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Tensors & Indices Recap

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Related lectures (42)

Shells I: Mechanics of Slender Structure Log in to Mediaspace to watch this video

Covers thin pressure vessels, differential geometry of surfaces, and plate buckling theories.

Mechanics of Slender Structure Log in to Mediaspace to watch this video

Covers the expression of the Kirchhoff-St. Venant energy in a covariant setting and the equilibrium equations for spherical shells, among other topics.

Algebraic Manipulations: Indices and Tensors in Continuum Mechanics Log in to Mediaspace to watch this video

Provides an overview of algebraic manipulations involving indices and tensors in continuum mechanics.

Covariance and Contravariance of Vectors Log in to Mediaspace to watch this video

Explains covariance and contravariance of vectors in multilinear algebra and tensor analysis, focusing on their behavior under changes in basis and scale.

Covariant Maxwell Equations Log in to Mediaspace to watch this video

Covers the covariant form of Maxwell equations and properties of the field strength tensor.

Lorentz Invariance and Covariant Tensors Log in to Mediaspace to watch this video

Explores Lorentz invariance, tensors in vector spaces, and electromagnetic potentials.

Principles of Quantum Physics Log in to Mediaspace to watch this video

Covers the principles of quantum physics, focusing on tensor product spaces and entangled vectors.

Tensors: Motivations and Introduction Log in to Mediaspace to watch this video

Covers the basics of tensors, including their definition, properties, and decomposition, starting with a motivating example involving Gaussian distributions.

Linear Shell Theory: Equilibrium and Energy Log in to Mediaspace to watch this video

Covers the expression of the Kirchhoff-Saint Venant energy in a covariant setting and explores equilibrium equations for spherical shells and linear shell theory.

Lorentz Covariant Formulation: Maxwell Equations Log in to Mediaspace to watch this video

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

Shells I: Mechanics of Slender Structures Log in to Mediaspace to watch this video

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

Linear Shell Theory: Equilibrium Equations Log in to Mediaspace to watch this video

Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.

Tucker Decomposition: Multilinear rank and applications in data compression Log in to Mediaspace to watch this video

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

Plates III: Mechanics of Slender Structure Log in to Mediaspace to watch this video

Covers Föppl-von Kármán equations, Airy potential, plate theory simplifications, and buckling of plates.

Linear Momentum Conservation and Stress in Continuum Log in to Mediaspace to watch this video

Explores the conservation of linear momentum and stress in a continuum, focusing on governing equations and constitutive laws.

Advanced Physics I: Definitions and Motion Log in to Mediaspace to watch this video

Covers advanced physics topics such as definitions, rectilinear motion, vectors, and motion in three dimensions.

Understanding Semiconductor Behavior: Charge and Conductivity Log in to Mediaspace to watch this video

Covers semiconductor behavior, focusing on energy levels, charge distributions, and conductivity in N-P-N structures and metal-semiconductor interfaces.

Membrane Theory of Shells Log in to Mediaspace to watch this video

Explores the membrane theory of shells to analyze forces in thin shell structures.

Membrane Theory of Shells Log in to Mediaspace to watch this video

Explores membrane forces in thin shell structures under various loadings, focusing on cylindrical and spherical shell roofs.

Untitled Log in to Mediaspace to watch this video

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