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partial-differential-equations

Choosing which series a boundary-condition pair calls for

taught

Match a stated pair of boundary conditions -- Dirichlet, Neumann, Robin, mixed -- to the sine, cosine, full, or transcendental eigenfunction series it forces, before attempting to solve.

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Why numerical methods, and what can go wrong When a Green's function does and doesn't exist in… Choosing which series a boundary-condition pair calls for Comparing the heat and wave equations Finite differences for the heat equation: the explicit scheme Heat conduction in two and three dimensions Long-time behavior and steady-state limits of a separated solution Shifting nonhomogeneous boundary data to… Solving the heat equation with a source term by eigenfunction… The method of images: additional domains (slab, wedge) Solving the heat equation on a finite rod with Dirichlet… Solving the heat equation on a finite rod with Neumann… Solving the heat equation on a finite rod with Robin… Fourier cosine series Fourier sine series From boundary conditions to a Sturm-Liouville… The regular Sturm-Liouville problem The separation-of-variables ansatz

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