipse. Setting the scaling = constrained option forces the same sc
ale to be used on both axes. If you don't set that, Maple chooses se
parate scales so as to make the picture as large as possible. Somethin
g tall and skinny would be stretched out in the horizontal direction.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 128 "5.
Get the help page on plot[options] and find out how to remove the ax
es from the diagram. (Hint: look at the second option.)" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "Set the option ax
es = none in the display line." }}}}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}}{MARK "1" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }