Tartalomjegyzék
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Analízis 3.-hoz köthető érdekességek (TODO list)
PDE
Vectoranalízis
Differenciálgeometria, Geometric control
Differenciálgeometria, irány a tenzoranalízis felé + általános relativitáselmélet felé
- Einstein notation - ezt már szinte teljesen megértettem, csak a raising meg lowering index-el vannak gondok.
-
Classical electromagnetism in the relativistic framework
(Richard_Fitzpatrick_Classical_Electromagnetism.pdf,
web version)
-
Reimannian manifold and metrics (Michael_Spivak_A_Comprehensive_Introduction_To_DiffGeom.pdf),
Metric tensor,
Exterior algebra, inner product,
Hodge dual
-
Bivector (2-vector, or tensor of rank 2).
Maxwell's equation as
$\partial \mathbf{F} = \mathbf{J}$
-
Lie algebra,
Multivector,
Cross product and its generalizations,
-
Tensors: Angular velocity tensor,
Electromagnetic tensor
(levezetések),
Four-current
-
Four-gradient,
Tensor derivative
-
Tensor, Tensor product,
Wedge product (visually)
-
d'Alambert operator
-
Four-vector (relativity theory),
Covariant vs. contravariant,
Linear form (one-form)
- Quantum physics: Bra-ket notation
-
Curvilinear coordinates,
Gaussian curvature