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\begin{document}

\title{Engineering and Science Mathematics 2B}
\author{Review for Midterm II}
\date{Wednesday, May 17, 8:15--9:30}
\maketitle

Location:
\begin{itemize}
\item Students whose last names start with \textbf{A--F} take the exam
in the \textbf{Research II Lecture Hall}.
\item Students whose last names start with \textbf{G--Z} take the exam
in the \textbf{Campus Center East Wing}.
\end{itemize}

Review Topics:

\begin{enumerate}

\item Inner products: Definition, examples, orthonormal basis,
projections.

\item Gram-Schmidt orthonormalization.

\item Can you show that the eigenvectors of a symmetric (Hermitian)
matrix are orthogonal provided the eigenvalues are distinct?

\item Can you show that the eigenvalues of a symmetric (Hermitian)
matrix are real?

\item Review diagonalization and change of basis (as for the last
midterm, but in particular in the context of symmetric or hermitian
matrices and the corresponding orthonormal bases consisting of
eigenvectors).

\item Fourier series (mainly complex case).  Compute the
Fourier series for easy examples (step function, low degree
polynomials, sine and cosine function).

\item Interpretation of change between the complex Fourier series and
Fourier cosine and sine series as a change of basis.

\item Basic properties of Fourier series (see, in particular,
Homework~6 Questions 2 and~3).

\item Fourier transform: definition and computation of the Fourier
transform for easy examples; basic properties.  Can you give a direct
proof of the Parseval theorem?  Can you prove the convolution theorem?

\item Delta function: basic properties and simple computations.

\end{enumerate}



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