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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Sturm–Liouville problems
Self-adjoint second-order boundary problems yield eigenvalues and orthogonal eigenfunctions under suitable conditions.
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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.
Calculus of variations
Variational calculus studies extrema of functionals depending on functions.
Dimensional similarity
Dimensionless groups compare physical systems while respecting the dimensions of quantities.
Knowledge connections
- Euler–Lagrange equations · Related · Map context
- Special functions · Related · Map context
- Fourier series · Prerequisite · Map context