Tensor Transformations

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Related lectures (30)

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Summary using nabla symbol

Covers the concept of nabla symbol, vector scalar, divergence, and cross product in 3D.

Continuity Equations: Internal Entropy Production

Explores continuity equations and internal entropy production in various coordinate systems, emphasizing scalar functions and vector quantities.

Vector Product: Antisymmetric Coordinates

Covers the vector product and its geometric interpretation in a Cartesian coordinate system.

Differential Operators: Vector Analysis

Covers differential operators, vector analysis, Fourier analysis, and potential fields with applications to gravity.

Covariant Derivatives and Christoffel Symbols

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

Rotations in Mechanics

Explores rotations in solid mechanics, from two-dimensional to three-dimensional scenarios, emphasizing small angles and different coordinate systems.

Vector Analysis Review

Covers unit vectors, coordinate system conversion, divergence, and rotational concepts in vector analysis.

Continuum Mechanics: Mass Conservation

Explores mass conservation in continuum mechanics, covering stress, dynamics, constitutive laws, and solid deformation.

Scalar Products in 2D and 3D Geometry

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Elements of Lie Groups and Algebras

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