Algebraic Manipulations: Indices and Tensors in Continuum Mechanics

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Page 3 of 4

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores orthogonality, Gram-Schmidt process, dot products, and solution minimization in systems.

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

Introduces continuum mechanics, focusing on conservation laws and kinematics for continuous media.

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

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Introduces special and general relativity, Einstein equations, and gravitational dynamics.

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

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

Covers the properties of vectors, including commutativity, distributivity, and linearity.