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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 18 "" 0 "" {TEXT -1 26 "
Basic Algebra and Calculus" }}{PARA 19 "" 0 "" {TEXT -1 28 "Dr. Saccon
e, Revised 1/18/01" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart
;" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 7 "Algebra" }}{PARA 0 "" 0 "" 
{TEXT -1 67 "Here are just a few examples of Maple's built-in algebra \+
functions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }{TEXT 257 7 "Factor." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 44 "This command factors polynomial expressio
ns." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "factor(a^3+3*a^2*b+3*
a*b^2+b^3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 7 "Ex
pand." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "
This command expands products of sums." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "expand((sin(x)+exp(x))^2);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 37 "Expand also knows certain identities." }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 17 "expand(sin(2*x));" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT 256 9 "Simplify." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 151 "Maple knows certain sets of rules for si
mplifying various types of expressions such polynomial, trigonometric,
 exponential and logarithmic expressions." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "simplify(sin(x)^2+ln(2*z)+cos(x)^2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 128 "Note that simplification is different t
han factorization. Factorization is a specific way of changing the for
m of an expression." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "simpl
ify(x^2+2*x+1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 103 "It can b
e frustrating, but sometimes Maple doesn't do things the way you would
 like it to. For example." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 
"simplify(ln(s*t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 330 "You woul
d think that Maple would know the rules of logarithms. The problem is \+
that Maple is so versatile that sometimes you have to tell it certain \+
things about the arguments that you pass on. In this case Maple know t
hat this identity will not hold for all numbers s and t. It will hold \+
if s and t are positive. We there use the " }{TEXT 259 7 "assume " }
{TEXT -1 52 "command to tell Maple something about our variables." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assume(s>0);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assume(t>0);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "simplify(ln(s*t));" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 140 "When you make assumptions about a variable, thereafter
 it prints with an appended tilde ~ to indicate that the variable carr
ies assumptions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 260 8 "Convert." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 261 8 "convert " }{TEXT -1 
113 "command will modify the form of certain expressions in a specifie
d way. Consider the following rational function." }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "(x^2+2)/(x^2-5*x+6)^2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&,&*$)%\"xG\"\"#\"\"\"F)F(F)F)*$),(F%F)*&\"\"&F)F'F)!
\"\"\"\"'F)F(F)F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "We conver
t this to a partial fraction as follows." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "convert((x^2+2)/(x^2-5*x+6)^2,parfrac,x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
-1 8 "Calculus" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 6 "Limits" }}{PARA 
256 "" 0 "" {TEXT -1 13 "Basic limits." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "f := x -> sin(x)/x;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "limit(f(x),x=0);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 72 "As a note of warning, Maple has a convention that certain
 commands a an " }{TEXT 262 6 "inert " }{TEXT -1 171 "counterpart that
 begins with an uppercase letter. For example, the command Limit is an
 inert form of limit. The output is simply a placeholder than can be e
valuated later." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 263 8 "Example." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "Limit(f(x),x=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-
%&LimitG6$-%\"fG6#%\"xG/F)\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
50 "We can evaluate this expression using the command " }{TEXT 264 6 "
value." }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "valu
e(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"fG6#\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 265 17 "One-sided limits." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(1/x,x=0,right);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "limit(1/x,x=0,left);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "
" {TEXT -1 15 "Differentiation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 12 "The command " }{TEXT 266 5 "diff " }
{TEXT -1 27 "takes the derivation of an " }{TEXT 267 11 "expression " 
}{TEXT -1 37 "with respect to a specified variable." }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 21 "f := x -> x^2+3*x+10;" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 13 "diff(f(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 64 "One can find higher order derivatives by repeating the va
riable." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "diff(sin(5*x),x);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "diff(sin(5*x),x,x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "diff(sin(5*x),x,x,x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "diff(H(x),x,x,x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 109 "Note in the last calculation the function H is undefined
. Maple therefore represents the result symbolically." }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 131 "Another way to find h
igher order derivative would be to use the \"$\" operator. This operat
or is used to create lists of expressions." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 268 8 "Example." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x$3;" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 19 "diff(sin(5*x),x$3);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 49 "This is another wa
y to find the third derivative." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 269 14 "More examples." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "di
ff(sin(cos(3*t)),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eva
l(%,t=Pi/4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "f := w -> C
*exp(A*w)*exp(B*w);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff
(f(w),w);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "diff(F(s)*G(s)
,s); " }{TEXT -1 17 "The product rule." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "diff(F(G(s)),s); " }{TEXT -1 15 "The chain rule." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 270 12 "The command " }
{TEXT -1 2 "D." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 142 "In the last result we see the symbol \"D(F)\" appearing \+
in the answer. A separate command is used when finding the derivatives
 of functions, or " }{TEXT 271 12 "procedures, " }{TEXT -1 32 "instead
 of ordinary expressions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }{TEXT 272 8 "Example." }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "f := x -> x^2+3*x+10;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "D(f);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{PARA 0 "" 0 "" {TEXT -1 144 "Note that the result is also a procedu
re. The difference is that we pass only the name of the function, name
 \"f\", and not the expression \"f(x)\"." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 
-1 11 "Integration" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 35 "The indefinite integration command " }{TEXT 273 4 "int " 
}{TEXT -1 42 "is similar to the differentiation command." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f := x -> x^2+3*x+10;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "int(f(x),x);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 58 "This answer i
s an antiderivative. Note that it is not the " }{TEXT 274 8 "general \+
" }{TEXT -1 50 "antiderivative, that is, there is no \"+C\" present." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "For def
inite integrals just add limits of integration." }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 17 "int(f(x),x=0..1);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 82 "Note that you cannot integrate repeatedly the same way \+
you can differentiate with " }{TEXT 275 5 "diff." }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 14 "int(f(x),x,x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 30 "However, there is still a way." }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "int( int(f(x),x), x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 34 "Improper integrals are no problem." }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 36 "myInt := Int(exp(-t),t=0..infinity);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "value(myInt);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 9 "Her
e the " }{TEXT 276 6 "inert " }{TEXT -1 107 "form of int, namely Int, \+
was used so we could see the \"pretty\" form of the integral before we
 evaluated it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 277 30 "Example. Integration by parts." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "int(t*exp(t),t);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 68 "Unfortun
ately Maple doesn't tell you what it did to find the answer." }}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "The Package " }{TEXT 286 7 "stude
nt" }}{PARA 0 "" 0 "" {TEXT -1 17 "There is a Maple " }{TEXT 278 8 "pa
ckage " }{TEXT -1 7 "called " }{TEXT 287 8 "student " }{TEXT -1 171 "t
hat has some resources for learning or reviewing basic techniques. A p
ackage is a collection of Maple commands that must be loaded before us
e. The command for loading is " }{TEXT 279 4 "with" }{TEXT -1 17 ". Be
low, I typed " }{TEXT 280 6 "with: " }{TEXT -1 162 "where the colon sp
ecifies that no output is to be generated from that command. Otherwise
 this command would output all the routines being loaded from the pack
age." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
17 "One command from " }{TEXT 281 8 "student " }{TEXT -1 3 "is " }
{TEXT 282 9 "intparts " }{TEXT -1 15 "which takes an " }{TEXT 283 6 "i
nert " }{TEXT -1 21 "integral, defined by " }{TEXT 284 4 "Int " }
{TEXT -1 78 "and applies symbolic integration by parts. The second par
ameter, in this case " }{XPPEDIT 18 0 "t;" "6#%\"tG" }{TEXT -1 46 ", s
pecifies which expression to differentiate." }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 25 "myInt := Int(t*sin(t),t);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 18 "intparts(myInt,t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "value(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "Thi
s way we can see the steps being done to find the answer." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 "To find out more o
n the package " }{TEXT 285 8 "student " }{TEXT -1 20 "use the online h
elp." }}}}{MARK "1 0" 6 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }