Commands

Command  Description  Example

restart

clear all Maple definitions

                                       restart:
with

load a Maple package  with( DEtools ); with( plots ):

help (also ?) display Maple on-line help

                                       ?DEplot
example

provide examples for a function example( plot );

limit

calculate a limit  limit( sin(x)/x, x=0 );
diff

compute the derivative of an expression diff( a*x*exp(b*x)*cos(c*y), x )

int

definite or indefinite integration int( sin(x), x=0..Pi );

value

evaluate an inert expression (typically used with Limit, Diff, or Int)

                                       G := Int( exp(-x^2), x );
                                       value( G );
Limit

inert (unevaluated) form of limit          Limit( sin(x)/x, x=0 );
Diff

inert (unevaluated) form of diff Diff( exp(x^2), x );

Int

inert (unevaluated) form of int Int( sqrt(x), x=0..1 );

plot

create a 2-dimensional plot of functions plot( u^3, u=0..1, title=` cubic` );

                                       plot( {sin(x), cos(x)}, x=0..Pi );
plot3d

create a 3-dimensional plot of functions plot3d( sin(x+y), x=0..2, y=0..1 );

DEplot

create a plot associated with an ODE or system of ODEs; see ?DEplot for more information

                                       ODE := diff( y(x),x ) = 2*x*y(x);
                                       DEplot( ODE, [y(x)], x=-2..2,
                                               y=-1..1, arrows=SMALL );
display

display a list of plot structures with( plots ):

                                       F:=plot(exp(x), x=0..1, style=line);
                                       G:=plot(ln(x), x=0..1, style=point);
                                       display( [F,G], title=`2 curves` );
solve

solve equations  solve( x^4 - 5*x^2 + 6*x = 2, x );
fsolve

solve using floating-point arithmetic fsolve( 1/10*t+t*exp(-2*t)=1, t);

subs

substitute values into an expression subs( x=r^(1/3), 3*x*ln(x^3) );

simplify

apply simplification rules to an expression simplify( exp( a+ln(b*exp(c)) ) );

factor

factor a polynomial  factor( (x^3-y^3)/(x^4-y^4) );
convert

convert an expression to a different form convert( x^3/(x^2-1), parfrac, x );

collect

collect coefficients of like powers collect( (x+1)^3*(x+2)^2, x );

rhs

right-hand side of an equation

                                       rhs( y = a*x^2 + b );
lhs

left-hand side of an equation

                                       lhs( y = a*x^2 + b );
numer

extract the numerator of an expression

                                       numer( (x+1)^3/(x+2)^2 );
denom

extract the denominator of an expression

                                       denom( (x+1)^3/(x+2)^2 );
evalf

evaluate using floating-point arithmetic evalf( exp( Pi^2 ) );

evalc

evaluate a complex-valued expression (returns a value in the form a+I*b)

                                       evalc( exp( alpha+I*omega ) );
evalb

evaluate a Boolean expression (returns true or false)

                                       evalb( exp(Pi) > Pi^E );
assign

perform assignments (often used after solve or dsolve)

                                       s:=solve( {x+y=1, 2*x+y=3}, {x,y} );
                                       assign( s );
seq

create a sequence

                                       { seq( [0,i], i=-3..3 ) };
dsolve

solve ordinary differential equations; see ?dsolve for a list of available options

                                       dsolve( diff(y(x),x)-y(x)=1, y(x) );
D

differential operator (often used when specifying derivative initial conditions for dsolve)

                                       ODE :=  diff(y(x),x$2) +y(x) = 1;
                                       IC := y(0)=1, D(y)(0)=1;
                                       dsolve( { ODE, IC }, y(x) );
assume

inform Maple of additional properties of objects

                                       assume( t>0 );
about

check assumptions on Maple objects

                                       about( t );