Mathematica Documentation and Packages Questions

1. What MMA books do people like?
2. How do I find out all the packages available to me?
3. Is there a quaternion package for MMA?
4. Does MMA have a tensor package?
5. Can I solve partial differential equations with MMA?
6. How do I solve Tridiagonal matrices?

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1. What people think is the best MMA book. The Wolfram book is OK, but I'd prefer something that went into more depth and didn't jump around as much.

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   I rather like "Mathematica for Scientists & Engineers" by Thomas B. Bahder, Addison-Wesley, 1995, 846pp, ISBN 0-201-54090-8. Chapter 8 of this book has a section on vectors and tensors, including MathTensor from Mathsolutions Inc

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2. Everyone seems to know all these packages that need to be loaded in before they can be used. They're not mentioned in the Wolfram book, at least, not 2nd ed. How do I learn about these packages too? Is there a book or gopher or ftp or web site that I can get a complete listing of all these packages?

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   Guide to Standard MMA Packages is a technical report that can be ordered from Wolfram. Costs about $20. It's the only reference I've found to the standard packages.

   
   

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3. Does anybody know of a quaternion package for Mathematica?

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   Searching MathSource, Wolfram Research's electronic libarary of MMA materials, using the keyword "quaternion" returns the following item:

   0207-694: Quaternions Jason Kastner Quaternions.m (13 Kb)

   This package implements Hamilton's quaternion algebra. MathSource is accessible by email mathsource@wolfram.com, by ftp/gopher mathsource.wolfram.com and WWW (http://www.wolfram.com/MathSource.html).

   
   

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4. Does MMA have a tensor package?

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   A commercial package called MathTensor http://smc.vnet.net/MathTensor.html is available, but there's also my freeware package Ricci, available at http://www.math.washington.edu/~lee/Ricci or through MathSource.

   
   

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5. Can I solve partial differential equations with Mathematica?

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   Mathematica has built-in PDE solvers. Look in the help browser's master index under PDE and you'll find the references on how to solve them. Have a look at the <
   

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6. How do I solve Tridiagonal Matrices?

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   <<LinearAlgebra`Tridiagonal`
   {a, b, c, d} = {{7, 1, 11}, {4, 8, 2, 12}, {5, 9, 3},{2,3,4,5}}
   

   Using TridiagonalSolve[a,b,c,d] returns
   {-(28/9), 26/9, 5/27, 20/81}