Tensor Operations: Dot and Cross Products

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Continuum Mechanics: Conservation Laws and Kinematics

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

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Rotation in Two Dimensions

Explores rotation in two dimensions, covering vector products, angular momentum, and kinetic energy of solids.

Covariant Derivatives and Christoffel Symbols

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

Studying Mechanics: Vector Calculus

Covers vector calculus, including scalar and vector products, with insights from Dr. Sylvain Bréchet.

Mechanics: Introduction and Calculus

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Chemical Environments: Representations and Correlations

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

Rotation in Two Dimensions

Explores rotation in two dimensions, covering vector product, moment of a force, statics, and kinetic energy theorems, with practical examples.

Vector Components and Operations

Covers vector components, projections, conventions, operations, and mathematical identities.

Tensor Products of Modules

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