Tensor Calculus by eigenchris 共 29 P

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https://www.youtube.com/playlist?list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx Tensor Calculus by eigenchris 共 29 P 其中 3 P,YouTube上连自动字幕都没有,剩下的 26 P用 FFmpeg将字幕烧录内嵌到视频里面去了 这是昨天上传的 Tensors for Beginners 的后继教程,感谢作者 eigenchris 所创作的精彩教学视频。
We are all in the gutter, but some of us are looking at the stars.
视频选集
(14/29)
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
15:50
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)
18:13
Tensor Calculus 17.5 - Covariant Derivative (Component Definition) - Optional
16:51
Tensor Calculus 18 - Covariant Derivative (extrinsic) and Parallel Transport
33:52
Tensor Calculus 19 - Covariant Derivative (Intrinsic) and Geodesics
22:50
Tensor Calculus 20 - The Abstract Covariant Derivative (Levi-Civita Connection)
28:53
Tensor Calculus 21 - Lie Bracket, Flow, Torsion Tensor
24:10
Tensor Calculus 22 - Riemann Curvature Tensor Geometric Meaning (Holonomy + Geod
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)
32:13
Tensor Calculus 26 - Ricci Tensor_Scalar Properties
28:59
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