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== Useful things ==

=== maxima ===
If you need symbolic math software and don't have access to Mathematica or Maple, check out [http://maxima.sourceforge.net/ maxima] (thanks to Aditya for the tip).  There are binaries for Windows and Linux, though installing on Mac is a bit more challenging.  On Linux, I found xmaxima provided a nice UI if you're not already an Emacs user.  --[[User:Chloe|Chloe]] 12:01, 21 January 2008 (PST)

=== Lagrange Multipliers ===
This will help with 7.42 a
If we have a function of <math>n</math> variables, <math>f(x_1,x_2,\ldots,x_n)</math> that we want to optimize under a constraint of the form <math>g(x_1,x_2,\ldots,x_n) = c</math> where <math>c</math> is constant, we can use Lagrange multipliers.  Basically do

<math>\nabla(f) = \lambda\nabla(g)</math>

where <math>\nabla(f)</math> is the gradient vector of <math>f(x_1,x_2,\ldots,x_n)</math>, <math>\nabla(g)</math> is the gradient vector of <math>g(x_1,x_2,\ldots,x_n)</math>, and <math>\lambda</math> is a constant to be determined.

You will get <math>n</math> equations of the form
<math>\frac{\partial f}{\partial x_i} = \lambda(\frac{\partial g}{\partial x_i})</math>, along with the original constraint equation <math>g(x_1,x_2,\ldots,x_n) = c</math>, makes <math>n+1</math> equations of <math>n+1</math> unknowns, which can be solved to find the optimum (minimum or maximum, to be determined using other means).  This method makes 7.42a much, much, much ... simpler.--[[User:Nick|Nick]] 17:37, 29 January 2008 (PST)

See [[Wikipedia: Lagrange multiplier|Wikipedia]] for some examples.

=== Matrices ===
More than you ever wanted to know about matrices: [http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3274/pdf/imm3274.pdf The Matrix Cookbook].  --[[User:Chloe|Chloe]] 11:46, 20 February 2008 (PST)

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