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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]
    Integral Transforms and Partial Differential Equations

  \item[Course Number]
    \LRE{201‭.1‭.0291}

  \item[Course web page]\mbox{}\\
    \url{https://www.math.bgu.ac.il//en/teaching/fall2022/courses/introduction-to-partial-differetial-equations}

  \item[Lecturer]
    Prof. Arkady Poliakovsky,
    \nolinkurl{<poliakov@bgu.ac.il>},
    Office 314

\item[Office Hours]
  \url{https://www.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{} The Fourier transform: convolutions, the inversion formula, Plancherel's theorem, Hermite functions, tempered distributions. The Poisson summation formula. The Fourier transform in R\^{}n.
\item{} The Laplace transform. Connections with convolutions and the Fourier transform. Laguerre polynomials. Applications to ODE's. Uniqueness, Lerch's theorem.
\item{} Classification of the second order PDE: elliptic, hyperbolic and parabolic equations, examples of Laplace, Wave and Heat equations.
\item{} Elliptic equations: Laplace and Poisson equations, Dirichlet and Neumann boundary value problems, Poisson kernel, Green's functions, properties of harmonic functions, Maximum principle
\item{} Analytical methods for resolving partial differential equations: Sturm-Liouville problem and the method of separation of variables for bounded domains, applications for Laplace, Wave and Heat equations including non-homogenous problems. Applications of Fourier and Laplace transforms for resolving problems in unbounded domains.
\end{enumerate}

\paragraph*{Bibliography}

\begin{enumerate}
\item{} Stein E. and Shakarchi R., Fourier analysis, Princeton University Press, 2003.
\item{} Korner T.W., Fourier analysis, Cambridge University Press, 1988.
\item{} Katznelson Y., An Introduction to Harmonic Analysis, Dover publications. 4. John, Partial differential equations, Reprint of the fourth edition. Applied Mathematical Sciences, 1. Springer-Verlag, New York, 1991.
\item{} Evans Lawrence C. Partial Differential Equations, Second Edition.
\item{} Gilbarg D.; Trudinger N. S. Elliptic partial differential equations of second order, Reprint of the 1998 edition. Classics in Mathematics. Springer-Ver lag, Berlin, 2001.
\item{} Zauderer E. Partial differential equations of applied mathematics, Second edition. Pure and Applied Mathematics (New York). A Wiley-Interscience Publication. John Wiley \& Sons, Inc., New York, 1989. xvi+891 pp. ISBN: 0-471-61298-7.
\end{enumerate}

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