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Method of characteristics

Characteristic curves reduce suitable first-order PDEs to equations along paths.

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  • Energy estimates

    Bounds on integrated solution quantities help establish stability and uniqueness.

  • Heat equation

    The heat equation models diffusion through time and spatial second derivatives.

  • Partial derivatives

    A partial derivative varies one coordinate while holding the others fixed.

  • Weak solutions

    Integral identities define solutions whose classical derivatives may not exist.

  • Boundary value problems

    Boundary data restrict a differential equation's solution on the edge of its domain.

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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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