From help-request at octave dot org Fri Feb  4 21:02:13 2005
Subject: Re: differential and integral calculus
From: Paul Kienzle <pkienzle at users dot sourceforge dot net>
To: Andreas Volz <lists at brachttal dot net>
Cc: help at octave dot org
Date: Fri, 4 Feb 2005 22:05:55 -0500

The symbolic toolbox in octave-forge can handle differentiation:

   octave:1> symbols
   octave:2> x=sym('x')
   x =

   x
   octave:3> f = x^3-2*x^2+5
   f =

   5.0+x^(3.0)-(2.0)*x^(2.0)
   octave:4> differentiate (f,x)
   ans =

   (3.0)*x^(2.0)-(4.0)*x

This can be improved somewhat with awkward syntax:

   octave:5> f = x^vpa("3")-vpa("2")*x^vpa("2")+vpa("5")
   f =

   5+x^3-2*x^2
   octave:6> differentiate (f,x)
   ans =

   3*x^2-4*x
   octave:7> f = Sin(x)*(x^vpa("3")-vpa("2")*x^vpa("2")+vpa("5"))
   f =

   (5+x^3-2*x^2)*sin(x)
   octave:8> differentiate (f,x)
   ans =

   (3*x^2-4*x)*sin(x)+cos(x)*(5+x^3-2*x^2)

To make it more usable, somebody could modify the type operations
to automatically recognize that they are working with integers and
create unlimited precision integers out of them.

There are also some primitive symbolic integration routines in the
underlying library GiNaC, but it only operates on polynomials.

- Paul

On Feb 3, 2005, at 2:32 PM, Andreas Volz wrote:

> Hi,
>
> I'm a octave newbie and try to work with differential and integral
> calculus. I need some help to get a working example for this. Could you
> help me?
>
> Here is a simple example:
>
> f(x)=x^3+-2x^2+5
> f'(x)=3x^2-4x
>
> and for example integrating f'(x) to see that f(x) results.
>
> And what is with more difficult calculations? I know only the german
> names, so perhaps I do a wrong translation. What is with chain rule
> (Kettenregel), quotient rule (Quotientenregel) or all the other funny
> things to do differential or integral calculus. Could octave detect
> which rule to use for which function or have I to tell octave the right
> rule? Can octave do a differential calculus for this?
>
> f(x)=(x^2-3x)*sin x
> f'(x)=?
>
> I hope someone could help me with this questions. Some friends are
> working with matlab or maple and told me this is working with this 
> apps.
> So I hope it works also with octave.
>
> regards
> Andreas
>
>
>
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