## 1505 Reputation

18 years, 217 days

```--------------------------------------
Mario Lemelin```
```Maple 14.00 Win 7 64 bits
Maple 14.00 Ubuntu 10,04 64 bitsmessagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987```

## Unfortunately...

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.

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

## Thanks a lot...

I never use plot that way.  Very interesting!  Thanks

mario.lemelin@cgocable.ca

## Am I the only one...

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?

## Sorry, I forgot to say that...

I am in document mode.

mario.lemelin@cgocable.ca

## term of cos(2*x)...

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

## Let's try it.......

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

```

Hey thanks!

mario.lemelin@cgocable.ca

## THe item...

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

## PDFCreator...

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

## Very interesting but.........

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

## PDE...

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

## Still a test, the last one...

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

## This is a test, do not reply!...

"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

## Here for the pretty printing...

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

## A little bit more than I asked for......

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

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