Lectures related to Metric signature

Sylvester's Inertia Theorem

Explores Sylvester's Inertia Theorem, relating eigenvalues to diagonal entries in symmetric matrices.

Time Dilation and Lorentz Contraction

Explores time dilation, Lorentz contraction, and isotropy in physics.

Stereographic Projection and Metric Tensors

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.

Conformal Transformations and Stress Tensor

Explores conformal transformations, stress tensor, and correlation functions in conformal field theory.

Advanced Physics I: Gyroscopic Effects and Solid Dynamics

Explores gyroscopic effects, solid dynamics, inertia tensors, and ball motion.

Solid Dynamics: Laws and Variants

Explores laws of dynamics, angular momentum, inertia tensor, and kinetic energy.

Gauss Theorem in R^n+1

Explores the Gauss theorem in R^n+1, covering regular domains, vector fields, surface integrals, and volume calculations.

Implicit Surface Parametrizations

Explores implicit surface parametrizations and the use of metric tensors in surface parameterization.

Inertia Tensor and Rotational Dynamics

Explores inertia tensor, main axes of inertia, and rotational dynamics of solids, including Steiner's theorem and balancing techniques.

Physics 1: Inertia Tensor Calculation

Covers the calculation of the inertia tensor for a thin ring, with examples demonstrating the process.

Spherically Symmetric Metrics

Explores spherically symmetric metrics in flat space and their implications in gravity and spacetime.

Metrics: Line and Convex Cone

Covers line metrics, convex cones, and linear metric combinations.

Linear Systems: Factorization and Cholesky

Explores linear systems, Cholesky factorization, LU factorization, and matrix precision.

Conformal Field Theory: Generators and Commutation Relations

Covers the definition of generators of the conformal group and the application of Wick's theorem.

Kinetic Energy of Solids

Discusses the kinetic energy of solids and the selection of benchmarks and points of affluence.

Linear Systems: Choleski Factorisation

Covers the Choleski factorisation method for solving linear systems efficiently.

Charged Particle in Minkowski Spacetime

Explores the worldline action of a charged particle in Minkowski spacetime, covering 4-vectors, intervals, Lorentz invariance, and charged particles in EM fields.

Calculation of Moment of Inertia for Rotating Objects

Explores the calculation of moment of inertia for rotating objects using examples of wheels and discs.

Experiences, Solids, General Movement

Explores the mechanics of solids and general movement with examples like spinning tops and propellers.

Inertial Equilibration: Inertial Invariance

Explores inertial invariance and equilibration in mechanically balanced systems, covering passive and active equilibration methods.