RE: Books for:Elementary Numerical Computing with Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg20382] RE: [mg20344] Books for:Elementary Numerical Computing with Mathematica
- From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
- Date: Mon, 18 Oct 1999 02:40:29 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Jan Krupa wrote:
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I am looking for book or article which teaches numerical computing with
mathemtica (esp. programming methods for numerical computing in
mathematica version >= 3.0).
There is a book
Elementary Numerical Computing with Mathematica
R.D.Skeel, J.B.Keiper
but it was written for Mathematica2.0 (or 2.2).
Does anybody please could suggest similar book for version 3.0?
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REPLY:
I don't think there are any other books on numerical computing with
Mathematica.
If you read the appropriate portions of The Mathematica Book and a
discussion of Numerics in the Help Browser I think you will be up on all the
differences in Mathematica numerics between versions 2 and the more recent
versions.
To find the discussion on numerics in the Help Browser select
Getting Started/Demos
Demos
Numerics Report (near the bottom of the second column)
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I have a copy of the book by R. Skeel, J. Keiper (no I don't want to sell
it), and I think
it's still relevant. However you may have a hard time finding a copy
because it's out of print. This book is an into to numerical computing that
uses Mathematica to work examples. So for example the book give significant
discussion on Simpson's rule even though it's probably obsolete due to
better methods used in Mathematica's NIntegrate.
If you want information on the fine points of using NIntegrate, NDSolve,
NSum, NProduct ... you should look them up in the Help Browser. Under
"Further Examples" you will find lots of good information. You might also
read the files at:
http://www.mathsource.com/Content22/General/Tutorials/Numerical/0203-948
http://www.mathsource.com/Content22/General/Tutorials/Numerical/0203-937
These tutorials are quite old but still relevant. However, they are
postscript files. If you need a program that can read them see
http://support.wolfram.com/Graphics/Formats/PS/Viewing.html
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Besides that many of the books about Mathematica cover numerical computing
quite a bit. You should go to a well stocked book store and take a look at
some of them.
In particular Mathematica In Action, by Stan Wagon covers a lot on how to
ensure the results from NDSolve are accurate, and how sensitive the solution
is to initial conditions.
-------------------
While the Extra Examples in the Help Browser are very helpful we still need
more information on functions like NIntegrate, NDSolve. I mean the method
option in NIntegrate can be GaussKronrod, DoubleExponential, Trapezoidal,
Oscillatory, MultiDimentional, MonteCarlo, or QuassiMonteCarlo. Under what
conditions do each of these methods work well? How efficient are they when
they work well? Under what conditions should they not be used? The default
method is GaussKronrod, and the only books I found that make any mention of
GaussKronrod devote all of two paragraphs to the subject!
Regards,
Ted Ersek
For Mathematica tips, tricks see
http://www.dot.net.au/~elisha/ersek/Tricks.html