Основы Maple

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

Copyright 2001 by Robert M. Corless
All rights reserved

Основы

Getting Started

Быстрый Старт

Sample Maple sessions

Примеры сессий Maple

Third session - heat conduction by Fourier series

Третья сессия - теплопроводность при помощи рядов Фурье

> restart;

> plots[setoptions](colour=black);

>I1 := int( sin(k*Pi*x)^2, x=0..1 );

>I1 := eval( I1, {sin(k*Pi)=0, cos(k*Pi)=(-1)^k} );

>I2 := int( x^2*(1-x^2)*sin(k*Pi*x), x=0..1);

>I2 := eval( I2, {sin(k*Pi)=0, cos(k*Pi)=(-1)^k} );

>I2 := collect( I2, k, factor );

>c := unapply( 2*I2, k );

>fn := n -> add( c(k)*sin(k*Pi*x), k=1..n );

>f5 := fn( 5 );

>plot( f5 - x^2*(1-x^2), x=0..1 );

>f10 := fn( 10 ):

>plot( f10 - x^2*(1-x^2), x=0..1 );

>un := n -> add( c(k)*exp(-k^2*Pi^2*t)*sin(k*Pi*x), k=1..n);

>u5 := un(5);

>diff( u5, t ) - diff( u5, x, x );

>u10 := un(10):

>diff( u10,t ) - diff( u10, x, x );

> plots[contourplot](u10, x=0..1, t=0..0.21, grid=[30,30], colour=black);

> restart:

> plots[setoptions](colour=BLACK);

>read "C:/books/ess/programs/fouriersine.mpl";

> macro(FSS=FourierSineSeries);

>f := FSS(x^2*(1-x^2),x);

>f5 := f(5);

>f10 := f(10):

> plot(f10-x^2*(1-x^2),x=0..1);

>f := FSS(cos(x),x);

>f15 := f(15):

> plot(f15-cos(x),x=0..1);

> restart;

> plots[setoptions](colour=black);

> FourierSineSeries2 := proc( f::operator )
local k, z;
description "FSS2(f::operator):"
" Improved Fourier series of f";
(n,x) -> add( limit( 2*int( sin(k*Pi*z)*f(z), z=0..1 ),k=j) * sin(j*Pi*x),j=1..n)
end proc;

> macro(FSS2=FourierSineSeries2);

>FSS2( x^2*(1-x^2), x );

Error, invalid input: FourierSineSeries2 expects its 1st argument,f,

to be of type operator, but received x^2*(1-x^2)

>f := FSS2( x -> x^2*(1-x^2) );

>f5 := f( 5, x );

>fc := FSS2( x -> cos(Pi*x) );

>fc( 10, x );

С официального разрешения © 2002 Waterloo Maple, Inc