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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2021--22--A term}\\[0.2\baselineskip]

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\begin{description}
  \item[Course Name]
    Fourier analysis for Electrical Engineering

  \item[Course Number]
    \LRE{212‭.1‭.9901}

  \item[Course web page]\mbox{}\\
    \url{https://math.bgu.ac.il//en/teaching/fall2022/courses/fourier-analysis-for-electrical-engineering}

  \item[Lecturer]
    Prof. Ilan Hirshberg,
    \nolinkurl{<ilan@bgu.ac.il>},
    Office 203

\item[Office Hours]
  \url{https://math.bgu.ac.il/en/teaching/hours}
\end{description}

\section*{Abstract}




\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}






\section*{Course topics}

\begin{enumerate}
\item{} Complex valued-functions and the complex exponential. Fourier coefficients of piecewise continuous periodic functions. Basic operations and their effects on Fourier coefficients: translation, modulation, convolutions, derivatives.
\item{} Uniform convergence: Cesaro means, the Dirichlet and Fejer kernels, Fejer's theorem. The Weierstrass approximation theorem for trigonometric polynomials and for polynomials. Uniqueness of Fourier coefficients. The Riemann-Lebesgue lemma. Hausdorff's moment problem. Convergence of partial sums and Fourier series for \$C\^{}2\$-functions.
\item{} Pointwise convergence: Dini's criterion. Convergence at jump discontinuities and Gibbs phenomenon.
\item{} \$L\^{}2\$-theory: orthonormal sequences and bases. Best approximations, Bessel's inequality, Parseval's identity and convergence in \$L\^{}2\$.
\item{} Applications to partial differential equations: the heat and wave equations on an interval with constant boundary conditions, the Dirichlet problem for the Laplace equation on the disk, the Poisson kernel.
\end{enumerate}

Bibliography:

\begin{itemize}
\item{} \textbf{Korner}, \emph{Fourier analysis}
\item{} \textbf{Stein and Shakarchi}, \emph{Fourier analysis}
\end{itemize}

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