Manifold, units and differential geometry (actually topology)

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)