Covariance and Contravariance of Vectors

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

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Differential Geometry of Surfaces

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.

Shells I: Mechanics of Slender Structures

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Tensors and Lorentz Transformations

Covers tensors, Lorentz transformations, and electrodynamics in relativistic notation.

Elements of Lie Groups and Algebras

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Vector Transformation and Tense

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Lorentz Transformations and Covariant Tensors

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

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

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.