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diff --git a/log/2022-09-15.md b/log/2022-09-15.md new file mode 100644 index 0000000..1dc1008 --- /dev/null +++ b/log/2022-09-15.md @@ -0,0 +1,28 @@ + +## Definitions + +"coordinate patch": an open set of points around a point on a manifold + +"coordinate function" or "chart": continuous function mapping every point in a patch to coordinates (tuples of N real numbers for an N-dimensional manifold) + +multiple charts may be needed to map all points on an entire manifold. a consistent set of charts covering an entire manifold is an "atlas". + + +## Progress + +Went through the second chapter, Manifolds, and did the exersizes. Short and +straight-forward, mostly definitions. Not going in to as much detail/definition +as would if studying Topology directly. + +Started on third chapter, Vector Fields and One Form Fields, and struggling +with terminology a bit. Looking ahead a bit, i'm expecting: + +- Chapters 2,3,4: definitions, geometry, derivatives on manifolds +- Chapters 5,6,7: calculus on manifolds (integration theorems) +- Chapters 7.8: curvature weirdness and the meat/math of general relativity +- Chapters 10,11: physics + + +## TODO + +report typo in scmutils: "Bad point: polar/cylindrial manifold" and "spherical/cylindrial" (should be "cylindrical"?) (in calculus/manifold.scm) |