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.
cheers
David Bailey
http://www.dbaileyconsultancy.co.uk
It is probably possible ("evaluation tracing" is the keyword to look
for) but most likely this is not what you want:
Mathematica usually solves problems in a way that differs very much
from the way that a human would solve them. With integrals, for
example, Mathematica may start by differentiating a very long and
complex expression and just try to match coefficients. Hence looking
at the individual steps is not going to tell you much unless you want
to debug/optimize Mathematica internals.
Best,
-Nikolaus
--
=C2=BBIt is not worth an intelligent man's time to be in the majority.
By definition, there are already enough people to do that.=C2=AB
-J.H. Hardy
PGP fingerprint: 5B93 61F8 4EA2 E279 ABF6 02CF A9AD B7F8 AE4E 425C
Unless you are a computer algebra guru I think you will not
be able to follow the way that Mathematica follows in order
to solve one problem, say an integration.
CAS algorithms are completely different than "by hand" evaluations.
Execute for example the following command to take a glance...
Trace[Integrate[x, {x, 0, 2*Pi}], TraceInternal -> True]
"Q: I'm searching for a program that will show step by step how my
equations are solved. Does Mathematica for Students have this capability?
Unfortunately, Mathematica will not provide step-by-step explanations
for your solutions. However, a program could be written in
Mathematica's high-level programming language to provide this feature.
Calculus WIZ, an interactive homework helper based on the most widely
used calculus textbooks, will show you the steps for each calculus
problem. Calculus WIZ is a stand-alone product that can be purchased
at your local campus bookstore or directly from Wolfram Research. "
You can find it at the following link:
http://www.wolfram.com/products/student/mathforstudents/qa.html#previous
Greetings
Sergio Terrazas
-----Mensaje original-----
De: David Bailey [mailto:da...@removedbailey.co.uk]
Enviado el: s=E1b 22/11/2008 4:11
Para: math...@smc.vnet.net
Asunto: Re: Displaying the solution step by step in Wolfram
Mathematica
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
[ www.mcs.st-and.ac.uk ] has kindly undertaken to maintain an archive that
provides downloadable notebooks and PDF files for various Presentations
solutions that have appeared on MathGroup.
http://blackbook.mcs.st-and.ac.uk/~Peter/djmpark/html/
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
djm...@comcast.net
http://home.comcast.net/~djmpark