Indicial Notation and Tensor Components

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Continuum Mechanics: Tensor Analysis and Kinematics

Covers tensor analysis, kinematics, and fluid mechanics in continuum mechanics.

Lorentz Covariant Formulation: Maxwell Equations

Covers Lorentz transformations, Maxwell equations, and charge conservation in Lorentz invariant physics.

Cohomology: Cross Product

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

Tensors and Lorentz Transformations

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

Covariant Derivatives and Christoffel Symbols

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

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.

Stress Components & Transformation of Tensors

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

Fluid Dynamics Fundamentals

Covers deriving fluid dynamics equations, including mass conservation and stress-strain relationships, through differential analysis and key mathematical concepts.

Scalar, Vector or Tensor? Gravity

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

Gravity and Motion

Explores force of motion, dimensions, gravity, tensor fields, and equivalence principle.