Author

Ibraheem Otuf

Date of Graduation

Fall 2016

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Xingping Sun

Keywords

Fourier series, Fourier transform, boundary value problem, partial diferential equation, Neumann problem, Laplace equation

Subject Categories

Mathematics

Abstract

Domain-sensitivity is a hallmark in the realm of solving boundary value problems in partial differential equations. For example, the method used in solving a boundary value problem on an finite cylindrical domain is very different from one that arises from a rectangular domain. The difference is also reflected in the types of functions employed in the processes of solving these boundary value problems, as are the mathematical tools utilized in deriving an analytic solution. In this thesis, we solve an important class of partial differential equations with boundary conditions coming from various domains, such as the n dimensional cube, circles, and finite and infinite rectangles. We first enlist the functions and assemble the mathematical tools needed for the various domains. We then take the strategy of "divide-and-conquer" to solve the boundary value problems in a successive fashion. The main goal of solving these problems is to determine quantitatively how heat flow at any given time.

Copyright

© Ibraheem Otuf

Open Access

Included in

Mathematics Commons

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