Exam Thursday 11/7.

1) Either:

a) Solve a system:
   Form matrix and right hand side vector: "for".  Initialize!
   Check condition number: "if".
   Solve: "\".
   Effect of error in data?
   "fprintf" etc.

or:

b) Find eigenvalues and eigenvectors:
   Form matrix: "for".
   Find eigenvalues and eigenvectors: "eig".
   Take eigenvalues and eigenvectors out of E and Lambda,
   Check whether A e_i is really lambda_i e_i
   Check length and orthogonality of the eigenvectors if A is symmetric.
   - matrix multiplication
   - "dot", "norm"
   "fprintf" etc.

2) Either:

a) Doing an infinite sum. (Not: homework example too messy)
   Initialize the sum and add terms t(n)=t_n in a "for" loop.
   Termination "if": |n*t_n| or just |t_n| if alternating?
                     t_n no longer changes the sum?  (Taylor series)
   Assessment "if": did we converge?  Error?
   Find t_n from previous t_n.
   "fprintf" etc.

or:

b) Symbolic math:
   "ezplot".
   "ezplot3".
   "ezsurf".
   "ezmesh".
   "ezcontour".
   Use "syms" and "sym".
   May need "help FUNCTION" or "help sym/FUNCTION".
   "int(SYMFUN,SYMVAR)", "int(SYMFUN,SYMVAR,START,END)".
   "diff(SYMFUN,SYMVAR)".
   "solve(SYMLHS==SYMRHS,VAR)".
   "collect(SYMEXPR,SYMVAR)".
   "expand(SYMEXPR)".
   "factor(SYMEXPR)", "factor(SYMEXPR,'OPT','VAL')", "factor(SYMNUM)".
   "partfrac(SYMRAT)".
   "taylor(SYMFUN,ORDER)".
   "subs(SYMEXPR,{SYMVAR ...},{SYMVAL ...})".
   "prod(SYMVEC)".
   "simplify(SYMEXPR)".
   "pretty(SYMEXPR)".
   "vpa(VAL)".
   "double(VAL)".
   "NUMFUN=matlabFunction(SYMFUN)".
   "fprintf" etc.

3) One of:

a) Log-log plots:
   Fit power relation to data: "polyfit".
   Find C and p.
   Plot it and the data: "loglog"
   Other plot functions.

or:

b) Plot of 2D data:
   Create mesh: "meshgrid".
   Create forcing and execute "SimplePoisson".
   "mesh".
   "surf".
   "contour".
   Other plot functions.

or:

d) Polar plot.  (Not: not covered).