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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Energy estimates
Bounds on integrated solution quantities help establish stability and uniqueness.
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Finite element method
Piecewise basis functions approximate weak formulations over a subdivided domain.
Method of characteristics
Characteristic curves reduce suitable first-order PDEs to equations along paths.
Boundary value problems
Boundary data restrict a differential equation's solution on the edge of its domain.
Heat equation
The heat equation models diffusion through time and spatial second derivatives.
Laplace and Poisson equations
The Laplacian equals zero for harmonic fields or a source term in Poisson's equation.
Knowledge connections
- Finite element method · Related · Map context
- Method of characteristics · Related · Map context