Основы Maple

Robert M. Corless
Department of Applied Mathematics
University of Western Ontario
London, Canada

Copyright 2001 by Robert M. Corless
All rights reserved

Programming in Maple

Программирование в Maple

Operators and modules

Операторы и модули

> restart;

>eval( diff(f(x),x), x=3 );

> restart;

>f := t -> t*sin(t) ;

> f(x^2+a);

>g := (t::complex(numeric)) -> t*arcsin(t) ;

Error, invalid input: g expects its 1st argument, t,

to be of type complex(numeric), but received x

> g(1+I);

> g(1.+I);

>g( 2. );

>g( 2.+0.*I );

>g( 2.-0.*I );

> restart;

>Aye := f -> unapply(int(f(x),x),x);

>Aye( t->t^2 );

>Aye( t->1/t );

>t -> sin(t);

> 2(anything);

> 2(a+b);

> restart;

> series( f(x), x=a, 4 );

> D(g(h));

>D( g@h );

> D(g*h);

>D(h) := 0;

>D(x) := 1;

> D(F@x);

> D(x^2);

> D(g^2);

> restart;

> interface(imaginaryunit=j);

> finite_differences := proc( h::{name,complex(numeric)} )
description "Generator for finite difference"
" operators with step size h ";
module()
export I, E, Delta, delta, S;
local t, x, k, N;
E := f -> (x->f(x+h));
Delta := f -> (t->((E(f)(t)-f(t))/h));
delta := f -> (x -> (f(x+h)-f(x-h))/(2*h) );
I := f -> unapply( int(f(t), t=0..x), x );
S := f -> unapply( sum(f(k*h), k=1..N), N );
end module;
end proc:

>hop := finite_differences( epsilon );

>with( hop );

>esin := E(sin);

>esin( phi );

>E( esin );

>E( esin )(a);

> (E@@2)(sin);

> (E@@3)(sin)(a);

>F := I( sin );

>DeltaF := Delta( F );

>DelF := DeltaF( t );

>limit( DelF, epsilon = 0 );

>S( m->m^2 );

>sinsum := S( n->sin(n*Pi) );

> sinsum( m );

> combine( %, trig );

>eval( %, epsilon=1/m );

>limit( %%, epsilon = 0 );

С официального разрешения © 2002 Waterloo Maple, Inc