Lectures related to Grassmann manifold and Retractions

Explores differentiability in functions and geometric interpretation of tangent planes.

Explores differentiability, tangent lines, and graph interpretation.

Open Balls and Topology in Euclidean Spaces

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

Conformal Symmetries in Euclidean and AdS Spaces

Explores conformal symmetries in Euclidean and AdS spaces, isometries, induced metric, Poincaré coordinates, and boundary structure.

Parametric Curves: Analysis and Applications

Covers the analysis of parametric curves and their tangent vectors, focusing on applications and geometric interpretations.

Connections: motivation and definition

Explores the definition of connections for smooth vector fields on manifolds.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Functions: Limits, Continuity, Differentiability

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.