Lecture Notes on Variational and Tensor Calculus


Variational Calculus: Part I: Chapters 1-2

Variational Calculus: Part II: Chapters 2-3

Tensor Calculus (The Dual of a Vector Space)

Tensor Calculus 4-5 (Tensors as Multilinear Maps; Integral Curves; The Commutator)

Tensor Calculus 6 (Parallel Transport; The Covariant Differential and Derivative)

Tensor Calculus 7 (The Covariant Derivative)

Tensor Calculus 8 (What is a Tensor Map? The Torsion Tensor of a Given Law of Parallel Transport)

Tensor Calculus
9 (Curvature as Vectorial Rotation; The Riemann Curvature Tensor)

Tensor Calculus 10 (Metric-Induced Parallel Transport; Metric Compatibility via Extremal Path)