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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 21 "INTRODUCTION TO MAPLE" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 287 "Maple is a powerful software t
ool for mathematical computations and visualization.\nThe purpose of t
his lab is for you to see some of the capabilities of a computer algeb
ra system such as Maple.\n\nStart Maple now, if you have not already d
one so. We will start with some basic arithmetic.\n" }{MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "1/3+2/7;" }{TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 61 "Note, all Maple commands must be term
inated with a semicolon." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "3*5;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "100!" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 37 "Maple can handle big numbers, such as" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 7 "2^2000;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 
"To calculate a square root:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "sqrt(2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 120 "Here, it keeps \+
the value symbolically so that it will not loose any precision. We can
 ask for a numerical approximation:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 138 "In \+
Maple, % refers to the output of the previous command. It can save lit
tle typing.\nIf we want more accuracy, we just have to ask for it:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "?evalf;" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 59 "Now, lets do a little algebra. We can multiply pol
ynomials:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "expand((x+1)*(
x^2-3));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 114 "It is easy to make a
 typographical error when typing a complicated expression. To prevent \+
such errors, first type:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 
"(x+1)*(x^2-3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "then insert th
e Maple command expand." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "
expand(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Naturally, we can f
actor this again:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor
(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "To combine a expression, \+
type" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "combine(2*x+4*y-x+2
*y);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Another useful command is
 simplify." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "(x^2-x)/(x^3-
x)-(x^2-1)/(x^2+x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simp
lify(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Maple can solve equat
ions, even when algebra may not help such as:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "solve(x^3=exp(x),x);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 30 "Solutions can be given labels:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 24 "sol:=solve(x^2+x-1=0,x);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 56 "The first and second solutions can be referred to be by
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sol[1];" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sol[2];" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 38 "Maple can solve a system of equations:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 11 "eq1:=x+y=1;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "eq2:=x-y=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 23 "solve(\{eq1,eq2\},\{x,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
27 "We can define an expression" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 19 "f:=2*x^3-5*x^2+x+2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Th
is is useful when repeatedly referring to a complicated expression" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(f);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 44 "To substitute x=6 into the expression, en
ter" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(x=6,f);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "But f(6) is more commonly used to
 indicate the value of the function f at x=6. \nTo define a function, \+
type" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f:=x->2*x^3-5*x^2+x
+2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "To evaluate f(6), simply t
ype" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(6);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 93 "We will now look at some of Maple's other
 capabilities. It can graph functions fairly easily." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 31 "plot(sin(x),x=0..3*Pi,y=-1..1);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "We can plot several functions on s
ame plane." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot(\{x,x^2,
x^3,x^4\},x=0..1,y=0..1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "To p
lot a implicit function, type" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "impli
citplot(x^2+y^2=4,x=-3..3,y=-3..3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 34 "Maple is very useful for 3D plots." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 40 "plot3d(x*exp(-x^2-y^2),x=-2..2,y=-2..2);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Differentiating Expressions" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(sin(x),x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f:=x^x;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 10 "diff(f,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "
Differentiating Functions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
10 "f:=x->x^x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "D(f);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Now D(f) is a derivative function.
 To evaluate f'(2), type" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
D(f)(2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "Integrating expressio
ns" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "int(cos(x)^4,x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(%,x);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 56 "Definite integrals can be computed in a similar fashion:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "int(sin(x)*cos(x),x=0..
Pi/2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 168 "With indefinite integr
als, there may not be a way of expressing the antiderivative in terms \+
of the basic functions. A definite integral is a number, so we can try
 that:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "int(sin(x^3),x=0.
.1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "To get a numerical approx
imation, type" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(%,20
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "int(sin(x)/x,x);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 144 "What is that? You should use the \+
question mark to get help. Si(x) is a function defined in terms of the
 integral. It is not elementery function." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 257 "" 0 "" {TEXT 257 10 "EXERCISES\n" }{TEXT -1 29 "1
. What is the derivative of " }{OLE 1 3585 1 "[xm]Br=WfoRrB:::wk;nyyI;
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{TEXT -1 34 " .\n2. What value of x>0 maximizes " }{OLE 1 3585 1 "[xm]
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