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{SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT -1 7 "Maple V" }}}{SECT 0 {PARA 
4 "" 0 "" {TEXT -1 18 "Brief Introduction" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 552 "In 1959 at MIT a group of researchers developed a system
 called MACSYMA, the first computer algebra system. That system was in
tended partially to convince the science community that computers coul
d perform significant intellectual tasks. The system could manipulate \+
symbols as well as numbers, and was useful for tasks for which compute
rs could not be used before. Since then several other computer algebra
 systems were developed, with different underlying philosophies. Three
 such systems have proved especially useful: Mathematica, Maple, and D
erive." }}{PARA 15 "" 0 "" {TEXT -1 138 "Mathematica is the Cadilac of
 computer algebra systems: it is expensive, uses a lot of system resou
rces, but delivers superb performance.\240" }}{PARA 15 "" 0 "" {TEXT 
-1 162 "Maple is the VW of computer algebra systems: it is affordable \+
and sturdy, cheap on system resorces, delivers adequate performance, b
ut lacks an aura of grandeur.\240" }}{PARA 15 "" 0 "" {TEXT -1 216 "De
rive is the car for the non-driver: it has all the features of a real \+
car, but it assists you in handling the controls whenever possible and
 in doing so may occasionally restrict your creativity to avoid mistak
es.\n" }}{PARA 0 "" 0 "" {TEXT -1 409 "To use Maple for Windows it hel
ps to be familiar with Microsoft Windows. When you start Maple, you wi
ll see its main window on the screen and after a seconds Maple will be
 ready for your input. On top of the main window you will find a menu \+
bar which offers several choices. You might want to see what each menu
 item has to offer before starting to use Maple. Three things should b
e kept in mind at all times:" }}{PARA 15 "" 0 "" {TEXT -1 200 "Maple h
as an extremely good help facility, as well as a \221Help Browser\222:
To get help on a particular topic, type help(keyword);\nto find a part
icular command, select 'Help | Glossary' or 'Help | Browse'." }}{PARA 
15 "" 0 "" {TEXT -1 155 "Every command in Maple must by typed in, acco
rding to some syntax rules. Use the help facilities to find out the ex
act form of each command and its options" }}{PARA 15 "" 0 "" {TEXT -1 
206 "Every command in Maple must end with a semicolon. If you forget t
o enter a semicolon, no computation will happen. However, you can simp
ly type a semicolon on the next line by itself to start the computatio
n" }}{PARA 0 "" 0 "" {TEXT -1 119 "The best way to learn Maple is to u
se it, so here are some examples that you should keep in mind througho
ut the course." }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 7 "Vectors" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 219 "A vector is an arrow in three dim
ensional space that is characterized by its length and direction. Mapl
e has a variety of functions defining and dealing with vectors. Before
 you can use them, you must issue the command " }{TEXT 256 13 "with(li
nalg);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "wi
th(linalg);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "To define a vecto
r, use the command: vector([x, y, z]), where x, y, z are the component
s of the vector." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "v1 := v
ector([1,2,0]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "v2 := ve
ctor([2,-1,2]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 114 "You can compu
te the dot and the cross product of vectors using the dotprod(v1, v2) \+
and crossprod(v1, v2) commands:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 16 "dotprod(v1, v2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 
"crossprod(v1, v2);" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 10 "Questions
:" }}{PARA 15 "" 0 "" {TEXT -1 32 "Visualize the vectors v1 and v2." }
}{PARA 15 "" 0 "" {TEXT -1 50 "Does the dot product result in a name o
r a vector?" }}{PARA 15 "" 0 "" {TEXT -1 52 "Does the cross product re
sult in a name or a vector?" }}{PARA 15 "" 0 "" {TEXT -1 50 "What migh
t the significance of the dot product be?" }}{PARA 15 "" 0 "" {TEXT 
-1 52 "What might the significance of the cross product be?" }}}}
{SECT 0 {PARA 4 "" 0 "" {TEXT -1 6 "Planes" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 241 "A linear plane is a surface in three dimensional space. \+
There are several ways to specify a plane. The most general form is Ax
 + By + Cz = D. The easiest representation of a plane has the form z =
 M*x + N*y +K for some constants M, N, and K." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 33 "P1 := z = x + y;\nP2 := z = x - y;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot3d(rhs(P1),x=-10..10,y=-10..10)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "plot3d(rhs(P2), x=-10.
.10,y=-10..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot3d(
\{x+y,x-y\},x=-10..10,y=-10..10);" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 
-1 10 "Questions:" }}{EXCHG {PARA 15 "" 0 "" {TEXT -1 30 "How does the
 plane z = 3 look?" }}{PARA 15 "" 0 "" {TEXT -1 30 "How does the plane
 z = x look?" }}{PARA 15 "" 0 "" {TEXT -1 30 "How does the plane z = y
 look?" }}{PARA 15 "" 0 "" {TEXT -1 31 "Do two planes always intersect
?" }}{PARA 15 "" 0 "" {TEXT -1 63 "If to planes intersect, what does t
heir intersection look like?" }}{PARA 15 "" 0 "" {TEXT -1 58 "How many
 points do you need to uniquely determine a plane?" }}{PARA 15 "" 0 "
" {TEXT -1 94 "How would you find the equation of the plane going thro
ugh points (1,1,0), (1,0,1), (1, 1, 1)?" }}}}}{SECT 0 {PARA 4 "" 0 "" 
{TEXT -1 15 "Curves in Space" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "A \+
curve in space is a function where one variable is mapped to a vector.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot([sin(t), cos(t),t=
0..2*Pi]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "with(plots):
\nspacecurve([t, sin(t), cos(t)],t=0..2*Pi,numpoints=200);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "spacecurve([sin(t)-t*cos(t),cos(t)+
t*sin(t),t^2],t=-0..100,numpoints=400);" }}}{SECT 0 {PARA 4 "" 0 "" 
{TEXT -1 10 "Questions:" }}{EXCHG {PARA 15 "" 0 "" {TEXT -1 32 "Find t
he equation of an ellipse." }}{PARA 15 "" 0 "" {TEXT -1 59 "What's a g
ood name for the above curve [t, sin(t), cos(t)]?" }}{PARA 15 "" 0 "" 
{TEXT -1 62 "What's a good name for the above curve [sin(t)-t cos(t), \+
...]?" }}{PARA 15 "" 0 "" {TEXT -1 46 "Find the equation of a spiral i
n 2 dimensions." }}{PARA 15 "" 0 "" {TEXT -1 33 "Find the equation of \+
a spiral in " }}}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 17 "Surfaces in Sp
ace" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Surfaces are functions of t
wo variables that have the form z = f(x, y)." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 44 "plot3d(-4*x / (x^2+y^2+1),x=-3..3, y=-3..3);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plot3d((x^2 + y^2) * exp(1-
x^2-y^2), x=-3..3,y=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
33 "plot3d(y^2-x^2, x=-4..4,y=-4..4);" }}}{SECT 0 {PARA 4 "" 0 "" 
{TEXT -1 10 "Questions:" }}{EXCHG {PARA 15 "" 0 "" {TEXT -1 165 "With \+
functions of one variable one is often interested in finding max/min. \+
Could there be a similar concepts for functions of 2 variables? What m
ight be the problem?" }}{PARA 15 "" 0 "" {TEXT -1 160 "If you remember
 how to find a max/min for functions of one variable, could there be a
 similar approach to functions of two variables? What might be the pro
blem?" }}{PARA 15 "" 0 "" {TEXT -1 77 "Try to find the minimum and max
imum of the first surface as best as possible." }}}}}{SECT 0 {PARA 4 "
" 0 "" {TEXT -1 20 "Multiple Integration" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 214 "Integration in one variable can be interpreted - sometim
es - as the area under a curve. In several variables it can be interpr
eted - sometimes - as the volume under a surface, but there are more o
ptions to explore." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot(
sqrt(3^2 - x^2), x=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
30 "int(sqrt(3^2 - x^2), x=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "plot3d(3^2 - x^2 - y^2, x=-3..3, y=-3..3);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "int(int(sqrt(3^2 - x^2 - y^2
), y = -sqrt(3^2-x^2)..sqrt(3^2-x^2)),x=-3..3);" }}}{SECT 0 {PARA 4 "
" 0 "" {TEXT -1 9 "Questions" }}{EXCHG {PARA 15 "" 0 "" {TEXT -1 96 "W
hat is the first equation, and what exactly does the number of the fir
st integration represent?" }}{PARA 15 "" 0 "" {TEXT -1 98 "What is the
 second equation, and what exactly does the number of the second integ
ration represent?" }}{PARA 15 "" 0 "" {TEXT -1 61 "How would you find \+
the volume of a square with side length 2?" }}{PARA 15 "" 0 "" {TEXT 
-1 54 "What do you think is the value of the double-integral " }
{XPPEDIT 18 0 "Int(Int(x,x = 0 .. 1),y = 0 .. 1);" "6#-%$IntG6$-F$6$%
\"xG/F(;\"\"!\"\"\"/%\"yG;F+F," }}}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 
13 "Vector Fields" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "fieldplot([0,x],x=-1..1,y=-1
..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "fieldplot([y,0], x
=-1..1,y=-1..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "fieldpl
ot([x,0], x=-1..1,y=-1..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
56 "fieldplot([-x/(x^2+y^2), -y/(x^2+y^2)],x=-1..1,y=-1..1);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "fieldplot3d([x/(x^2+y^2+z^2)
,y/(x^2+y^2+z^2),z/(x^2+y^2+z^2)],x=-3..3,y=-3..3,z=-3..3);" }}}{SECT 
0 {PARA 4 "" 0 "" {TEXT -1 10 "Questions:" }}{EXCHG {PARA 15 "" 0 "" 
{TEXT -1 58 "What objects in nature can be modeled with a vector field
?" }}{PARA 15 "" 0 "" {TEXT -1 59 "What objects in physics can be mode
led with a vector field?" }}{PARA 15 "" 0 "" {TEXT -1 96 "Describe in \+
your own words the last 2D vector field above. What might cause such a
 vector field?" }}{PARA 15 "" 0 "" {TEXT -1 96 "Describe in your own w
ords the last 3D vector field above. What might cause such a vector fi
eld?" }}}}}}{MARK "7 7 1 0 0" 49 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }