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eigenchris

Tensor Calculus

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29 items
Last updated on Jul 4, 2020
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Tensor Calculus 0: Introduction
12:43
Tensor Calculus 1: Multi-variable Calculus Review (Updated with correction)
17:09
Tensor Calculus 2: Cartesian/Polar Coordinates, and Basis Vectors
11:39
Tensor Calculus 3: The Jacobian
11:20
Tensor Calculus 4: Derivatives are Vectors
12:02
Tensor Calculus 5: Derivative Transformation Rules (Contravariance)
12:57
Tensor Calculus 5.1: Derivative Operators are Vectors Discussion
10:10
Tensor Calculus 6: Differential Forms are Covectors
15:49
Tensor Calculus 7: Covector Field Components
14:19
Tensor Calculus 8: Covector Field Transformation Rules (Covariance)
13:24
Tensor Calculus 9: Integration with Differential Forms
18:34
Tensor Calculus 10: Integration with Differential Forms Examples
17:20
Tensor Calculus 11: The Metric Tensor and Arc Lengths (flat space)
14:34
Tensor Calculus 12: The Metric Tensor in Curved Spaces for Measuring Arc Length
23:09
Tensor Calculus 13: Gradient vs "d" operator (exterior derivative/differential)
19:07
Tensor Calculus 14: Gradient explanation + examples
14:40
Tensor Calculus 15: Geodesics and Christoffel Symbols (extrinsic geometry)
21:40
Tensor Calculus 16: Geodesic Examples on Plane and Sphere
20:55
Tensor Calculus 17: The Covariant Derivative (flat space)
18:12
Tensor Calculus 17.5: Covariant Derivative (Component Definition) - Optional
16:50
Tensor Calculus 18: Covariant Derivative (extrinsic) and Parallel Transport
33:51
Tensor Calculus 19: Covariant Derivative (Intrinsic) and Geodesics
22:50
Tensor Calculus 20: The Abstract Covariant Derivative (Levi-Civita Connection)
28:52
Tensor Calculus 21: Lie Bracket, Flow, Torsion Tensor (contains error; see pinned comment)
24:10
Tensor Calculus 22: Riemann Curvature Tensor Geometric Meaning (Holonomy + Geodesic Deviation)
29:13
Tensor Calculus 23: Riemann Curvature Tensor Components and Symmetries
25:31
Tensor Calculus 24: Ricci Tensor Geometric Meaning (Sectional Curvature)
28:54
Tensor Calculus 25 - Geometric Meaning Ricci Tensor/Scalar (Volume Form)
32:12
Tensor Calculus 26 - Ricci Tensor/Scalar Properties
28:59