Covariance and Contravariance for Tensors of Order 1

Contravariant and Covariant Tensors of Rank 2

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Christoffel Symbols in Spherical Coordinates

Derivatives of the Metric Tensor in Terms of Christoffel Symbols

The Jacobian Matrix

Outer Products and Contraction of Tensors

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The Transformation Law for Christoffel Symbols

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The Covariant Derivative of a Contravariant Vector

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The Geodesic Equation

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Chain Rule For Finding Derivatives

The Covariant Derivative of a Tensor