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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Noether's theorem
Continuous variational symmetries lead to conservation laws under the theorem's hypotheses.
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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.
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.
Knowledge connections
- Tensors · Related · Map context
- Hamiltonian systems · Related · Map context