Covariance: Understanding the Concepts

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Covariant and Contravariant Tensors: Maxwell Field Strength

Explores contravariant and covariant tensors, Maxwell field strength, and Lorentz invariance in linear transformations and metric properties.

Mechanics of Slender Structure

Covers the expression of the Kirchhoff-St. Venant energy in a covariant setting and the equilibrium equations for spherical shells, among other topics.

General Covariance in Gravity

Explores general covariance in gravity, covering equations, curvature tensor, and static gravity field.

Covariant Maxwell Equations

Covers the covariant form of Maxwell equations and properties of the field strength tensor.

Tensors & Indices Recap

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

Chemical Environments: Representations and Correlations

Explores chemical environment representations, symmetrized correlations, and machine learning applications at the atomic scale.

Stress Components & Transformation of Tensors

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

Shells II: Mechanics of Slender Structure

Covers the expression of energy, dimensional reduction, equilibrium equations, and the relationship between covariant and contravariant components in shell mechanics.

Tensor Analysis: Coordinate Systems

Covers tensor analysis for arbitrary coordinate systems and introduces Christoffel symbols.

Transformation Laws: Diagonalization of Symmetric Tensors

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