Lectures related to Diffeomorphism and implicit functions

Explores coordinate changes between polar and Cartesian coordinates, and introduces the spherical coordinate system.

Explores differentiability and coordinate transformations between polar and spherical systems.

Coordinate Change: Polar and Spherical Coordinates

Covers coordinate changes, focusing on polar and spherical coordinates and their transformations, determinants, and invertibility.

Volume Calculation of Revolution Bodies

Explores volume calculation of revolution bodies using mathematical formulas and inequalities.

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Principal Ideal Domains: Structure and Homomorphisms

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Implicit Differentiation: Solving Equations Locally

Explores implicit differentiation and the Implicit Function Theorem for finding unique functions locally.

Coordinate Vector Operations

Explores coordinate vector operations, from digitizing points to transforming and manipulating geometric spaces using coordinates.

Chinese Remainder Theorem: Rings and Fields

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Coordinate Systems and Frames: LocSat - Session 2

Explores geodesy, coordinate transformations, and system design for various locations.

Translations and Homotheties

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.

Local Diffeomorphisms

Explores local diffeomorphisms and their properties, including local inverses and neighborhood mappings.

Cylindrical and Spherical Coordinates, Rotations

Covers cylindrical and spherical coordinates, transformations between coordinate systems, and rotations in physics.

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Linear Algebra: Subspaces and Transformations

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Tensor Analysis: Coordinate Systems

Covers tensor analysis for arbitrary coordinate systems and introduces Christoffel symbols.

Lie Groups: Representations and Transformations

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

Translations and Homotheties

Covers translations, homotheties, and geometric transformations using vectors and matrices.

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Motivations for studying group actions

Covers group actions, bijections, evaluations, translations, homomorphisms, and inverses within universal actions.