Maple Symbolic Algebra Package 

A. J. Meir 

 

Copyright (C) A. J. Meir. All rights reserved. 

This worksheet is for educational use only. No part of this publication may be reproduced or transmitted for profit in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system without prior written permission from the author. Not for profit distribution of the software is allowed without prior written permission, providing that the worksheet is not modified in any way and full credit to the author is acknowledged. 

 

 

Introduction to Maple 

 

More on Maple 

 

Even more on Maple 

 

Some examples to whet your appetite: 

 

> restart:with(geom3d):
icosahedron(i,point(o,0,0,0),1):
 

> draw(i(color=yellow),lightmodel=light2,
title=`An Icosahedron`,orientation=[0,30]);
 

Plot
 

> diff(sin(x^2+3),x);
 

`+`(`*`(2, `*`(cos(`+`(`*`(`^`(x, 2)), 3)), `*`(x)))) (1)
 

> int(x^3+3*cos(5*x+4),x=0..3);
 

`+`(`-`(`*`(`/`(3, 5), `*`(sin(4)))), `/`(81, 4), `*`(`/`(3, 5), `*`(sin(19)))) (2)
 

> plot(exp(-x^2),x=-4..4);
 

Plot_2d
 

> restart:with(DEtools):
 

> D(D(x))(t)+9*x(t)=4*cos(a*t);x(0)=0;D(x)(0)=0;
 

 

 

`+`(((`@@`(D, 2))(x))(t), `*`(9, `*`(x(t)))) = `+`(`*`(4, `*`(cos(`*`(a, `*`(t))))))
x(0) = 0
(D(x))(0) = 0 (3)
 

> dsolve({D(D(x))(t)+9*x(t)=4*cos(a*t),x(0)=0,D(x)(0)=0},x(t));
 

x(t) = `+`(`/`(`*`(4, `*`(cos(`+`(`*`(3, `*`(t)))))), `*`(`+`(`-`(9), `*`(`^`(a, 2))))), `-`(`/`(`*`(4, `*`(cos(`*`(a, `*`(t))))), `*`(`+`(`-`(9), `*`(`^`(a, 2))))))) (4)
 

> sol(t):=-8/(-9+a^2)*sin((3-a)*t/2)*sin((3+a)*t/2);
 

`+`(`-`(`/`(`*`(8, `*`(sin(`+`(`*`(`/`(1, 2), `*`(`+`(3, `-`(a)), `*`(t))))), `*`(sin(`+`(`*`(`/`(1, 2), `*`(`+`(3, a), `*`(t)))))))), `*`(`+`(`-`(9), `*`(`^`(a, 2))))))) (5)
 

> env(t):=-8/(-9+a^2)*sin((3-a)*t/2);
 

`+`(`-`(`/`(`*`(8, `*`(sin(`+`(`*`(`/`(1, 2), `*`(`+`(3, `-`(a)), `*`(t))))))), `*`(`+`(`-`(9), `*`(`^`(a, 2))))))) (6)
 

> a:=1:plot([sol(t),env(t),-env(t)],t=0..25,color=[black,red,red]);
 

Plot_2d
 

> a:=2:plot([sol(t),env(t),-env(t)],t=0..25,color=[black,red,red]);
 

Plot_2d
 

> a:=5/2:plot([sol(t),env(t),-env(t)],t=0..25,color=[black,red,red]);
 

Plot_2d
 

> a:=29/10:plot([sol(t),env(t),-env(t)],t=0..25,color=[black,red,red]);
 

Plot_2d
 

>