Hints to Exercises: Mathematica
Problem Set 1

Computational Physics with Numerical Recipes
James P. Sethna
Physics 480/680, Spring 2008
http://www.physics.cornell.edu/~sethna/teaching/ComputationalPhysics/

1.1 Preliminaries

(a) Use Table to create a set of {x, y} pairs, and ListPlot. You'll need to 
set PlotStyle to {AbsoluteThickness[3], RGBColor[0,1,0]} and PlotJoined->True.
Use Show with PlotRange to expand the region around {0,1}. You can give the 
graphs a name (g = ListPlot[...]) and then use Export["g.gif", g] to save
the files, or you can print directly from Mathematica by selecting the graph
and Print from the file menu. 

(b) You can use Import to read the file "NoisyYofT.dat" into a matrix. 
You can use SetDirectory to change directories to get to the file, as in
	SetDirectory["C:\\Teaching\\480680\\ps01"]
Taking the transpose puts it into a form that you can use ListPlot on. 


1.2 Condition Number

Typing in matrices and vectors is done with curly brackets and commas. You can
use MatrixForm to look at a nicely formatted representation of the matrix. 

(a) A . x is another way of writing Dot[A, x].

(b) Try ?SingularValues.

(c) Try ?LinearSolve. Remember to subtract (1,-1) and divide by the machine
accuracy.


1.3 Sherman Morrison formula

Notice that both E and C are protected; I used the variables e and cyc. I
used a Table with two nested If statements to build my matrices:
	T = Table[If[i == j, ..., If[Abs[i - j] == 1, ...]], {i,...},{j...}];
You'll need Inverse and Outer. (For example, C-T = Outer[Times, u, v]. 


1.4 Timing Sine.

Use Table to build a list x with a million entries. Make sure the entries are
floats (maybe by using N[2 pi m/M]). The function Sin is listable, so 
Timing[Sin[x]] should work.