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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 18 "MAPLE for Calculus" }}{PARA 
257 "" 0 "" {TEXT -1 20 "1210-2 November 2007" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 276 "Here are some notes abou
t how MAPLE might help you check Calculus work, but you might also get
 the idea that it will be helpful if you need to write a paper or do a
 research project in Math, Science, or Engineering, in which mathemati
cal output and computations are important." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 237 "We use the version \"Maple 8\"
 in the Math Department, although you can also find \"Maple 10\" here \+
and on most Campus computers.  Maple 8 documents can be opened by Mapl
e 10, but not vise-verse.  (But you can save as MAPLE 8 from MAPLE 10.
)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 261 "MAP
LE acts as a rudimentary word processor, along with its math abilities
, so you can choose to create a mixed text/math document in MAPLE (suc
h as this one), or you can do computations in MAPLE and copy the outpu
t to another word processor like Microsoft Word." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 24 "1)  TEXT and MATH fields
" }}{PARA 0 "" 0 "" {TEXT -1 170 "There are text areas and math areas \+
in a MAPLE document.  This is a text area, and you can type text and u
se the menu bar options to change the appearance of your text.  " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 144 "To creat
e a Math area, click with your mouse on the [> symbol in the menu bar,
 and MAPLE will create a COMMAND FIELD in the next available line:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 
-1 178 "Commands in a command field end with ; or : followed by <RETUR
N> (or <ENTER>).  To enter multiple-line commands before executing, ho
ld down the \"Shift\" key while you hit <RETURN>" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 250 "3+4;   #comment fields begin with #\n45*5;  #
math commands end with ; or :, \n       #followed by \"Return\" or \"E
nter\"\n3*4:   #with the colon :, no output is shown\nsqrt(2);\nevalf(
%);  #evalf stands for evaluate \n           #in floating point  arith
metic" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"$D#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$\"\"##\"\"\"
F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+iN@99!\"*" }}}{PARA 0 "" 0 "
" {TEXT -1 153 "There was a Math prompt here.  I moused \"T\" in the m
enu bar to turn it into a new text field, and then highlighted and del
eted the bracket on the left,  " }{TEXT 256 7 "because" }{TEXT -1 3 " \+
I " }{TEXT 257 10 "don't like" }{TEXT -1 1 " " }{TEXT 258 8 "brackets
" }{TEXT -1 10 " when I'm " }{TEXT 259 6 "typing" }{TEXT -1 6 " text.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 7 "2) HE
LP" }}{PARA 0 "" 0 "" {TEXT -1 209 "There is a \"HELP\" button at the \+
top right of your menu.  Some options you will find there include a \"
New User's Tour\", \"Introduction\", \"Topic Search\", and all of thes
e will be useful for you to peruse further." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 30 "3) PRINTING, EXPORTING, SAVING
" }}{PARA 0 "" 0 "" {TEXT -1 263 "Use the options under \"File\", in t
he upper left corner of your menu bar. It's good to save your MAPLE fi
le every now and then, in case you mess up. To print a hard copy in th
e Math Department, a dialog box will appear and you will need to type \+
in the UNIX command" }}{PARA 258 "" 0 "" {TEXT -1 11 "lpr -P_____" }}
{PARA 0 "" 0 "" {TEXT -1 150 "where you replace the underscore with th
e name of the printer you want to print to, usually the building and r
oom number in which the printer resides." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT 263 13 "4) DOING MATH" }}{PARA 0 "" 0 "" 
{TEXT -1 250 "I thought it might be fun to redo some of the math we've
 been doing in homework and in class, using MAPLE.  You can do the com
putational part of any such problem using MAPLE, and as long as you kn
ow you could do it by hand you're not cheating anyone." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 12 "Derivatives:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "g:=x->x^3; #this is the synt
ax define a function,\n           #in this case it's g(x)." }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*$)
9$\"\"$\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "g(1)
;\ng(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "(
g(x+h)-g(x))/h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*$),&%\"xG\"\"
\"%\"hGF)\"\"$F)F)*$)F(F+F)!\"\"F)F*F." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 64 "Limit((g(x+h)-g(x))/h,h=0);\n   #capital Limit displa
ys the limit" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&LimitG6$*&,&*$),&%
\"xG\"\"\"%\"hGF,\"\"$F,F,*$)F+F.F,!\"\"F,F-F1/F-\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "limit((g(x+h)-g(x))/h,h=0);\n    #lower case limit co
mputes it" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"$\"\"\")%\"xG\"\"
#F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "diff(g(x),x);  #th
e diff commands computes the limit\n               #using differentiat
ion rules" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"$\"\"\")%\"xG\"\"
#F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "f(x)=x*(sin(x^2))^
2/sqrt(1+x^2);\n   #do you rem" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%
\"fG6#%\"xG*(F'\"\"\"-%$sinG6#*$)F'\"\"#F)F/,&F)F)F-F)#!\"\"F/" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 
265 0 "" }{TEXT -1 28 "Do you remember the function" }}{PARA 259 "" 0 
"" {XPPEDIT 18 0 "f(x) = x*sin(x^2)^2/(1+x^2)^(1/2);" "6#/-%\"fG6#%\"x
G*(F'\"\"\"-%$sinG6#*$)F'\"\"#F)F/,&F)F)F-F)#!\"\"F/" }{TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 38 "Let MAPLE find its derivative for you!" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 266 36 "Antidi
fferentiation and integration:" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 19 "Try these commands:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 50 "int(x^2,x); #antidifferentiation (without the  +C)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "int(x^2,x=0..3); #definite integrat
ion" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "Int(x^2,x=0..3); #what the previous command computed
" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 46 "Her
e's a current webworks problem  (Set 8, #7)" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 53 "Int(sqrt(49-x^2),x=-7..7);\nint(sqrt(49-x^2),x=-7..
7);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 267 9 "
Plotting:" }}{PARA 0 "" 0 "" {TEXT -1 63 "Now where did that answer co
me from?  Geometry!  Here's a clue:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "with(plots):  #load the plotting library" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "plot(sqrt(49-x^2),x=-7..7,scaling=
constrained);\n   #once you make the plot and click on it, a lot\n   #
of menu options become available at the top of\n   #your worksheet" }}
{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 114 "You co
uld even check various parts of a more complicated graphing problem.  \+
Here's one of the problems from class:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "f:=x->2/(x^2+2*x-3)+1;" }}{PARA 11 "" 1 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "plot(f(x),x=-5..5,y=
-8..8,color=black);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 41 "?plot;  # to find out more about plotting
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "diff(f(x),x);  #first d
erivative" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 52 "f(-1); #local maximum value, clear from last comman
d" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "maximize(f(x),x=-2..0); #a really easy way to maximiz
e" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "?maximize;  #can I also find the x-value?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "maximize(f(x),x=-2..0,location=true
);\n  #find the x-value too." }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}
{PARA 0 "" 0 "" {TEXT 269 12 "More limits:" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 45 "limit(f(x),x=infinity); #horizontal asymptote" }}
{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 51 "?limit;  #can I compute 1-sided limits?  \n         " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "limit(f(x),x=1,right); #one-sided l
imits!" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "limit(f(x),x=1,left);" }}{PARA 11 "" 1 "" {TEXT -1 0 
"" }}}{PARA 0 "" 0 "" {TEXT 268 20 "The sky's the limit!" }{TEXT -1 
141 "  Can you set up the Newton iteration scheme for the current webw
orks?  We did an example like this in class, and the notes should be p
osted." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
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