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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Hamiltonian systems
A Hamiltonian function generates evolution of paired position and momentum variables.
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Dimensional similarity
Dimensionless groups compare physical systems while respecting the dimensions of quantities.
Noether's theorem
Continuous variational symmetries lead to conservation laws under the theorem's hypotheses.
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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- Noether's theorem · Related · Map context
- Dimensional similarity · Related · Map context