Comparing Tangent Vectors: Parallel Transport

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Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Differentiating vector fields along curves: Examples and finite differences

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Connections: motivation and definition

Explores the definition of connections for smooth vector fields on manifolds.

Comparing Tangent Vectors: Parallel Transport

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Covariant derivatives along curves

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Comparing Tangent Vectors: Parallel Transport

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Covariant Derivatives and Christoffel Symbols

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