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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 54 "Click on a box with a + inside to
 expland the section." }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 28 "Function
s versus expressions" }}{PARA 0 "" 0 "" {TEXT -1 107 "Maple makes a bi
g distinction between functions and expressions.  Youu should too!  He
re are some examples." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f:=
x->5*x^2+1; " }{TEXT -1 26 "This defines a function f." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f(2);f(x); " }{TEXT -1 97 "Evaluati
ng a function at a certain point gives an expression, a particular val
ue of the function." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f(co
s(y));" }{TEXT -1 90 "  Another value of the function.  It is an expre
ssion with a y in it, not a function of y." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "diff(f(x),x);" }{TEXT -1 47 " diff differentiates e
xpressions, not functions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 
"D(f);" }{TEXT -1 56 "D differentiates functions, giving back another \+
function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "D(f)(3);" }
{TEXT -1 41 "Of course, you can evaluate the function " }{TEXT 256 4 "
D(f)" }{TEXT -1 6 " at 3." }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 25 "Co
mbinations of functions" }}{PARA 0 "" 0 "" {TEXT -1 92 "Maple allows y
ou to define things like the product of two functions, their compositi
on, etc." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "(sin^2)(x); sin(
x)^2; a:=sin^2; " }{TEXT -1 42 "The last item defines a function calle
d a." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "a(x); a(5.0);" }
{TEXT -1 78 " Here a is evaluated at x and at 5.0 (the decimal forces \+
Maple to approximate)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "(c
os*sin)(x); g:=cos*sin; " }{TEXT -1 43 "Product expression versus prod
uct function." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "(cos@sin)(
x); h:=cos@sin; " }{TEXT -1 49 "Composition expression versus composit
e function." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "g(4); h(4); \+
" }{TEXT -1 99 "You can evaluate these new functions at a few points. \+
 Maple won't approximate until you ask it to." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 10 "evalf(%); " }{TEXT -1 94 "Evaluate the last expr
ession entered (not necessarily what lies just above in the worksheet!
)." }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 18 "Plotting functions" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(f(x),x=-4..4,y=0..20); \+
" }{TEXT -1 20 "Plot the expression " }{TEXT 257 4 "f(x)" }{TEXT -1 3 
".  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(f,-4..4,0..20)
; " }{TEXT -1 92 "Plot the function.  The first range specified is for
 the argument, the second for the range." }}}}}{MARK "1 2 0 0" 6 }
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