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Manifold, units and differential geometry (actually topology)
Автор: Gabriele Carcassi
Загружено: 2025-09-01
Просмотров: 5976
Описание:
We are going to see how the definition of tangent vector as derivation does not work in physics and what is that we actually need instead.
Intro (0:00)
Tangent spaces and units (0:23)
Objection! (2:08)
Apply the definition (2:46)
Unitless derivations are not physically useful (5:13)
Units/coordinates are vector spaces (7:28)
Manifolds allow for different units/coordinates (12:48)
Differentiability and infinitesimal variations (16:27)
"Basis" are actually maps (19:13)
Tensors are maps between variations (22:29)
Closing remarks (23:34)
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