Lectures related to Local Invertibility: Vector Fields

Explores bijective functions, coordinate transformations, and graphical representations in two dimensions.

Explores differentiability for functions and matrices, covering partial differentiability, the Jacobean matrix, and the chain rule.

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

Explores partial differentiability, the chain rule, and invertibility of vector fields.

Explores examples of divergence in vector fields and their physical meanings.

Explores the divergence theorem and corollaries related to Green identities in the plane, demonstrating their application through examples.

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Explores gradient in scalar fields, directional derivatives, and level sets.

Covers tensors, Lorentz transformations, and electrodynamics in relativistic notation.