Re: differential and integral calculus

[billkreamer]

----- Original Message -----
From: "Andreas Volz" <address@hidden>
To: <address@hidden>
Sent: Thursday, February 03, 2005 14:32
Subject: differential and integral calculus



> 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.
>
You may have seen other responses to your quetion stating that Octave is a
numerical program, rather than a symbolic one. In your example above, even
if you had a program that would integrate symbolically, you should be aware
that evaluating an indefinite integral introduces an arbitrary constant. For
example:
The integral of 3x^2 - 4x  is     x^3 - 2x^2 + C   , where C is the
arbitrary constant.

Octave has routines for evaluating a definite integral numerically.
>
> f(x)=(x^2-3x)*sin x
> f'(x)=?
>
Athough Octave will not provide a symbolic answer for the above example, you
can use the formula below to provide approximations for plotting the
derivative:

f'(x) = limit[as dx approaches zero]((f(x + dx) - f(x))/dx)

Choose dx to whatever accuracy you desire.



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