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Maple
Maple for Windows
Bert G. Wachsmuth
In 1959 at MIT a group of researchers developed a system called MACSYMA, the first
computer algebra system. That system was intended partially to convince the science
community that computers could perform significant intellectual tasks. The system could
manipulate symbols as well as numbers, and was useful for tasks for which computers 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 Derive. Mathematica is the Cadilac of computer algebra systems: it
is expensive, uses a lot of system resources, but delivers superb performance. Maple is
the VW of computer algebra systems: it is affordable and sturdy, cheap on system resorces,
delivers adequate performance, but lacks an aura of grandeur. Derive is the car for the
nondriver: 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 mistakes.
To use Maple for Windows it helps to be familiar with Microsoft Windows. When you start
Maple, you will 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 be kept in mind at all times:
 Maple has an extremly good help facility, as well as a ‘Help Browser’:
 To get help on a particular topic, type help(keyword); 
 to find a particular command, select Help  Browse 

 Every command in Maple must by typed in, according to some syntax rules. Use the help
facilities to find out the exact form of each command and its options 
 Every command in Maple must end with a semicolon. If you forget to enter a semicolon, no
computation will happen. However, you can simply type a semicolon on the next line by
itself to start the computation 
A Brief Maple Session
Start Maple and type the lines on the left. Maple should act in the way indicated.
Remember, Maple is a Windows program so you can use the familiar window resizing commands,
cutandpaste, scrolling, etc.
help(intro); 
Displays an introductory help message about Maple 
123  5/2 * (44/7  99/2)^2; 
add fractions and numbers 
evalf(%); 
gives a floatpoint (decimal) approximation of last result. The single percent stand
for the ‘last computed expression’ 
evalf(Pi,100); 
show decimal approximation of Pi to 100 decimals 
P := x > x^2  x  6; 
defines a function P(x) 
P(sqrt(2)); 
evaluates P at root(2) 
factor(P(x)); 
factors P(x) over the rationals 
expand(%); 
expands a factored expression 
solve(P(x)=0,x); 
solve the equation P(x) = 0 for x 
plot(P(x),x=5..5) 
plots polynomial for x in [5,5] 
f := x > x^3  2*x; 
defines a function f(x) 
plot({P(x),f(x)},x=5..5); 
plots P(x) and f(x) in one coordinate system 
Here is a short list of useful Maple functions. Use the help facility to find out more
about each command.
Essential Commands
diff 
find derivatives 
plot 
create a twodimensional plot of an expression 
evalf 
evaluate an expression 
simplify 
simplify an expression 
int 
integrate expressions (definite /indefinite integral) 
solve 
solve an equation or system of equations 
limit 
calculate the limiting value of an expression 
subs 
substitute one expression into another 
% 
single percent stand for last computed expression 
%% 
double percent stand for secondtolast computed expression 
More Commands
assume 
make assumptions such a a variable being positive 
normal 
normalize a rational expression 
convert 
convert an expression to a different form 
numer 
extracts numerator of fraction 
denom 
extracts denominator of fraction 
rhs, lhs 
extract righthandside or lefthandside of an equations 
expand 
simplify an expression by distribution law 
seq 
generates a sequence according to some rule 
factor 
factor a polynomial 
sum 
finds the sum of expressions 
fsolve 
find approximate solutions 

Functions
abs(x) 
absolute value 
exp(x), E^x 
exponential function 
sin(x), cos(x), tan(x) 
trig. Functions 
log(x), ln(x) 
natural logarithm 
sqrt(x) 
square root function 
arctan(x), arcsin(x), arccos(x) 
inverse trig. Functions 
Constants
Pi 
constant Pi = 3.1415 
infinity 
positive infinity 
E or exp(1) 
exponential number e = 2.7182 

Simple Programming
defining simple functions 
fname := x > expression;

iterations 
for i from 1 by 2 to 10 do
expression;
od;

defining general functions 
fname := proc(x)
expression1;
expression2;
...;
end;

conditional evaluation 
if condition1 then
statement
else
statement
fi;


There are several nice booklets available which explain Maple with a student's
viewpoint in mind. One such booklet is usually provided when you purchase the Student
Edition of Maple. Another very nice book is Maple V: First Leaves' by B.W. Char and
others, Springer Verlag 1992.
