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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 26 "Tips for Maple Instructor
s" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {TEXT -1 269 "P
osted with permission of Robert J. Lopez. Copyright 1996 by Robert J. \+
Lopez. All rights reserved. \n\nThis article has been published in Map
leTech, Vol 3, NO. 2, 1996. \n\nRobert J. Lopez\nDepartment of Mathema
tics\nRose-Hulman Institute of Technology\nTerre Haute, IN 47803 " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 584 "This column is the first in a series dedicated
 to the pedagogy of \"Maple in instruction.\"  I quote that phrase bec
ause as Education Editor, and as a long-time classroom instructor, I r
ealize how intensely personal each teacher's classroom philosophy can \+
be.  Transcending those differences, this column is offered as an aid \+
to all who see advantage in using Maple as part of the instructional e
ffort.  I hope this column becomes a forum where common problems can b
e identified and resolved, where useful hints and strategems can be fo
und, and where pedagogical insights can be shared." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 415 "In this first column, I \+
get to stand on the soapbox and pontificate my own views on the use of
 Maple, and distill my own experiences with Maple in the classroom.  E
ach item I've honed and polished is a result of having made the very w
orst possible errors in the use of Maple with students.  Each rule and
 principle enunciated is an admission that I learned the hard way what
 worked and didn't work in the classroom." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 408 "I urge all readers who have their
 own experiences with Maple in instruction, successes and failures ali
ke, to communicate with me by e-mail (r.lopez@rose-hulman.edu), fax(81
2-877-3198), or letter (Math Dept., Rose-Hulman Institute of Technolog
y, Terre Haute, IN 47803).  As much as possible, I would like this col
umn to address real issues, from real classes.  Only the column's read
ers can make that happen." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 256 21 "Toolbox or Wonderland" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 581 "Before launching stude
nts into the realm of Maple, it behooves the instructor to decide whet
her Maple is a toolbox, or an enveloping environment.  If Maple is a t
oolbox, then it merely takes its place along with pencil and paper, an
d the student adds Maple facility to the traditional skills in mathema
tics.  If, like Alice falling into Wonderland, we enter Maple as into \+
a total new dimension, then Maple becomes the way mathematics is met a
nd mastered.  While each perspective determines how Maple will be used
 in teaching, often resources determine which perspective is adopted.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 705 "If M
aple is a tool to be experienced in a lab setting, then precise and we
ll-crafted exercises and projects are essential.  Students who have un
pleasant experiences with Maple are not likely to enjoy the extra effo
rt it takes to master Maple and still master the pencil and paper skil
ls of the traditional class.  Adequate help in the lab setting is a ne
cessity, and seeing Maple used to solve problems in the lecture is a p
rerequisite.  Students need to see how Maple can be used to explore ma
thematics and to solve problems.  A projection system in the lecture r
oom, with students manning the keyboard, is a good way to foster the a
ttitude that Maple belongs to the students, not just to the instructor
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 947 "If \+
resources permit, Maple can be used in the classroom itself, with stud
ents running their own Maple sessions as part of the lecture experienc
e.  Not only will Maple be available for lectures and assignments, but
 it can be used for tests, also.  Then, skills acquired with Maple can
 replace traditional emphases for doing mathematics.  Maple becomes a \+
tool of first recourse for teaching, learning, and doing mathematics. \+
 This is a different challenge than preparing labs, for now, the instr
uctor has to find new learning activities, Maple-based, that generate \+
insight and understanding.  The instructor has to devise new strategem
s for inductive learning and experimentation, new behaviors that give \+
more initiative to the students.  Anyone who has tried it, finds that \+
as soon as users turn on the computer in a computer class, no two are \+
at the same place after the first seconds have elapsed.  The instructo
r is now more guide than lecturer." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT 257 20 "Operative Philosophy" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 272 "Either of the pe
dagogic perspectives above must be infused with an operational philoso
phy for implementing Maple.  My aphorism is \"simplicity, with one way
 of doing things.\"  I articulate this with Lopez's Little Law, Lopez'
s Large Law, and Corollary One of the Large Law." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 552 "Lopez's Little Law requi
res the student \"assign as few variables as possible.\"  To prevent s
tudents from confusing themselves with an excess of assigned names, an
d from torpedoing themselves by inadvertently using an assigned variab
le as if it weren't assigned, I enunciate the Little Law.  A working s
tyle of keeping x, y, z, and t unassigned, using q, q1, q2, ..., as ta
gs on assigned quantities, computing first and using the GUI to go bac
k and assign tags to desirable outcomes, all form part of a consistent
 implementation of mathematics in Maple." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 803 "Lopez's Large Law dictates \"neve
r put on the left a variable in use on the right.\"  This prohibition \+
against using on the left of an assignment operator (:=) a variable ap
pearing on the right of that, or another assignment operator, is desig
ned to prevent two difficulties.  First, the assignment x := x + 1, pe
rfectly valid in a language like FORTRAN, is a disaster in Maple where
 it causes a recursive call to x that in earlier releases of Maple wou
ld induce an ungraceful crash.  Even though Maple's Release 4 now catc
hes this particular usage, other instances of assigning a variable to \+
a function of itself will not be flagged, but will create confusion fo
r the novice user.  This case warrants the articulation of Corollary O
ne of the Large Law, \"never assign a variable to any version of itsel
f.\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 507 "
For example, if q represents a quantity we want to simplify, the very \+
tempting assignment q := simplify(q) clearly violates the Large Law.  \+
In particular, this assigmnent means that somewhere in the worksheet t
he variable q changes meaning.  If a part of the worksheet containing \+
\"q\" is re-executed, which version of \"q\" is being referenced?  The
 one before the reassignment or the one after?  Hence, an equivalent a
rticulation of Corollary One is \"use distinct labels for each Maple o
utput of consequence.\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 658 "But the more important reason for the Large Law, fo
r prohibiting variables in use \"on the right side\" of assignment ope
rator (:=) from appearing as names (or tags) on the \"left side,\" is \+
to prevent \"working variables\" from becoming \"contaminated\" with a
ssigned values.  Such contamination is the bane of easy experimentatio
n because it forces the user to re-execute lines scattered throughout \+
the worksheet.  Watching a student navigate around a worksheet while t
rying to remember which lines have been, and yet need to be re-execute
d, is a harrowing experience.  The student who passes the threshold of
 frustration or confusion is lost to Maple use forever." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 300 "The objective shoul
d be to prevent students from becoming confused and frustrated with us
ing Maple.  Simple things like using the ditto (\") for referencing th
e chronologically last valid Maple output matter.  I never use the dit
to, and forbid my students to use it by the threat that I will not rea
d " }}{PARA 0 "" 0 "" {TEXT -1 448 "any worksheet containing one.  My \+
goal is to prevent students from creating unreadable worksheets.  The \+
GUI allows all sorts of \"compute and hide\" tricks where variables ar
e assigned, cut from the worksheet, but the assigned values persist.  \+
This makes for unreadable worksheets.  The ditto is a willing ally in \+
creating such havoc, but forbidding the ditto is only a small part of \+
making sure students are not the authors of their own misfortunes." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 270 "Worse th
an the ditto is the inserted line.  Inserting new inputs between old o
nes allows students to craft worksheets unfathomable not only to their
 instructors, but to themselves.  Such inserts are an attraction of a \+
GUI, but the comcomitant dangers must be understood." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 13 "Growing Pains
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 53 "Make \+
a conscious decision how the information from a " }{TEXT 259 5 "solve
" }{TEXT -1 129 " command will be incorporated into the worksheet.  Th
ere are two strategies that work.  First, the students should be taugh
t the " }{TEXT 260 6 "assign" }{TEXT -1 245 " command.  This is to und
erstand, and implement.  The unpleasant side effect is that it require
s a tedious unassigning of all assigned variables.  After students hav
e become reasonably comfortable with Maple, they should be persuaded t
o use the " }{TEXT 261 4 "subs" }{TEXT -1 145 " command.  This is a mo
re powerful and robust approach to the problem of transferring informa
tion from an equation to a variable.  We illustrate." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "q := 3*y \+
= 6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG/,$%\"yG\"\"$\"\"'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "q1 := solve(q,\{y\});" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#q1G<#/%\"yG\"\"#" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 165 "Notice how the
 output of the solve command is a set containing the single equation y
 = 2.  The solve command itself does not cause y to assume the value 2
.  But the " }{TEXT 300 6 "assign" }{TEXT -1 14 " command does." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "assign(q1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 88 "But now we have sullied a
 working variable that has to be unassigned by tediously typing" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 9 "y := 'y';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yGF$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#%\"yG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 192 "This is simple to understand, and the young eyes of my s
tudents don't balk at the extra typing required.  Eventually, however,
 it's more efficient to learn the following substitution strategy." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "Y := subs(q1, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"YG\"\"#
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%\"yG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 340 "By substitution we pass the information in q1,
 namely that y = 2, to an image of y.  The replacement is made in the \+
image, and the resulting value is assigned to the variable Y.  Note ho
w using Y as a stand-in for y avoids violating Lopez's Large Law!  And
 note how that same information about y can be passed to an expression
 containing y." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "subs(q1, sqrt(y));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*$\"\"##\"\"\"F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 32 "My experience has been that the " }
{TEXT 264 4 "plot" }{TEXT -1 2 ", " }{TEXT 265 5 "solve" }{TEXT -1 5 "
 and " }{TEXT 266 6 "assign" }{TEXT -1 129 " commands can be used imme
diately.  The abstraction required to understand the substitution stra
tegy should not be taken lightly." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 262 18 "Conscious Decision" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 143 "Maple distinguishes
 between expressions (formulas) and functions, as has been explored in
 past issues of MapleTech.  In essence, the assignment" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f := 1
+x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&\"\"\"F&*$%\"xG\"\"#F
&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
12 "creates the " }{TEXT 263 10 "expression" }{TEXT -1 1 " " }
{XPPEDIT 18 0 "x^2" "*$%\"xG\"\"#" }{TEXT -1 50 ", not a function.  Ma
ple will not understand f(2)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&\"\"\"F$*$-%\"xG6#\"\"#F)F$" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 322 "That the output is non
sense unfortunately escapes many students.  A student who spends any a
mount of time in a lab struggling with such an unfathomable object wil
l not take long coming to the conclusion that Maple makes math harder.
  You'll know, since that student will show up with a drop slip in han
d pretty soon after." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 121 "The temptation is large to teach students about the wo
nderful implementation that Maple has for true functional notation." }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 18 "F := unapply(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG:6#%
\"xG6\"6$%)operatorG%&arrowGF(,&\"\"\"F-*$9$\"\"#F-F(F(" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "creates a
 mapping named F, whose rule (or formula) is " }{XPPEDIT 18 0 "1+x^2" 
",&\"\"\"\"\"\"*$%\"xG\"\"#F$" }{TEXT -1 152 ".  It is even more tempt
ing to create the function F via Maple's arrow notation, just like in \+
those wonderful math texts we all used in graduate school." }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "F :
= x -> 1 + x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG:6#%\"xG6\"6$
%)operatorG%&arrowGF(,&\"\"\"F-*$9$\"\"#F-F(F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 5 "F(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
254 "It's so realistic!  But is it ever a syntactic burden on the stud
ents.  That's because it violates the rule of simplicity and doing thi
ngs only one way.  The student now has to remember all these things:  \+
expression vs. function, for expressions you use " }{TEXT 267 4 "subs
" }{TEXT -1 74 ", for functions you use parentheses, for expressions p
re-existing you use " }{TEXT 268 7 "unapply" }{TEXT -1 128 ", but for \+
new functions you use arrows.  We haven't yet mentioned how functions \+
and expressions require different syntax in the " }{TEXT 269 4 "plot" 
}{TEXT -1 346 " command and how differentiation of expressions and fun
ctions require different operators.  It's plot(f,x=0..1) for the expre
ssion f, but plot(F,0..1) for the function F.  It's diff(f,x) for the \+
expression f, and D(F) for the function F.  And the predefined name of
 the sine function is sin, but there is no such predefined name for th
e function " }{XPPEDIT 18 0 "x^2" "*$%\"xG\"\"#" }{TEXT -1 159 " or fo
r the constant function x -> 2.  Dealing with these matters takes time
 and energy.  You will definitely spend time explaining syntax and not
 mathematics." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 647 "Pedagogically, we need to make a conscious decision: wil
l we stick to just expressions, or will we introduce both functions an
d expressions.  We should not just drift into a mix of the two.  If fu
nctions are introduced, it should be by design, knowing all the conseq
uences of that choice.  Functional notation can be made to work in the
 Maple classroom, but it does take extra effort on the part of the ins
tructor to guarantee that students learn the special syntax.  The inst
ructor determined to implement functional notation early in a Maple-ba
sed math class will need to spend time explaining the distinctions bet
ween functions and expressions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 270 21 "Maple and the Student" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 426 "Maple typically \+
makes mathematics \"harder\" for the student, but less tedious.  \"Har
der\" means \"more conceptual\" and for many students, that's truly ha
rder.  Maple requires that the student learn syntax.  They do have to \+
learn where the commas go.  But that's actually the easy part.  Studen
ts seem to have least difficulty with learning the thirty or forty com
mands that will will get them through three semesters of calculus." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 405 "It is a \+
bit more difficult for them to acquire consistent and effective \"oper
ational procedures\" for using Maple.  That is why I articulated the L
ittle and Large Laws.  I found that students struggled more with how t
o think about Maple than with where the next parenthesis needed to go.
  A consistent working strategy is essential for acquiring facility wi
th using Maple as a regular problem solving tool." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 303 "But the hardest part of \+
learning to use Maple effectively is to learn to approach mathematics \+
\"structurally.\"  Perhaps this anecdote will illustrate best my point
.  In a class where we discussed calculating the coordinates of the in
tersection of two curves, I had students graph the curves, and use the
 " }{TEXT 271 5 "solve" }{TEXT -1 212 " command to obtain x-coordinate
s of the intersections.  Turned loose, more than a few students compla
ined that solve(f(x) = g(x), y) didn't return the y-coordinate.  And t
hat's after I had showed them how to use " }{TEXT 273 4 "subs" }{TEXT 
-1 72 " to obtain the companion y-coordinate for each x-coordinate ret
urned by " }{TEXT 272 5 "solve" }{TEXT -1 107 ".  It takes time for st
udents to abstract processes like solving an equation, and to realize \+
that the word " }{TEXT 301 5 "solve" }{TEXT -1 319 " stands for a comp
lex algebraic process leading to the isolation of one of the variables
 in a equation.  It is this abstraction, formulating a structural view
 of mathematics, that occurs during the learning phase of Maple.  Yes,
 students are learning where to put the commas.  But more, they need t
o clarify words like " }{TEXT 302 5 "solve" }{TEXT -1 2 ", " }{TEXT 
303 10 "substitute" }{TEXT -1 6 ", and " }{TEXT 304 8 "evaluate" }
{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 583 "Listen carefully to students who say they are going to \+
\"solve a derivative.\"  If their mapping of the words to the ideas is
 fuzzy, they will not learn to use Maple efficiently.  The stumbling b
lock is the lack of articulation in their minds about the meaning of t
he words.  They can learn the syntax quickly.  They struggle with abst
raction, and with articulating structure in the processes they see as \+
symbol pushing.  That is why they have to see the instructor apply Map
le to mathematics, because they will be hard pressed to render the app
ropriate conceptualization on their own." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 801 "Maple is not a panacea.  Not ever
y student will profit from using Maple to learn mathematics.  Students
 who can abstract, can learn the connection between a Maple command an
d a mathematical concept, excel in a Maple environment.  Students with
 difficulties in abstraction fail to see the structure in mathematics,
 and consequently fail to see how to use Maple to articulate that stru
cture.  They have survived in mathematics classes by performing rote m
anipulations, and seek to pass classes like calculus by mastering the \+
processes of differentiation and integration.  In classes without tech
nological aids, such students earn passing grades.  In a class where s
uch manipulations are relegated to the computer, the student who can't
 abstract has nothing to fall back on.  Maple makes their lot worse." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 274 
21 "The Ultimate Question" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 354 "All those engaged in using Maple in teaching, or \+
contemplating such use, must answer an untimate question.  \"What is t
he purpose of Maple in the life of the student?\"  If there is no clea
r answer to this question, then there are no guidelines for what use w
ill be made of Maple, for what exercises will be devised, and for what
 pedagogy will be employed." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 459 "Maple allows an instructor to create wonderful
 simulations.  As a language for making mathematical things happen pai
nlessly (at least in comparison to making them happen in FORTRAN), it \+
is a great tool for writing simulations.  Such simulations are an impo
rtant contribution to the learning experiences of all students.  But i
t is the instructor writing the simulation who learns to use Maple.  T
he student learns the content of the simulation, but not Maple." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 468 "If the g
oal of Maple usage in the curriculum is to give the student a tool wit
h which to become a pro-active learner and doer of mathematics, then t
he student must learn Maple.  And this does not mean learning where th
e commas go.  It means the student must learn to make the abstractions
 that allow tools like Maple to be applied.  So, deciding beforehand w
hat is the role of Maple in the students' lives really does determine \+
policy in the Maple enhanced curriculum." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 312 "If learning Maple is important fo
r the student, then provision has to be made for this learning to take
 place.  Who will introduce Maple to the student?  Where will the stud
ent access Maple?  Is Maple available on tests?  What exercises?  The \+
traditional ones found in today's texts, or new ones created by whom?
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 477 "If t
he role and implementation of Maple are carefully throught out, the in
troduction of Maple into a curriculum can be an exhilarating experienc
e for both faculty and students.  Where difficulties are experienced, \+
they can probably be traced to conflicting stances on the fundamental \+
issues raised in this column.  We owe it to our institutions and to ou
r students to be sure we have provided the very best environment for t
heir success in mathematics, science and engineering." }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "We close this first " 
}{TEXT 305 20 "Tips for Instructors" }{TEXT -1 240 " column with a few
 observations on the new Release 4 interface, and with one observation
 on the new piecewise command in Maple.  I am indebted to Louise Yaman
e of the technical staff at Waterloo Maple for drafting the notes on t
hese items. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT 275 25 "Release 4 Interface Hints" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 259 "Release 4 provides more control o
ver the layout of the worksheet.  Plotting, mathematical notation in t
ext regions, opening multiple documents, and the way vectors are print
ed in the linalg package all require a few moments thought for a prope
r understanding." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 276 8 "Plotting" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 186 "Release 4 allows plots to be displayed either \+
in-line or in a separate plot window.  This option can be changed in t
he Plot Display submenu of the Options menu or by issuing the command \+
" }{TEXT 279 29 "interface(plotdevice = name);" }{TEXT -1 7 " where " 
}{TEXT 283 4 "name" }{TEXT -1 76 " is one of the allowable names.  For
 the plot window options, choose one of " }{TEXT 280 6 "inline" }
{TEXT -1 4 " or " }{TEXT 281 6 "window" }{TEXT -1 129 ".  If you use t
he separate window option, you will not notice very many changes betwe
en Release 3 and Release 4.  If you use the " }{TEXT 282 6 "inline" }
{TEXT -1 214 " option, you will notice that when you generate the plot
, you do not see the plot tool bar.  In order to see this, you must se
lect the plot and then the context dependent tool bar will change to t
he plot tool bar. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT 277 22 "Standard Math Notation" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 358 "Release 4 supports standard ma
th notation in all areas of the Maple worksheet, especially in text re
gions.  The summation sign on the main tool bar allows you to add Mapl
e commands and mathematical expressions to the text regions of your wo
rksheet.  With the cursor in a text region, click on the summation ico
n in the main tool bar.  Alternatively, execute " }{TEXT 284 9 "contro
l m" }{TEXT -1 340 " from the keyboard.  A question-mark surrounded by
 a rectangle appears at the insertion point.  Now, using valid Maple s
yntax, enter a mathematical expression.  When you are done entering th
e Maple code for the mathematical notation you want to insert into you
r text, press the F5 function key to terminate this mode.  Continue ty
ping text." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 459 "Another secret for working with mathematical notation in a tex
t region is copying an existing bit of mathematical notation and pasti
ng it elsewhere to avoid having to re-enter the code for it.  Click so
mewhere inside the existing mathematical notation.  The context bar at
 the top of the worksheet now exhibits the linear Maple notation for t
his expression.  Copy that code.  Place the cursor at the new insertio
n point in the document, and click.  Execute a " }{TEXT 285 9 "control
 m" }{TEXT -1 19 " and then a paste (" }{TEXT 286 9 "control v" }
{TEXT -1 223 ").  Exit this mode by pressing the function key F5.  If \+
the copied notation is to be edited, edit the linearized code in the c
ontext bar.  Note that you can't copy the code in the contect bar if y
ou have first executed the " }{TEXT 287 9 "control m" }{TEXT -1 69 ". \+
 You have to do that after copying the contents of the context bar." }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 114 "You can
 choose to have the expression displayed as a Maple text command or as
 standard math notation by using the " }{TEXT 278 1 "x" }{TEXT -1 287 
" on the context sensitive tool bar.  You can also toggle between havi
ng this expression be live Maple input or inert commentary in the text
 region by using the maple leaf icon on the context sensitive tool bar
.  (Place the cursor in the expression for the tool bar to change appe
arance.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 288 27 "Multiple Document Interface" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 720 "Release 4 has the ability to open
 multiple Maple worksheets.  Some platforms allow the option of having
 the kernels associated with these worksheets either shared or separat
e (running in parallel).  If you are running the shared kernels versio
n, whatever worksheet that you open will share its information with al
l other worksheets.  This can create confusion for students and instru
ctors alike.  Students may make assignments in one worksheet and then \+
close the worksheet.  Since the worksheet is no longer visible, they m
ay think that the assignments from that worksheet are no longer active
.  This is not the case.  Once an assignment has been made, it can be \+
cleared only by unassigning the variables or executing a " }{TEXT 289 
7 "restart" }{TEXT -1 10 " command. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 530 "In particular, observe that closing, b
y File/Close (or F4), a worksheet in which assignments have been made,
 does not erase those assignments.  So, closing one such worksheet and
 opening a second puts the user at risk of having the second worksheet
 behave erratically since the second worksheet will now contain the as
signments made in the first.  This situation could not happen in Relea
se 3, so Release 4 requires acquiring new working habits!  Many users \+
may already have developed the habit of beginning each worksheet with \+
a " }{TEXT 290 7 "restart" }{TEXT -1 83 ".  This seems like a good wor
king strategy for Release 4 on shared kernel machines." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 291 7 "Vectors" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "In the " }
{TEXT 292 6 "linalg" }{TEXT -1 79 " package the object created by the \+
vector command behaves like a column vector." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}
{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "v := vector([1,2,3]);\nw := \+
vector([4,5,6]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG-%'VECTORG6#
7%\"\"\"\"\"#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG-%'VECTORG
6#7%\"\"%\"\"&\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 8 "The way " }{TEXT 293 1 "v" }{TEXT -1 5 " and " }
{TEXT 294 1 "w" }{TEXT -1 120 " are displayed implies they may be row \+
vectors (i.e., 1 x 3 matrices), but simple experiments show that they \+
behaves as " }{TEXT 306 6 "column" }{TEXT -1 37 " vectors, that is, as
 3 x 1 matrices." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 65 "evalm(transpose(v) &* w);\ndotprod(v,w);\neva
lm(v &* transpose(w));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#K" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#K" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#-%'MATRIXG6#7%7%\"\"%\"\"&\"\"'7%\"\")\"#5\"#77%F.\"#:\"#=" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "In
 the first case we have the transpose of " }{TEXT 295 1 "v" }{TEXT -1 
56 " behaving as a row vector multiplying the column vector " }{TEXT 
296 1 "w" }{TEXT -1 137 " to yield the dot product of v with w.  In th
e second case we have the outer product of the column vector v multipl
ying the transpose of " }{TEXT 297 1 "w" }{TEXT -1 138 ", a row vector
.  Dimensionally we have (1 x 3)(3 x 1) and (3 x 1)(1 x 3).  Yet, the \+
screen image is not consistent with these conclusions." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 186 "Included in the sha
re library of Release 4 is a file of code, written by Mike Monagan, th
at will cause Maple to display the default vector, just shown to be a \+
column vector, as a column." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "with(share):\nreadshare(pvac
,system):" }}{PARA 6 "" 1 "" {TEXT -1 70 "See ?share and ?share,conten
ts for information about the share library" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 9 "print(v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATR
IXG6#7%7#\"\"\"7#\"\"#7#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 258 "The name \"pvac\" is derived from th
e phrase \"print vector as column.\"  There is a variable \"pvac\" def
ined by this file that, when set to \"true\" causes printing of vector
s as columns, and when set to \"false\" restores the default behavior \+
of the pretty printer." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "pvac := false:\nprint(v);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%'VECTORG6#7%\"\"\"\"\"#\"\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "pvac := true:\nprint(v);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7#\"\"\"7#\"\"#7#\"\"$" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 96 "In
 fact, the behavior of this utility is described in the help file for \+
it, accessed by entering" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?pvac" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 928 "The code for this functi
onality can be put into an initialization file so that every time Rele
ase 4 is launched the code is automatically loaded.  The file containi
ng the code is the text file pvac.mpl, found at the end of the path ma
plev4/share/system/pvac.  If this code is put into a text file named m
aple.ini (under Windows) or maple.init (on a Macintosh), and placed in
to the lib subdirectory of maplev4 (under Windows) or into the maplvev
4 subdirectory itself on the Mac, it will be read each time Maple is l
aunched.  If the pvac code is made into an initialization file, you wi
ll get a syntax error if you then try to load it from the share librar
y.  It can't be loaded from share if it is already loaded.  (I have be
en running this code in my initialization file since it was first writ
ten, have distributed it to \"generations\" of students at Rose-Hulman
 Institute of Technology, have used its functionality in the text " }
{TEXT 299 29 "Maple Labs for Linear Algebra" }{TEXT -1 95 ", Terry Law
son and Robert J. Lopez, John Wiley & Sons, 1996, and have had no prob
lems with it.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 189 "It is unfortunate, however, that the pvac code, which ex
isted for nearly two years before Release 4 was shipped, has not been \+
extended to pretty print the transpose of a vector as expected." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 20 "print(transpose(v));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*trans
poseG6#%\"vG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 60 "The transpose command actually does create the transpos
e of " }{TEXT 298 1 "v" }{TEXT -1 178 ", but the pretty printer does n
ot print it as a row-like object.  Perhaps this oversight will soon be
 corrected.  When it is, both faculty and students alike will be well \+
served." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 307 30 "Piecewise Continuous Functions" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "Release 4 provides a robust " }
{TEXT 313 9 "piecewise" }{TEXT -1 150 " command for defining and manip
ulating piecewise continuous functions.  The new piecewise command cre
ates objects that are understood by the commands " }{TEXT 314 4 "plot
" }{TEXT -1 2 ", " }{TEXT 315 4 "diff" }{TEXT -1 2 ", " }{TEXT 316 5 "
limit" }{TEXT -1 2 ", " }{TEXT 317 3 "int" }{TEXT -1 11 ", and even " 
}{TEXT 318 6 "dsolve" }{TEXT -1 38 ".  Consider, for example, the func
tion" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "g:=piecewise(x<0,0,x<=1,x,x<=2,2-x,0);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"gG-%*PIECEWISEG6&7$\"\"!2%\"xGF)7$F+1F+\"\"
\"7$,&\"\"#F.F+!\"\"1F+F17$F)%*otherwiseG" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 22 "for which Maple allows" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(g, x = -1..3);" }}
{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6$7Y7$$!\"\"\"\"!F*7$$!1LLLLQ6G
\"*!#;F*7$$!1nmmT.\\p$)F.F*7$$!1LLL$))Qj^(F.F*7$$!1LLL$=Kvl'F.F*7$$!1o
mmTs!G!eF.F*7$$!1MLL3yO5]F.F*7$$!1,++vE%)*=%F.F*7$$!1MLL3WDTLF.F*7$$!1
,++vvQ&\\#F.F*7$$!1mmmm&4`i\"F.F*7$$!1KLLLQW*e)!#<F*7$$!1qmm;arvUFMF*7
$$\"1I#*******H,Q!#>FR7$$\"1&*******RXpVFMFV7$$\"1(*******\\*3q)FMFY7$
$\"1++++(=\\q\"F.Ffn7$$\"1nmm\"fBIY#F.Fin7$$\"1LLLLO[kLF.F\\o7$$\"1KLL
L&Q\"GTF.F_o7$$\"1*****\\s]k,&F.Fbo7$$\"1JLLLvv-eF.Feo7$$\"1,++D2YlmF.
Fho7$$\"1+++v\"ep[(F.F[p7$$\"1MLL$e/TM)F.F^p7$$\"1LLLeDBJ\"*F.Fap7$$\"
1++]([Wdb*F.Fdp7$$\"1mmm;kD!)**F.Fgp7$$\"1mmT+07U5!#:$\"1NL$e*\\zy&*F.
7$$\"1mm;f`@'3\"F\\q$\"1PLL3k%y8*F.7$$\"1++]nZ)H;\"F\\q$\"1-++DB:q$)F.
7$$\"1mmmJy*eC\"F\\q$\"1NLL$o@5a(F.7$$\"1+++S^bJ8F\\q$\"1,+++'[Wo'F.7$
$\"1+++0TN:9F\\q$\"1/++]*ek%eF.7$$\"1++]7RV'\\\"F\\q$\"1.++v3mN]F.7$$
\"1+++:#fke\"F\\q$\"1/++]ySNTF.7$$\"1LLL`4Nn;F\\q$\"1pmmm/\\ELF.7$$\"1
+++],s`<F\\q$\"1,+++&)ziCF.7$$\"1mm;zM)>$=F\\q$\"1NLL3_;!o\"F.7$$\"1++
+qfa<>F\\q$\"12+++ISX#)FM7$$\"1mm\"zy*zd>F\\q$\"1eLL37-?UFM7$$\"1LL$eg
`!)*>F\\q$\"1(3nm;%RY>!#=7$$\"1nm;W/8S?F\\qF*7$$\"1++]#G2A3#F\\qF*7$$
\"1LLL$)G[k@F\\qF*7$$\"1++]7yh]AF\\qF*7$$\"1nmm')fdLBF\\qF*7$$\"1nmm,F
T=CF\\qF*7$$\"1LL$e#pa-DF\\qF*7$$\"1+++Sv&)zDF\\qF*7$$\"1LLLGUYoEF\\qF
*7$$\"1nmm1^rZFF\\qF*7$$\"1++]sI@KGF\\qF*7$$\"1++]2%)38HF\\qF*7$$\"\"$
F*F*-%'COLOURG6&%$RGBG$\"#5F)F*F*-%+AXESLABELSG6$%\"xG%!G-%%VIEWG6$;F(
Ffw%(DEFAULTG" 2 303 303 303 2 0 1 0 2 9 0 4 2 1.000000 45.000000 
45.000000 10030 10061 10056 10074 0 0 0 20030 0 12020 0 0 0 0 0 0 0 1 
1 0 0 0 0 0 0 0 0 0 0 1 }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Moreove
r, we can implement those analyses so necessary in learning calculus.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "limit(g, x = 1, left);\nlimit(g, x = 1, right);\nlimi
t(g, x = 1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 
"The derivative of g(x) is the piecewise function" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dg := diff(
g, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dgG-%*PIECEWISEG6)7$\"\"!
2%\"xGF)7$%*undefinedG/F+F)7$\"\"\"2F+F07$F-/F+F07$!\"\"2F+\"\"#7$F-/F
+F77$F)2F7F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 26 "whose graph is obtained by" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "plot(dg, x = -1..3, \+
discont = true, color=black);" }}{PARA 13 "" 1 "" {INLPLOT "6(-%'CURVE
SG6$7S7$$!\"\"\"\"!F*7$$!1w#p(e%G?y*!#;F*7$$!1A>B'esBf*F.F*7$$!1k^2AZ3
z$*F.F*7$$!1nX]ZIQk\"*F.F*7$$!1j_^7=q]*)F.F*7$$!1\\\"yX&>f_()F.F*7$$!1
y]lr1YZ&)F.F*7$$!11FT0OJN$)F.F*7$$!12B](*o%Q7)F.F*7$$!16S&eRFj!zF.F*7$
$!1hQS+ht9xF.F*7$$!1,>+!o\\!*\\(F.F*7$$!1X]VIwZ#G(F.F*7$$!1fC&3LqP2(F.
F*7$$!1X[J3TC%)oF.F*7$$!14*[$)4z)emF.F*7$$!1O2tt`'zY'F.F*7$$!1E#eiK()e
C'F.F*7$$!1Y!oXi5$\\gF.F*7$$!1IF3F[jLeF.F*7$$!1![$*\\Yg#GcF.F*7$$!1>(Q
L'Q(RT&F.F*7$$!1$G#)*p=><_F.F*7$$!1iM#e!f$\\+&F.F*7$$!15W^7;Y%y%F.F*7$
$!1C\\1#4QDf%F.F*7$$!1AG1KaD&Q%F.F*7$$!1wxlh@6rTF.F*7$$!1rnd\\ZhhRF.F*
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^lF*7$$\"1Z!*GwJgaGFd^lF*7$$\"18X?KnjvGFd^lF*7$$\"19-j&Qk\\*GFd^lF*7$$
\"1P1edg6<HFd^lF*7$$\"1%4XqxGp$HFd^lF*7$$\"1!ow$oK0eHFd^lF*7$$\"1n`+-@
FyHFd^lF*7$$\"\"$F*F*Fht-%+AXESLABELSG6$%\"xG%!G-%%VIEWG6$;F(F_am%(DEF
AULTG" 2 303 303 303 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 
10030 10061 10056 10074 0 0 0 20030 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 
22255 22306 0 0 0 0 0 1 }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "Furthe
rmore, the indefinite integral of g(x) is obtained as the piecewise de
fined G, with G given by" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "G := int(g, x);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"GG-%*PIECEWISEG6&7$\"\"!1%\"xGF)7$,$*$F+\"\"##\"
\"\"F/1F+F17$,(F.#!\"\"F/F6F1F+F/1F+F/7$F12F/F+" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "and with graph given
 by" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "plot(G, x = -1..3);" }}{PARA 13 "" 1 "" {INLPLOT "6%-
%'CURVESG6$7S7$$!\"\"\"\"!F*7$$!1LLLLQ6G\"*!#;F*7$$!1nmmT.\\p$)F.F*7$$
!1LLL$))Qj^(F.F*7$$!1LLL$=Kvl'F.F*7$$!1ommTs!G!eF.F*7$$!1MLL3yO5]F.F*7
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408 0 0 0 0 0 1 }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 249 "A comparison t
o Release 3, where most users would have defined g(x) as a Maple proce
dure, is informative.  Using a new name to be consistent with Corollar
y One of the Large Law (use distinct names for each significant output
), we write the procedure" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "g3 := proc(x) \nif x<0 then 0\n  el
if x<=1 then x\n  elif x<=2 then 2-x\n  else 0\nfi;\nend:" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "which now
 allows an evaluation such as" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "g3(0.5);" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"&!\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "but does not allow plotting.  Obse
rve:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "plot(g3(x),x = 0..2);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
8 "" 1 "" {TEXT -1 38 "Error, (in g3) cannot evaluate boolean" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "Be
fore the " }{TEXT 308 4 "plot" }{TEXT -1 109 " function is executed, t
he arguments g3(x) and x = 0..2 are evaluated.  In fact, evaluating ju
st g3(x) yields" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "g3(x);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 8 "" 
1 "" {TEXT -1 38 "Error, (in g3) cannot evaluate boolean" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "So the er
ror occurs " }{TEXT 311 6 "before" }{TEXT -1 5 " the " }{TEXT 309 4 "p
lot" }{TEXT -1 190 " function starts executing.  The error occurs beca
use Maple cannot evaluate x < 0 since x has no numerical value yet.  A
 simple solution - but not a very enlightening one - is to use quotes:
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 
"plot('g3(x)',x=0..2);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 52 "The quotes prevent g3(x) from evaluating \+
before the " }{TEXT 310 4 "plot" }{TEXT -1 91 " command is called and \+
has a chance to give  x a numerical value.  Alternatively, plot the " 
}{TEXT 319 8 "function" }{TEXT -1 19 " g3 instead of the " }{TEXT 320 
7 "formula" }{TEXT -1 16 " g3(x), that is:" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "plot(g3,0..2);" }}{PARA 
0 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 280 "Howeve
r, we are now into the great overhead of programming procedures, and r
emembering the different syntax for plotting a function as contrasted \+
to plotting an expression.  This extra syntax burden typically obscure
s the point of the example of the piecewise continuous function." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 251 "We concl
ude with an illustration of another way of defining g3(x) so as to ret
urn unevaluated if the argument is not numeric.  Like the quotes, this
 device is useful in other contexts (e.g., defining a function whose o
utput is the result of a call to " }{TEXT 322 6 "fsolve" }{TEXT -1 31 
", and which is compatible with " }{TEXT 321 4 "plot" }{TEXT -1 132 ".
)  It is provided for the sake of the instructor who wishes to have a \+
fuller understanding of the tools being used for instruction." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 154 "gg := proc(x)\n  if type(x,numeric) then\n    if x<0 then 0\n  \+
    elif x<=1 then x\n      elif x<=2 then 2-x\n      else 0\n    fi;
\n    else 'gg'(x)\n  fi;\nend:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 140 "The quotes in 'gg'(x) are needed \+
to stop what would otherwise be a recursive call: gg(x) would call its
elf recursively forever.  Now we have" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "gg(.3);\ngg(x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$\"\"$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#
ggG6#%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 42 "But surely the improved functionality for " }{TEXT 312 9 
"piecewise" }{TEXT -1 48 " in Release 4 is the true ally of the classr
oom." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {HYPERLNK 
17 "Part 2" 1 "tips2.mws" "" }{TEXT -1 3 " - " }{HYPERLNK 17 "Part 3" 
1 "tips3.mws" "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 }
{VIEWOPTS 1 1 0 1 1 1803 }