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\begin{document}

\title{Engineering and Science Mathematics 2B}
\author{Review for the Final Exam}
\date{May 24, 2003, 18:30--20:30, Sports Hall 1}
\maketitle

\begin{enumerate}

\item Solve a system of linear equations, \emph{matrix inversion}: See
handouts.  

\item Concept of vector space, linear independence, basis; linear
transformations: definition, \emph{representation by a matrix},
\emph{change of basis};.

\item Eigenvalues and eigenvectors, in particular with regard to the
special properties; determinants; diagonalization.

\item Fourier Series: compute the series, properties.  Concentrate on
the complex Fourier series!

\item Fourier transform: Compute the transform, inverse Fourier
transform, properties, \emph{Fourier transform of convolution},
Parseval theorem.

\item Delta function: Definition, representations.

\item Probability: Outcomes, events, sample spaces, definition of
probability, conditional probability, \emph{Bayes' rule}.

\item Permutations and Combinations.

\item Distributions: Know the Binomial, Poisson, and Gaussian
distribution.  Know how to compute the mean and variance using the
moment generating function.



\end{enumerate}

\begin{itemize}
\item Note that the exam is in Sports Hall 1, not in the Naber Hall as
published on the IUB exam schedule.

\item No calculators.

\item Most problems will be similar to the ones on the homework
sheet. 

\item Many computations will involve complex numbers.  If you have
difficulties with complex numbers, you should practice manipulating
them.

\item The ESM 2A homework sheets for Linear Algebra and Probability
are on the web and a good source for practice problems.

\texttt{http://math.iu-bremen.de/stoll/teaching/ESM2A-2003-Spring/schedule.html}

\item The following topics should be revised, as they may be required
as part of some question: Equations for lines and planes; distance of
a point to a line or plane; distance between two lines;
Orthonormal bases, Gram-Schmidt orthnormalization, Hermitian Matrices
and operators.


\end{itemize}



\end{document}
