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Re: Displaying the solution step by step in Wolfram Mathematica

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  • Subject: [mg93716] Re: [mg93673] Displaying the solution step by step in Wolfram Mathematica
  • From: "David Park" <djmpark at>
  • Date: Mon, 24 Nov 2008 04:11:13 -0500 (EST)
  • References: <11152412.1227263748089.JavaMail.root@m02>

I didn't immediately answer this because if it is about actually solving
general integral equations it is beyond what I have experience with. But
some of the responses referred to the straight evaluation of integrals and
that I can say something about.

The Presentations package has a subsection called Student's Integral that
allows the step by step evaluation of definite or indefinite integrals. This
contains commands for operating on an integral expression. It doesn't just
show the steps that Mathematica might (or might not) use but allows the
student (or researcher) to specify the steps to be used. The sub-package
comes with a BasicIntegralTable, such as students might use, or allows users
to construct their own integral table. Alternatively at any point an
integral can be turned over to the regular Mathematica Integrate or
NIntegrate command.

The user writes an integrate command (with a small i) that keeps it in an
unevaluated form, and then operates on it by various commands. The user can
operate on the integrand, say by using Apart or CompletTheSquare. Integral
sums can be broken our and constants taken outside of the integral. The user
can use change of variable, integration by parts or trigonometric
substitution. Integration by parts throws off a panel of information showing
the internal substitutions. Trigonometric substitution throws off a triangle
diagram showing the expressions on each side. Definite integrals return a
LimitsBracket expression such as is usually seen in textbooks that can then
be evaluated.

Peter Lindsay at the Mathematical Institute in the University of St Andrews
[ ] has kindly undertaken to maintain an archive that
provides downloadable notebooks and PDF files for various Presentations
solutions that have appeared on MathGroup. 

A Step by Step Integration example for the volume of a surface of revolution
using integration by parts will be shown there.

Mathematica does many things automatically and most users prefer it that
way. For teaching purposes this is often a problem. Nevertheless, it is
possible to work around it and create definitions and possibly formatting
that allows students to work conveniently at a more basic level. The
developers of Mathematica can't get every convenient thing, for every field,
in there. But that doesn't mean that Mathematica doesn't have the capability
to tackle these kinds of applications. It is just that users and third party
developers have to develop some of these applications.

Mathematica is not so much a tool for doing mathematics as a meta-tool for
making the tools to conveniently do mathematics on specific applications.

David Park
djmpark at 

From: yarlan7 at [mailto:yarlan7 at] 


 I have such a question: Is it possible to display in Mathematica the
solution for example of integral equation step by step? Not only the
final solution. If yes, how to do it? I've not found anything about
this in Documentation Center unless I missed it.


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