Tensors and Normal Coordinates

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Page 3 of 4

Explores the definition and properties of the metric tensor, enabling control of geometric quantities and lengths.

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Covers stress components, tensor transformation, and invariants in continuum mechanics.

Explores developable surfaces, parametrization, equations verification, and conformally flat surfaces.

Discusses tensor transformations and diagonalization of symmetric tensors, focusing on stress analysis and the significance of principal stresses.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Explores the second fundamental tensor and its role in calculating normal curvature on surfaces.

Covers the basics of tensors and indices, including contravariant vectors and tensor operations.