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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Laplace and Poisson equations
The Laplacian equals zero for harmonic fields or a source term in Poisson's equation.
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Separation of variables
Product-form trial solutions reduce suitable PDEs to ordinary differential equations.
Wave equation
The wave equation links temporal and spatial second derivatives to describe propagation.
Boundary value problems
Boundary data restrict a differential equation's solution on the edge of its domain.
Energy estimates
Bounds on integrated solution quantities help establish stability and uniqueness.
Finite element method
Piecewise basis functions approximate weak formulations over a subdivided domain.
Knowledge connections
- Wave equation · Related · Map context
- Separation of variables · Related · Map context