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Maple 7: A Quick Reference
Prepared by:
Douglas Meade
Department of Mathematics
University of South Carolina
January 2002, updated for Maple 7
(Earlier editions for Maple 6, Maple V, Release 5, and Maple V, Release 4)
Symbols and Abbreviations
Symbol Description Example := assignment f := x^2/y^3; ; terminate command; display result int( x^2, x ); : terminate command; hide result int( x^2, x ): .. specify a range or interval plot( texp(-2t), t=0..3 ); { } set delimiter (a set is an unordered list) { y, x, y }; [ ] list delimiter (lists are ordered) [ y, x, y ]; % refers to previous result (percent) Note: Was " until Maple V, Release 5
Int( exp(x^2), x=0..1 ): % = evalf( % ); " " (see ?strings)
string delimiter (double quote) Note: Changed in Maple V, Release 5 (see %)
plot( sin(10x) + 3sin(x), x=0..2*Pi, title="An interesting plot" ); A name := This is a name.; || (see also ?cat)
concatenate string or name Note: Was. prior to Maple 6
a||3; a||(1..3); ´ ´(see ?uneval) delayed evaluation (single quote) x := ´x´; -> (see ?-> and ?proc)
mapping (procedure) definition f := (x,y) -> x^2*sin(x-y); f(Pi/2,0); @ composition operator (cos@arcsin)(x); @@ repeated composition operator (D@@2)(ln);
Mathematical Operations, Functions, and Constants
Symbol Description Example +, - , , /, ^ add, subtract, multiply, divide, power 3x^(-4) + x/Pi; sin, cos, tan, cot, sec, csc
trigonometric functions sin( theta-Pi/5 ) - sec( theta^2 );
arcsin, arccos, arctan, arccot, arcsec, arccsc
inverse trigonometric functions arctan( 2*x );
exp exponential function exp( 2x ); ln natural logarithm ln( xy/2 ); log10 common logarithm (base 10) log10( 1000 ); abs absolute value abs( (-3)^5 ); sqrt square root sqrt( 24 ); ! factorial k!; =, <>, <, <=, >, >= equations and inequalities Note: E no longer exists; use exp(1)
diff( y(x), x ) + x*y(x) = F(x); exp(Pi) > Pi^exp(1); Pi, I π, i (mathematical constants) Note: Maple is case-sensitive
exp( Pi*I );
infinity infinity (∞) int( x^(-2), x=1..infinity );
NOTES:
- The document is also available on the World Wide Web in either PDF (http://www.math.sc.edu/ meade/maple/maple- ref.pdf) or PostScript (http://www.math.sc.edu/ meade/maple/maple-ref.ps).
- Please send comments, corrections, and suggestions for improvements to [email protected].
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 limit calculate a limit limit( sin(ax)/x, x=0 ); diff compute the derivative of an expression diff( axexp(bx^2)cos(cy), x ) int definite or indefinite integration int( sqrt(x), x=0..Pi ); Limit inert (unevaluated) form of limit Limit( sin(ax)/x, x=0 ); Diff inert (unevaluated) form of diff Diff( axexp(bx^2)cos(cy), x ); Int inert (unevaluated) form of int Int( sqrt(x), x=0..Pi ); value evaluate an inert expression (typically used with Limit, Diff, or Int)
G := Int( exp(-x^2), x ); value( G ); plot create a 2-dimensional plot plot( u^3, u=0..1, title="cubic" ); plot3d create a 3-dimensional plot plot3d(sin(x)cos(y),x=0..4Pi,y=0..Pi); display combine multiple plot structures into a single plot or modify optional settings in a plot (in plots package)
F:=plot( exp(x), x=0..3, style=line ); G:=plot( 1/x, x=0..3, style=point ); plots[display]([F,G], title="2 curves"); solve solve equations or inequalities solve( x^4 - 5x^2 + 6x = 2, { x } ); fsolve solve using floating-point arithmetic fsolve( t/10 + texp(-2t) = 1, t ); dsolve solve ordinary differential equations; see ?dsolve for a list of available options
dsolve( diff(y(x),x)-y(x)=1, y(x) );
odeplot create 2D and 3D plots from solutions obtained by dsolve (with type=numeric); see ?odeplot for more options (in plots package)
S:=diff(x(t),t)=-y(t),diff(y(t),t)=x(t): IC:=x(0)=1,y(0)=1: P:=dsolve({S,IC}, {x(t),y(t)}, numeric): odeplot(P, [[t,x(t)],[t,y(t)]], 0..Pi); odeplot(P, [x(t),y(t)], 0..Pi); DEplot create plot associated with an ODE or system of ODEs; see ?DEplot for more information (in DEtools package)
ODE := diff( y(x),x ) = 2xy(x); DEplot( ODE, [y(x)], x=-2..2, y=-1..1, arrows=SMALL ); 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) ); simplify apply simplification rules to an expression simplify( exp( a+ln(bexp(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 = ax^2 + b ); lhs left-hand side of an equation lhs( y = ax^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 ); subs substitute values into an expression subs( x=r^(1/3), 3xln(x^3) ); eval evaluate an expression with specific values eval( 3xln(x^3), x=r^(1/3)); 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 or FAIL)
evalb( evalf( exp(Pi) > Pi^exp(1) ) );
assign perform assignments (often used after solve or dsolve)
S:=solve( {x+y=1, 2*x+y=3}, {x,y} ); assign( S ); x; y; seq create a sequence seq( [0,i], i=-3..3 ); for... from... to... by... in... while... do
... end do
repetition statement; see ?do for syntax (Note: od is an acceptable substitute for end do)
tot := 0; for i from 11 by 2 while i < 100 do tot := tot + i^ end do; if... then... elif
... else... end if
conditional statement; see ?if for syntax (Note: fi is an acceptable substitute for end if)
if type(x,name) then ’f’(x) else x+1 end if;
assume inform Maple of additional properties of objects assume( t>0 ); about check assumptions on Maple objects about( t );
