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: ------------------ 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? ------------------------ 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) ------------------- 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 ------------------- 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