Tensor Properties

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Tensors & Indices Recap

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

Covariance and Contravariance of Vectors

Explains covariance and contravariance of vectors in multilinear algebra and tensor analysis, focusing on their behavior under changes in basis and scale.

Linear Momentum Conservation and Stress in Continuum

Explores the conservation of linear momentum and stress in a continuum, focusing on governing equations and constitutive laws.

Special Relativity

Covers the main points of special relativity, including symmetries, transformations, 4-vectors, Maxwell equations, and proper time.

Flat Space-Time: Conditions and Theorems

Covers the necessary conditions and theorems to have flat space-time and discusses the symmetry properties of the Riemann tensor.

Continuum Mechanics: Mass Conservation

Explores mass conservation in continuum mechanics, covering stress, dynamics, constitutive laws, and solid deformation.

Shells I: Mechanics of Slender Structure

Covers thin pressure vessels, differential geometry of surfaces, and plate buckling theories.

Indicial Notation and Vectors

Explores indicial notation, vectors, and the transformation law in the context of mass flux density.

Scalar, Vector or Tensor? Gravity

Discusses defining tensors, space-time dimensionality, and challenges in formulating a relativistic theory of gravity.