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Dimensional similarity

Dimensionless groups compare physical systems while respecting the dimensions of quantities.

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  • Hamiltonian systems

    A Hamiltonian function generates evolution of paired position and momentum variables.

  • Tensors

    Tensors encode multilinear quantities with consistent transformation laws under coordinate changes.

  • Calculus of variations

    Variational calculus studies extrema of functionals depending on functions.

  • Distributions as generalized functions

    A distribution acts linearly and continuously on test functions, allowing generalized derivatives.

  • Euler–Lagrange equations

    Stationarity of a smooth variational problem gives differential conditions with appropriate boundary constraints.

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Mathematical Physics

Explore fields and transforms; variational and spectral methods; symmetry and conservation. Concepts and connections are available independently of video coverage.

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