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Calculus of variations

Variational calculus studies extrema of functionals depending on functions.

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  • Euler–Lagrange equations

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

  • Fourier series

    Periodic functions can be expanded in harmonic components with convergence interpreted under suitable hypotheses.

  • Special functions

    Functions such as Bessel and Legendre functions solve recurring differential equations in geometry and physics.

  • Tensors

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

  • Dimensional similarity

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

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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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