Mechanical Displacements and Moment Balance

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Covers the concept of small displacements in mechanics and the assumptions made for moment balance.

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

Explores mathematical preliminaries of tensors and their transformations under basis rotations.

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

Provides an overview of continuum mechanics, focusing on stress tensor analysis and transformation laws in material behavior under stress.

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

Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.

Explores the continuity of tensors, focusing on T₂(W) and element k, discussing stability and interpolation properties.

Covers eigenvalues, eigenvectors, and the Fibonacci sequence, exploring their mathematical properties and practical applications.

Covers the Tucker decomposition and its applications in data compression, explaining the notion of multilinear rank and the HOSVD method.

Introduces structural mechanics for life sciences, emphasizing equilibrium, vectors, tensors, and problem-solving strategies.

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