Partial Differential Equations
Explore equations and data; model equations; weak solutions and discretization. Concepts and connections are available independently of video coverage.
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The wave equation links temporal and spatial second derivatives to describe propagation.
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The heat equation models diffusion through time and spatial second derivatives.
The Laplacian equals zero for harmonic fields or a source term in Poisson's equation.
Boundary data restrict a differential equation's solution on the edge of its domain.
Bounds on integrated solution quantities help establish stability and uniqueness.
Piecewise basis functions approximate weak formulations over a subdivided domain.
Explore equations and data; model equations; weak solutions and discretization. Concepts and connections are available independently of video coverage.