Tartalomjegyzék

Analízis 3.-hoz köthető érdekességek (TODO list)

PDE

• Schrödinger egyenlet
• HyperPhysics - Schrödinger egyenlet
• HyperPhysics - Schrödinger egyenlet (advanced)
• Schrödinger egyenlethez köthető
• Eckhaus egyenlet

Vectoranalízis

• Vector calculus

Differenciálgeometria, Geometric control

• Quora - diffgeom - applications
• Quora - What is geometric control theory
• Car steering system
• Keenan Crane - Curvature flow
• SF2842 Geometric Control Theory
• Total derivative

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

MIT Open Course:
• Mathematics
• Computational Science and Engineering I
• Mathematical Methods for Engineers II