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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Heat equation
The heat equation models diffusion through time and spatial second derivatives.
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Method of characteristics
Characteristic curves reduce suitable first-order PDEs to equations along paths.
Partial differential equations
A PDE relates a multivariable unknown function to its partial derivatives.
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.
Knowledge connections
- Wave equation · Related · Map context
- Separation of variables · Related · Map context
- Partial differential equations · Related · Map context
- Method of characteristics · Related · Map context