it is not free but it is a wonderfull book to have.  It's a little bit pricey thou.  The link of Joe give it all.

About your firts question, I have

Int(x*sin(2*x)-x*sin(x),x=0..Pi):%=value(%)

In a mathematical point of view, the answer is correct.  But in a practical point of view, I say to my students to take the absolute value since there is no sense in a negative value

mario.lemelin@cgocable.ca

In the "Table of integrals, series and products" of Gradshteyn and Ryzhik, page 307 the answer is

Int(exp(-x^2),x=0..infinity)=sqrt(Pi)/2

and since Maple give the same answer, my response is that your tutorial sheet is wrong.

mario.lemelin@cgocable.ca

I never use plot that way.  Very interesting!  Thanks

mario.lemelin@cgocable.ca

Interresting enough, I did the problems but question myself concerning the second question by the fact that Maple cannot find the antiderivative meaning

f:=cos((1+sin(x))^(1/2))

int(f,x)

int(cos((1+sin(x))^(1/2)),x)

So if you cannot find the integral, how can you plot it?

I am in document mode.

mario.lemelin@cgocable.ca

In Maple 11.02, i try it and this is what i get:

> deq := diff(y(x), x, x)+4*y(x) = cos(2*x);

                          /  2      \                    
                          | d       |                    
                   deq := |---- y(x)| + 4 y(x) = cos(2 x)
                          |   2     |                    
                          \ dx      /                    
> dsolve(deq, y(x));
                                                   1           
              y(x) = sin(2 x) _C2 + cos(2 x) _C1 + - sin(2 x) x
                                                   4           

Remember that the solution of a non-homogenous ODE y = yh + yp where yh is the homogenous part and yp the particular part so that may explain why you have two term.  But as you can see, I only have one....

mario.lemelin@cgocable.ca

> diff(sin(x), x);
                                   cos(x)
> 

Hey thanks!

mario.lemelin@cgocable.ca

The item seems to be an image with nothing in it.  Please let's continue this through my email below.  An 3.09 Meg file is not to big for internet.

mario.lemelin@cgocable.ca

I use a PC.  In Maple, the only way to create a PDF file is to print the worksheet to a virtual printer created by a software call PDFCreator.  Instead of printing on your usual printer, you select the PDF printer and you will get a PDF file ready to be seen with Acrobat Reader.  Here is the link to the site.

http://www.pdfforge.org/

mario.lemelin@cgocable.ca

Thanks for the help page, very interesting.   I will  use it.  BUt I still have 2 problems

1.  I am a lazy person, sometimes, I want to write less so I thought that I could write x(t)' and have the same output than if I wrote diff(x(t),t).  Is it possible?

2.  My pulleys problem is still an open case.  Need help :-)

mario.lemelin@cgocable.ca

Hi

I understand that if you make the change as you made of cos(x*y) to f(x,y), you obtain a PDE in wich the solution is not as obvious as it look.

diff(diff(diff(diff(diff(f(x,y),x),x),y),y),y) = diff(f(x,y),x)*x^3*y^2+6*f(x,y)*x^2*y-6*diff(f(x,y),x)*x/y

Since I never use Maple to solve PDE, my first try show that Maple cannot solve it.  Can you explain a little how to solve it to have the simple solution cos(x*y)?

mario.lemelin@cgocable.ca

Diff(cos(x*y),x,x,y,y,y) = -sin(x*y)*x^3*y^2+6*cos(x*y)*x^2*y+6*sin(x*y)*x

mario.lemelin@cgocable.ca

"Diff(cos(x*y),x,x,y,y,y) = -sin(x*y)*x^3*y^2+6*cos(x*y)*x^2*y+6*sin(x*y)*x"

mario.lemelin@cgocable.ca

For having a pretty printing, you can do this way:

Diff(cos(x*y),x$2,y$3):%=value(%)

it should be has pretty has the image you have sent.

Mario

For the pleasure of applications, I asked the students to solve:

Int(sec(x)/(x+2),x=-1..1)

Maple cannot.  So they calculate the Pade approximant R[4,4] and then they were able to calculate the primitive of that rationnal function (with a little work)

If I do

int(f, x = -1 .. 1.)

Maple give back 1.369112680 and with Pade 1.387637 while with Taylor they get 1.3643

with O(x^10).  When I plot the three function on the interval [-1..1], they all look great.  Witch of these three answers shoul I relie on?  I think that the Padé approximant is a little bit off due to the long manipulations for solving the integral.

By the way, how do you do to put the output of Maple in this windows?

Thanks