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partial-differential-equations

Fourier sine series

taught

Expand a function on [0, L] in a series of sines alone, computing each coefficient directly from orthogonality rather than a memorized formula.

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Choosing which series a boundary-condition pair calls for Comparing the heat and wave equations Complex Fourier series Convergence of a Fourier series at a point Even, odd, and periodic extensions Finite differences for the heat equation: the explicit scheme Heat conduction in two and three dimensions Laplace's equation by separation of variables on a disk 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… Term-by-term differentiation and integration of a… Solving the heat equation on a finite rod with Dirichlet… The full Fourier series Fourier sine series Fourier cosine series From boundary conditions to a Sturm-Liouville… Orthogonality of Sturm-Liouville eigenfunctions Parseval's equality Orthogonality of the sine and cosine functions Inner products: generalizing the dot product

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