Introduction to Maple

all commands end with a semicolon (;) or a full colon (:) (the latter
	supresses the output)

% stands for the output of the previous command

assignment of a value is done with :=

= is used for the equality in an equation, etc.

help(topic);
	same as ??topic

restart		clear internal memory

Pi		the constant 3.1415...
I		the imaginary unit, sqrt(-1)

define functions:
	f:=x->x^2;
	g:=(x,y)-> x+y^3;
	p := x -> piecewise( x<0, -1, x>1, 2*x, x^2 );
	turn an expression into a function: h := unapply(x^2 + 1/2, x);

ifactor		integer factorization
factor
simplify
normal		simplify fractions
expand
seq		create a sequence

evalf	floating point evaluation
	e.g.:	evalf( sqrt(3));
		evalf( % , 50 ); (50 digits)

sum	e.g.:	sum( (1+i)/(1+i^4), i=1..10 );
		sum( 1/k^2, k=1..infinity );

product	e.g:	product( ((i^2+3*i-11)/(i+3)), i=0..10 );

convert		e.g.,	to polar: evalf( (3+5*I)/(7+4*I) , 50 );
			convert( (a*x^2+b)/(x*(-3*x^2-x+4)), parfrac, x );
			convert( cot(x), exp );

standard functions, constants: Pi, GAMMA, exp

assigning variable names:	e.g.:	expr1 := (41*x^2+x+1)^2*(2*x-1);
					expr2 := expand(expr1);

equations		eqn := x^3-1/2*a*x^2+13/3*x^2 = 13/6*a*x+10/3*x-5/3*a;
			solve( eqn, {x} );
			eval( eqn , x=1/2*a );

			solve( {eqn1, eqn2, eqn3, eqn4}, {a, b, c, d} );
			eval( {eqn1, eqn2} , % );

			solve( arccos(x) - arctan(x)= 0, {x} );

			solve( abs( (z+abs(z+2))^2-1 )^2 = 9, {z});

			solve( {x^2<1, y^2<=1, x+y<1/2}, {x,y} );

			ineq := x+y+4/(x+y) < 10:
			solve( ineq, {x} );

			expr := 2*sqrt(-1-I)*sqrt(-1+I):is( expr <> 0 );
			

graphics    display	if the plot is produced with "characters",
			you can have it displayed in a separate window with
			the command

				plotsetup(x11);

			(for users of Linux/Unix). For other options, see
			help(window). 

			E.g., to save the plot as a Postscript file, use
			plotsetup(ps), but you might achieve this also by
			"printing" from the plot window.

		2D	plot( tan(x), x=-2*Pi..2*Pi, y=-4..4, discont=true,
			      title="y = tan(x)" ); 

			plots package:
				implicitplot( { x^2+y^2=1, y=exp(x) }, x=-Pi..Pi,
					y=-Pi..Pi, scaling=CONSTRAINED ); 

			plottools package:

				c := circle( [0, 0], 1, color=green ):display( c,
					scaling=CONSTRAINED, title="Unit Circle" ); 

		3D	plot3d( x*exp(-x^2-y^2), x=-2..2, y=-2..2, axes=BOXED,
				title="A Surface Plot" );

				can rotate the plot using the mouse

			p := display( seq( cutout(v, 4/5), v=stellate(dodecahedron(), 3) ),
				style=PATCH ):
				q := display(cutout(icosahedron([0, 0, 0], 2.2), 7/8) ):
				display( p, q, scaling=CONSTRAINED, title="Nested Polyhedra" );

		animation (plots package)

			animate3d( cos(t*x)*sin(t*y), x=-Pi..Pi, y=-Pi..Pi, t=1..2 );

				use Play from Animation menu

		inequalities

			inequal( { x+y > 0, x-y <= 1, y = 2 }, x=-3..3,
				y=-3..3, optionsfeasible=(color=red),
				optionsopen=(color=blue, thickness=2),
				optionsclosed=(color=green, thickness=3),
				optionsexcluded=(color=yellow) );

derivatives	diff( f(x), x);
		diff( f(x), x, x);

antiderivatives	int(f(x), x);

integrals	int(f(x), x=1..2);

limits		limit( (2*x+3)/(7*x+5), x=infinity );

		limit( tan(x+Pi/2), x=0, left );
		limit( tan(x+Pi/2), x=0, right );

series		approx1 := series( sin(4*x)*cos(x), x=0 );

		increase order of the series:
			Order := 12;

		plot the series truncation and the original:

		poly1 := convert( approx1, polynom );	
		plot( {sin(4*x)*cos(x), poly1}, x=-1..1, y=-2..2, title = 
			cat( convert(expr, string)," vs. Series
			Approximation" ) );

next sections:	7. Differential equations
		8. Linear algebra
		9. Finance and statistics
		10. Programming
		11. Online help
		12. Summary