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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "#basic arithmetic - \+
using Maple as a calculator" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
7 "#2 + 2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "# a colon at \+
the end of the line suppresses the output" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 5 "#2/2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "
#use brackets" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "#(3/5) + (
7/124);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "#exponentiation \+
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}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "#2**3;" }}}{EXCHG {PARA 0 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#abs(x)/x;" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 31 "# the constant pi is written Pi" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "# the base of natural logs is writt
en E" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "# the exponential f
unction is exp(  )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "# ln(
 ) is the natural log function - log10( ) is the log function to the b
ase 10, etc" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "# trig funct
ions are sin( ), cos( ), sec( ), tan( ), cot( ), csc( )" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "# inverse trig functions are arcsin
( ),...etc" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "# I is the square root of -1" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "# I = sqrt(-1)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "# use solve to solve one equation" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "#solve( x = sin(x));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "#solve ( arccos(x) = arctan(
x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "#plot (sin(x), x=-2
*Pi..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "#plot (\{x, \+
sin(x)\}, x= -2*Pi..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
132 "# note that the command is plot (set of expressions, variable = h
orizontal range).  Sets of whatever are enclosed in curly brackets." }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "#plot (\{arccos(x), arctan
(x)\}, x=-Pi/2..Pi/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "#
 define functions using the arrow notation" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 22 "#g:= x -> x*arctan(x);" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "#g(0);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "# diff returns an expression -D ret
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(x),x);" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
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"" {MPLTEXT 1 0 9 "#D(g)(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 203 "# let's try some integration - we can find indefinite integrals
 for g(x) and for the derivative of g, of course this second one is ju
st g.  Note that Maple does not include the constant of integration c.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "#int(g(x),x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "#int(D(g)(x),x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "#int((diff(g(x),x),x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "# for a definite integral, just specify limits" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "#int (D(g)(x), x= 0..1);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "# Maple will also calculate
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mit(f, x=a) where a can be any real number or infinity or -infinity" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "#limit(arctan(x), x=infini
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}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "#limit(1/x, x=0, right);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "#limit(1/x ,x=0, left);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "#limit((sin(x)/x), x=0)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "#limit ((1 + (1/x))^x,
 x=infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 178 "# what ab
out a function which is not the derivative of any other fn, ie there i
s no antiderivative?  We will integrate such functions by numerical me
thods.  What does Maple do?? " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 18 "#int(exp(x^2), x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
139 "# I is the root of -1, erf is an error function, really just the \+
integral again.  Maple will of course do numerical approximations but.
...." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
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