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The two dimensional wave equation - Trinity University

The 2D wave equationSeparation of variablesSuperpositionExamplesThe two dimensional wave equationRyan C. DailedaTrinity UniversityPartial Differential EquationsMarch 1, 2012 DailedaThe 2D wave equationThe 2D wave equationSeparation of variablesSuperpositionExamplesPhysical motivationConsider a thin elastic membrane stretched tightly over arectangular frame. Suppose the dimensions of the frame area band that we keep the edges of the membrane fixed to the the membrane from equilibrium results in somesort of vibration of the goal is to mathematically model the vibrations of themembrane 2D wave equationThe 2D wave equationSeparation of variablesSuperpositionExamplesWe letu(x,y,t) =deflection of membrane from equilibrium atposition (x,y) and a fixedt, the surfacez=u(x,y,t) giv

The 2D wave equation Separation of variables Superposition Examples We let u(x,y,t) = deflection of membrane from equilibrium at position (x,y) and time t.

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