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partial-differential-equations

D'Alembert's formula for the wave equation

taught

Derive and apply the closed-form solution of the whole-line wave equation by factoring the wave operator into two characteristic (transport) factors.

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Required by

Local knowledge map

Local knowledge map

Causality in three dimensions -- the solid light cone Duhamel's principle, unified via Green's functions The CFL condition Domain of dependence, range of influence, and finite propagatio… Duhamel's principle for the wave equation Representing a solution as a convolution The Green's function for the wave equation D'Alembert's formula for the wave equation Boundary condition types: Dirichlet, Neumann, Robin Characteristics for a system Characteristics with variable coefficients Duhamel's principle for the heat equation Reducing a 2nd-order PDE to canonical form via characteristics The Green's function for the Dirichlet problem, revisited Writing a first-order system in matrix form Deriving the wave equation Solving linear first-order PDEs by characteristics Initial value problems and particular antiderivatives Order, linearity, and homogeneity of a PDE

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