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{SECT 0 {PARA 18 "" 0 "" {TEXT 282 34 "DISCOVERING MATHEMATICS WITH MA
PLE" }{TEXT 281 0 "" }}{PARA 258 "" 0 "" {TEXT 283 77 "An Interactive \+
Exploration for Mathematicians, Engineers, and Econometricians" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 28 "Chapter
1. A Tour of Maple V" }}{PARA 257 "" 0 "" {TEXT -1 0 "" }}{SECT 0
{PARA 3 "" 0 "" {TEXT -1 21 "Worksheet 1a. Numbers" }}{PARA 0 "" 0 ""
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 342 "It is a well-known sayin
g that the practical side of a subject can not be fully mastered by me
rely reading about it or listening to experts, one needs to be activel
y involved. It is certainly true that in order to get some proficiency
with the Maple system you need to sit down in front of the computer, \+
switch on and start learning by doing." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 46 "Information about this Comput
er Algebra Course" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 ""
{TEXT -1 143 "But before you start, you should know a thing or two abo
ut the worksheets that are part of this Computer Algebra course. The m
ain subdirectory " }{TEXT 256 7 "Book\\R5" }{TEXT -1 152 " itself has \+
six subdirectories, each corresponding to a chapter. These subdirector
ies contain one session, two worksheets and two assignment worksheets.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 378 "The \+
Maple sessions are aimed at demonstrating the many possibilities Maple
has to offer. Apart from the first session - this is the one we have \+
just gone through in the preceding section - each of the remaining fiv
e Maple sessions focuses on a specific field of application. All sessi
ons with their input groups, output, and text regions are reproduced e
ntirely in printed form." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 56 "The worksheets can be recognized by the chapter's \+
name: " }{TEXT 258 11 "TourW1a.mws" }{TEXT -1 52 " is the first worksh
eet associated with the session " }{TEXT 259 10 "TourS1.mws" }{TEXT
-1 287 " and Chapter 1: A tour of Maple V. The printed form of these t
welve worksheets does not include the full output, and a few input lin
es are left out as well.You are expected to conscientiously work throu
gh the worksheets, with close attention to the remarks, suggestions an
d instructions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 ""
{TEXT -1 83 "Likewise, there are twelve assignment worksheets with sim
ilar names, for instance: " }{TEXT 260 11 "TourA1b.mws" }{TEXT -1 130
" is the second assignments worksheet associated with the first chapte
r. It goes without saying that the assignments are text only." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "In the pr
esent worksheet (" }{TEXT 261 11 "TourW1a.mws" }{TEXT -1 287 "), the f
irst of twelve, we shall get acquainted with Maple on a very basic lev
el. We shall see how instructions and commands should be given (input)
, how input errors can be discovered and removed, and learn about the \+
way in which Maple deals with integers, rational numbers, and reals. \+
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "In th
e worksheet " }{TEXT 262 11 "TourW1b.mws" }{TEXT -1 395 " we shall pay
attention to computations with variables. In Chapter 2 we will use Ma
ple to examine functions and sequences. Chapter 3 is about matrices an
d vectors. In Chapter 4 attention will be paid to summation and to Map
le's random generator. In Chapter 5 we will look at derivatives and in
tegrals. Finally in Chapter 6 we will consider linear transformations,
eigenvalues and eigenvectors. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 28 "G
iving Instructions to Maple" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA
0 "" 0 "" {TEXT -1 329 "Usually, it will be clearly indicated what sho
uld be typed in, but occasionally you will have to decide for yourself
. The different regions or groups, composed of lines of input, output,
or text are clearly distinguishable by the differences in colour and \+
type of font. In the printed form these differences are less pronounce
d. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 365 "L
et us start by making the active worksheet as large as possible. Next,
place the cursor on the first input line, immediately after the promp
t. This can be achieved by clicking the left mouse button on this posi
tion, or by using the arrow keys. Now type the following Maple instru
ction, and make sure to include spaces and the semicolon. Then hit the
key. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 ""
{TEXT -1 13 "5*(17 + 21); " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 ""
{TEXT -1 157 "Observe that Maple immediately produces the correct answ
er to this most simple of exercises (5 times the sum of 17 and 21) in \+
a newly created output region. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 774 "Also note that the cursor jumps to the n
ext input line where it patiently waits for your next instruction. In \+
order to prevent the cursor from jumping too far ahead, which might ma
ke it difficult for you to read the suddenly disappearing text block i
n between these successive input regions, we have inserted a dummy inp
ut line following each regular input group. In print this dummy line i
s not reproduced. As soon as you have finished reading the text, you c
an move the cursor with the mouse or with the arrow keys (use the scro
ll bar) to the next input line following the text block. A mistake in \+
the input can be easily corrected by moving the cursor to the relevant
position in the input line after which you can remove the error with \+
either ~~ or keys. " }}{PARA 0 "" 0 "" {TEXT -1 427 "Th
e output of a Maple instruction cannot be edited, only copied or remov
ed, if so required. Just place the cursor somewhere inside the output \+
region and press the ~~~~ key to remove the entire output. Selecting \+
a (large) part of the worksheet can be done by moving the cursor to th
e beginning of the selection and clicking the left mouse button right \+
at the end of the selected part while keeping the key pressed \+
down." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 170
"Now move the cursor to the previous input line, replace the plus sign
by a minus sign, and press the key. Maple adjusts the answer \+
by replacing old output by new." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 352 "Maple does not act on an instruction unt
il the key is pressed. Even then, if the instruction is not cl
osed off by a semicolon or colon, still nothing happens. Or so it seem
s. In fact Maple is waiting until the input instruction is properly te
rminated by semicolon or colon, indicating that the input instruction \+
is complete. Let us try and see." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 26 "Type the next instruction " }{TEXT 257 7
"without" }{TEXT -1 41 " closing symbol (; or :) and hit ." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "2*(175 - \+
16)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 222 "The curs
or jumps to the next input line and a warning message is issued which \+
speaks for itself. Completing the instruction or closing it off with a
semicolon (in the present case) is sufficient to force Maple into act
ion." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 202 "
Maple ignores spaces, a feature we can use to enhance the readability \+
of the instructions, not for the benefit of Maple, but for ourselves. \+
Only within numbers or names of commands no spaces must occur." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 495 "Next we \+
shall find out how Maple treats numbers and in what way Maple works wi
th the ordinary arithmetic operations of addition (+), subtraction (-)
, multiplication (*), division (/), and exponentiation (^). In reverse
order this is the usual order of operation: multiplication before add
ition and exponentiation before multiplication. In case of equal prior
ity, the execution order is from left to right. There is only one exce
ption to this rule. Two successive exponential operations, like in " }
{TEXT 265 5 "2^3^4" }{TEXT -1 151 ", is not allowed. If in doubt, use \+
parentheses or some other kind of bracketing, because operations of br
acketed expressions are always executed first." }}{PARA 0 "" 0 ""
{TEXT -1 230 "Carefully type in the following nine expressions, exactl
y as they appear below. Observe that they are separated by commas. In \+
this way a sequence of instructions is created, which will produce a s
imilar sequence of output results." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "2-3+4, 2-(3 + 4), 2/(3/4), 2
/3/4, (2 + 5/3)*3^2, " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "2 + 5/3*3^
2, 2 + 5/(3*3)^2, 2^(3^2), (2^3)^2;" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 ""
{TEXT -1 166 "Inspect the resulting output and make sure you agree wit
h the outcome of each instruction. Observe with care the placing of th
e parentheses. Now give the instruction:" }}{PARA 0 "" 0 "" {TEXT -1
0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "2^3^4;" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 50 "and consider the error message that Mapl
e returns." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT
-1 160 "You probably noticed that fractions appearing in Maple output \+
are not replaced by approximate numerical values. But Maple does write
fractions in lowest terms. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA
0 "" 0 "" {TEXT -1 155 "Let us consider a large integer: 2 to the powe
r one thousand will do nicely. Give the Maple code for this number, hi
t the key and see what happens." }}{PARA 0 "" 0 "" {TEXT -1 0
"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 182 "The backslash (\\) marks the place where the outp
ut is broken off, to continue on the next line without interruption. M
aple uses the backslash in output that is too long for one line." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 163 "Next let
Maple calculate 1000!, which is, as you know, the product of all posi
tive integers up to and including 1000. Again, give the Maple code on \+
the next line. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 402 "Bef
ore we continue our tour of Maple, it makes sense to remove from the s
creen the very large output caused by these numbers. This can be done \+
in several ways. First, select the relevant output region and then pre
ss the ~~~~ key. Alternatively, replace the closing semicolon of the \+
corresponding Maple instruction by a colon, and hit . Output is
now suppressed, because new output replaces old." }}{PARA 0 "" 0 ""
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "At this point you can try
and complete " }{HYPERLNK 17 "assignment 1" 1 "TourA1a.mws" "assignm
ent1" }{TEXT -1 15 " of worksheet " }{TEXT 266 11 "TourA1a.mws" }
{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "assign
ment1" {TEXT -1 110 "In order to find out how far we can go, let us tr
y a huge integer next. What about 2 to the power ten million?" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
11 "2^10000000:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 592 "Apparent
ly, even for Maple this is too large an object. Dropping the exponent \+
to one million leaves a power of 2 that is not too large for Maple' ta
ste; even so, one should not instruct Maple to expand this huge number
, because it would take Maple a very long time indeed. Moreover, once \+
the calculation of this large number has started, it can not be interr
upted. In other words, Maple does not react to clicking the but
ton on the icon bar. The only way out is the brute force way of haltin
g the Maple program by pressing simultaneously the , , and \+
~~~~ keys (followed by " }{TEXT 263 1 "E" }{TEXT -1 417 "nd Task unde
r Windows95), which will cause the loss of unsaved information. Genera
lly, a computational process consists of a sequence of so-called prima
ry calculations. A primary calculation can not be interrupted, but has
to run its full course. The computational process can only be interru
pted or stopped (by clicking the button) when one primary calcu
lation is completed and before the next one is started." }}{PARA 0 ""
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 123 "Maple is able to ke
ep track of the time needed to complete a calculation. This can be don
e by means of the Maple procedure " }{TEXT 264 7 "time( )" }{TEXT -1
220 ", a procedure that calculates the computing time (in seconds) ela
psed since the start of the Maple session. The total amount of time Ma
ple has used for computations can also be found in the Time window on \+
the status bar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 53 "now := time(): 2^100000: computime := time() \+
- now; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 ""
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {HYPERLNK 17 "Assignment 2" 1 "To
urA1a.mws" "assignment2" }{TEXT -1 14 " of worksheet " }{TEXT 267 11 "
TourA1a.mws" }{TEXT -1 75 " asks for the determination of the computin
g time of a similar computation." }}{PARA 0 "" 0 "assignment2" {TEXT
-1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 ""
{TEXT -1 22 "Numerical Computations" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 507 "We have established that Maple performs
exact computation on integers and rational numbers, provided the inte
gers in question are not outrageously large. These number types have i
n common that they can be expressed uniquely with only finitely many d
igits. Let us call any finite expression, exclusively built from finit
ely many rational numbers and the four standard arithmetic symbols (+,
-,*,/), a finite representation. Irrational numbers do not have such f
inite representations. For instance, the number " }{XPPEDIT 18 0 "Pi"
"6#%#PiG" }{TEXT -1 75 " (the ratio of the circumference of a circle a
nd its diameter), the number " }{XPPEDIT 18 0 "e" "6#%\"eG" }{TEXT -1
42 " (the base of the natural logarithm), and " }{XPPEDIT 18 0 "sqrt(2
)" "6#-%%sqrtG6#\"\"#" }{TEXT -1 338 " have no finite representation i
n this sense. In spite of this, we often like to know the approximate \+
size of these numbers too, that is to say, how large they are compared
with the unit of measurement, the number 1. We know that all real num
bers can be written as infinite decimal fractions in essentially one w
ay only. For instance, in " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0
"" 0 "" {TEXT -1 29 " " }{XPPEDIT 18 0 "Pi
" "6#%#PiG" }{TEXT -1 18 " = 3.141592653... " }{MPLTEXT 1 0 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "the first
ten digits of the number " }{XPPEDIT 18 0 "Pi" "6#%#PiG" }{TEXT -1
116 " are given. But how does this decimal expansion continue? Nobody \+
knows for sure what the billionth decimal digit of " }{XPPEDIT 18 0 "P
i" "6#%#PiG" }{TEXT -1 163 " is. Nevertheless, it is not a matter of c
hoice, there is only one such digit. Not knowing it is of no great imp
ortance, but is does mean that in order to include " }{XPPEDIT 18 0 "P
i" "6#%#PiG" }{TEXT -1 125 " in our calculations we are forced to make
do with only finitely many digits and thus with an inexact, approxima
te value for " }{XPPEDIT 18 0 "Pi" "6#%#PiG" }{TEXT -1 180 " . On requ
est, Maple will transform exact values into approximate values, and wh
at is more, we may even choose the number of digits precision Maple sh
ould use in its calculations. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 35 "Now give the following instruction:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
13 "evalf(Pi,48);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "This give
s the floating point representation of " }{XPPEDIT 18 0 "Pi" "6#%#PiG
" }{TEXT -1 134 " rounded to 48 digits. Because of rounding, only the \+
final digit may be wrong, all other digits are correct. Check this, by
comparing " }{TEXT 268 12 "evalf(Pi,48)" }{TEXT -1 6 " with " }{TEXT
269 12 "evalf(Pi,50)" }{TEXT -1 25 ". With the Maple command " }{TEXT
270 6 "Digits" }{TEXT -1 85 " we can change the number of digits preci
sion for internal computations with floats. " }}{PARA 0 "" 0 "" {TEXT
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Digits := 50; eval
f(Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "Setting " }{TEXT 271 6
"Digits" }{TEXT -1 114 " to 50 forces Maple to carry out all subsequen
t floating point calculations in 50 digits arithmetic with rounding."
}}{PARA 0 "" 0 "" {TEXT -1 10 "Now reset " }{TEXT 272 6 "Digits" }
{TEXT -1 26 " to 10, its default value." }}{PARA 0 "" 0 "" {TEXT -1 0
"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 59 "As we mentioned before, exact or symbolic expressi
ons like " }{XPPEDIT 18 0 "Pi" "6#%#PiG" }{TEXT -1 2 ", " }{XPPEDIT
18 0 "sqrt(2)" "6#-%%sqrtG6#\"\"#" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "ln
(3)" "6#-%#lnG6#\"\"$" }{TEXT -1 134 " and so on, can also be shown as
floats. Naturally, this does not change their actual exact values; as
king Maple to show 48 digits of " }{XPPEDIT 18 0 "Pi" "6#%#PiG" }
{TEXT -1 29 " does not alter the value of " }{XPPEDIT 18 0 "Pi" "6#%#P
iG" }{TEXT -1 192 " for future calculations! Further, floats are 'cont
agious' in the following sense. If an expression contains floats next \+
to (exact) rational numbers then it automatically evaluates to a float
." }}{PARA 0 "" 0 "" {TEXT -1 50 "Try this out by giving the following
instructions:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> "
0 "" {MPLTEXT 1 0 54 "(1/2 + 1/3)*2, evalf((1/2 + 1/3)*2), (1/2 + 1/3)
*2.0; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "In this way it is easy
to calculate (approximate) values of well-known functions such as " }
{TEXT 273 2 "ln" }{TEXT -1 5 " and " }{TEXT 274 3 "sin" }{TEXT -1 31 "
without having to use Maple's " }{TEXT 275 6 "evalf " }{TEXT -1 8 "co
mmand." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 36 "sqrt(3), evalf(sqrt(3)) = sqrt(3.0);" }}{PARA 0 "> "
0 "" {MPLTEXT 1 0 41 "sin(11/10), evalf(sin(11/10)) = sin(1.1);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "evalf(ln(2/5)); ln(0.4); evalb(% = \+
%%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "In the third input line
we used the command " }{TEXT 277 5 "evalb" }{TEXT -1 19 ". Recall tha
t with " }{TEXT 276 5 "evalb" }{TEXT -1 63 " Boolean expressions are e
valuated with two possible outcomes: " }{TEXT 278 4 "true" }{TEXT -1
4 " or " }{TEXT 279 5 "false" }{TEXT -1 4 ". " }}{PARA 0 "" 0 ""
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 205 "In the next chapter we s
hall consider in detail the mathematical functions known to Maple, and
the use of functions in general. Here let it suffice to ask Maple for
information on the logarithmic function." }}{PARA 0 "" 0 "" {TEXT -1
0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "?ln" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1
104 "Carefully read the information on this function; don't skip the e
xamples, much can be learned from them." }}{PARA 0 "" 0 "" {TEXT -1 0
"" }}{PARA 0 "" 0 "" {TEXT -1 13 "Now turn to " }{HYPERLNK 17 "assign
ment 3" 1 "TourA1a.mws" "assignment3" }{TEXT -1 15 " of worksheet " }
{TEXT 280 11 "TourA1a.mws" }{TEXT -1 101 ", in which the logarithmic \+
function should be used to determine the number of digits of the integ
er " }{XPPEDIT 18 0 "2^10000000" "6#*$\"\"#\")+++5" }{TEXT -1 2 " ." }
}{PARA 0 "" 0 "assignment3" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1
0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "This is where we conclude the firs
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