Mathematical Basics: Index Notation and Tensors

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Related lectures (30)

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Tensors and Lorentz Transformations

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

Algebraic Manipulations: Indices and Tensors in Continuum Mechanics

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

Chemical Environments: Representations and Correlations

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

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Vector Transformation and Tense

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Covariant Derivatives and Christoffel Symbols

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

Elements of Lie Groups and Algebras

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

Tensors & Indices Recap

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

Special and General Relativity

Introduces special and general relativity, Einstein equations, and gravitational dynamics.

Fluid Dynamics Fundamentals

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