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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Euler–Lagrange equations
Stationarity of a smooth variational problem gives differential conditions with appropriate boundary constraints.
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Calculus of variations
Variational calculus studies extrema of functionals depending on functions.
Sturm–Liouville problems
Self-adjoint second-order boundary problems yield eigenvalues and orthogonal eigenfunctions under suitable conditions.
Dimensional similarity
Dimensionless groups compare physical systems while respecting the dimensions of quantities.
Distributions as generalized functions
A distribution acts linearly and continuously on test functions, allowing generalized derivatives.
Fourier series
Periodic functions can be expanded in harmonic components with convergence interpreted under suitable hypotheses.
Knowledge connections
- Calculus of variations · Related · Map context
- Sturm–Liouville problems · Related · Map context
- Calculus of variations · Prerequisite · Map context