WATERLOO MAPLE

WHAT IS MAPLE??

Maple is a general purpose computer algebra system, designed to solve mathematical problems and produce high-quality technical graphics. It is easy to learn, but powerful enough to calculate difficult integrals in seconds. Maple incorporates a high-level programming language which allows the user to define his own procedures; it also has packages of specialized functions which may be loaded to do work in group theory, linear algebra, and statistics, as well as in other fields. It can be used interactively or in batch mode, for teaching or research.

MAPLE CONSTANT / COMMAND EXAMPLES
All of Maple's commands and constants are CASE SENSITIVE

Basic Commands

> Pi; (Maple constant for Mathematical Pi ≈ 3.14...)

> infinity; (Maple constant for ∞)

> sqrt(x); (Returns the square root of x)

> a:=5; (Stores 5 into variable a)

> ceil(5.5); (Rounds the number up - in this case, 6 will be returned)

> floor(5.5); (Rounds the number down - in this case, 5 will be returned)

> evalf( Pi ); (Returns numerical approximation of Pi)

> evalf( 4/5 ); (Returns numerical approximation of 4/5 - in this case, answer w ill be .8000)

Function Assignments and Calls

> f:=x->x^2+5; (Stores x^2+5 into function f(x) -- f(x) = x^2 + 5)

> f(5); (Returns the value of function f(x) with x=5 - in above case y(5) = 30)

> g:=(x,y,z)->x+2*y+z; (Declares g(x,y,z) - a function of more than one parameters)

> g(1,2,3); (Calls the g(x) function with x=1, y=2, and z=3 - in above case g(1,2,3) = 8)

Algebra Commands

> solve( 30 = 5*x , x ); (Solves equation for variable x - in this case, answer will be +6, -6)

> plot( f(x) , x=-5..5); (Plots a graph f(x) onto the screen with domain -5 to 5)

> plot( f(x) , x=-5..5 , y=-8..8 ); (Plots graph f(x) onto screen with domain -5 to 5 and range -8 to 8)

> expand( (x+2)*(x-5) ); (Expands the factor out - in this case x² - 3x - 10 will be returned)

> factor( x² - 3x - 10 ); (Factors the given equation - in this case (x+2)*(x-5) is returned)

Calculus Commands

> diff( f(x) , x ); (Takes the derivative of f(x) with respect to x - in this case, answer will be 2x)

> diff( f(x) , x$2 ); (Takes the 2nd derivative of f(x) with respect to x - in this case, answer will be 2)

> int( f(x) , x ); (Takes the indefinite integral of f(x) with respect to x)

> int( f(x) , x , x=1..5 ); (Evaluates the integral of f(x) with respect to x from 1 to 5)

> limit( f(x) , x=5 ); (Takes the limit of f(x) as x approaches 5)

> limit( f(x) , x=5 , right ); (Takes the limit of f(x) as x approaches 5 from the RIGHT side)

Differential Equations Commands

> with( DEtools ); (Imports a number of commands into maple for use with Differential Equations)

> DE1:=diff(y(x),x,x)-x*y(x)=0; (Assigns Airy's Equation to DE1)

> DE2:=diff(y(x),x)=2*x*y(x)/(x^2-(y(x))^2); (Assigns a non-linear differential equation to DE2)

> DEplot(DE1,y,x=0..5,y=-3..3); (Plots the direction fields of DE1 with y the dependant variable)

> DEplot(DE1,y,x=0..5,{[0,0],[0,1]},y=-3..3); (Plots the direction fields of DE1 the lines going through the two points (0,0) and (0,1) superimposed on top of the graph)

Conversions

> convert( 1.5 , rational ); (Converts the number to its rational form - 3/2 is returned in this case)

> convert( 123 , binary ); (Converts the number to its binary form - 1111011 is returned in this case)

> convert( 123456 , hex ); (Converts the number to hex - '1E240' is returned in this case)

Environment Variables

> Digits := 10; (Number of digits of precision that Maple uses - by default, this number is set to 10)

> Rounding := nearest; (DEFAULT VALUE - Maple always rounds to the nearest number)

> Rounding := 0; (Maple always rounds towards zero)

> Rounding := infinity; (Maple always rounds towards positive infinity)

> Rounding := -infinity; (Maple always rounds towards negative infinity)

** Environment variables affect the current session ONLY - if something gets messed up, you can always close and open up Maple again and all the environment variables will be back to their default values **

REMEMBER: Maple includes a complete help system with it. If you're unsure about a command, or just want to learn more about it, just move the blinking cursor over the command in question and hit F1. The help screen for that command will automatically come up.