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\title{Numerical Methods II}
\author{Review for Midterm II}
\date{Wednesday, March 31, 2004 in the Research I Lecture Hall}
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\begin{enumerate}
  
\item Stability of numerical methods for ordinary differential
  equations.  In particular, understand Question 6(b) from last
  semester's final exam; understand stiffness (see, e.g., the example
  in SM, p.~345).

\item Methods for step size control and extrapolatory improvement of
  solutions.  (No details, but review the basic ideas.)

\item Implementation issues for implicit multistep methods.  (No
  programming required, but you should be able to comment on practical
  problems).

\item Linear boundary value problems, in particular the computation of
  the local truncation error.

\item Shooting: Understand the basic idea and be able to describe the
  procedure.

\item Matrix eigenvalue problems: Know the technical tools (plane
  rotation matrices, Householder reflections, Frobenius norm and its
  invariance under orthogonal transformations), Jacobi method, QR
  method, Gershgorin theorem, QR decomposition of a tridiagonal matrix
  by plane rotations, inverse iteration, elementary perturbation
  analysis.

\item Optimization: Golden ration search and Brent's method in one
  variable, know the basics of the Gradient and the Conjugate
  Gradient methods in several variables.
  
\end{enumerate}


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