Diffeomorphism and implicit functions

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

Explores differentiability and coordinate transformations between polar and spherical systems.

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

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

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

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

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

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

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

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