Change of Coordinates: Analysis Week 8

Related lectures (29)

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Covers the inverse function theorem, Jacobian matrix, injective functions, bijective functions, and spherical coordinates.

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Explores invertible matrices, injective functions, and the theory of reciprocal functions.

Covers spherical coordinates and the determinant of Jacobi in linear algebra.

Covers examples of coordinate transformations, focusing on polar and spherical coordinates.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Covers the definitions of coordinate changes and the Laplacian of a function.

Discusses center of gravity, variable change, spherical coordinates, and bijectivity in mathematical analysis.

Explains the inverse function identity and provides examples with ln(x), sin(x), and cos(x).

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.