The metric tensor

---Contents of this video---
00:00 - Introduction
02:58 - Definition of metric tensor
10:40 - Example: metric in 2D Cartesian coordinate system
13:20 - Transformation of metric under a change of coordinates
21:05 - Example: metric in polars from that in Cartesians
29:11 - Example: calculating arc length in Cartesian and in polar coordinates
34:35 - Raising and lowering indices using the metric
38:33 - Length of vector
40:16 - Constant metric

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