Lectures related to Lorentz Transformations and Covariant Tensors

Lorentz Invariance and Covariant Tensors

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

Tensors and Lorentz Transformations

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

Special and General Relativity

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

Lorentz Covariant Formulation: Maxwell Equations

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

Covariant and Contravariant Tensors: Maxwell Field Strength

Explores contravariant and covariant tensors, Maxwell field strength, and Lorentz invariance in linear transformations and metric properties.

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Lie Groups: Representations and Transformations

Explores Lie groups, scalar fields, and vector spaces transformations.

Elements of Lie Groups and Algebras

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

Linear Algebra: Lecture Notes

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Tensor Products and Symmetric Power

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Linear Algebra: Matrices and Vector Spaces

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Covariant Maxwell Equations

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

Indicial Notation and Vectors

Explores indicial notation, vectors, and the transformation law in the context of mass flux density.

Linear Transformations: Matrices and Bases

Covers the determination of matrices associated with linear transformations and explores the kernel and image concepts.

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Lorentz Transformations: Symmetries and Boosts

Explores Lorentz transformations, boosts, and symmetries in Newtonian mechanics.

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

Shells I: Mechanics of Slender Structures

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