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MathGroup Archive 2004

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Re: Step by step answer ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51571] Re: [mg51534] Step by step answer ?
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Sat, 23 Oct 2004 00:21:59 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200410220220.WAA07219@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

If you want to see how derivatives are calculated step-by-step, go to 
calc101.com.  To see how indefinite integrals are calculated 
step-by-step, go to calc101.com but you have to pay a modest fee in this 
case (except for some "canned" examples).

However, the procedures shown at that site, especially for integrals do 
not have to be using -- and probably do NOT use -- the actual algorithm 
that the Mathematica kernel uses!

For example, an efficient way to evaluate many integrals of rational 
functions is to write down the form of the integral (involving perhaps 
inverse trig functions, logs, etc.) with as-yet-unknown coefficients, 
then to differentiate the form of the result, equate it with the given 
function to be integrated, and solve algebraic equations for the unknown 
coefficients.

On the other hand, this is NOT the way that integration of rational 
functions is normally taught in calculus!

Bruno Robin wrote:
> Hi all,
> 
> It seems that mathematica does not provide a step by step answer like
> a teacher. Do yo know a tool that does it ?

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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