Local Invertibility: Vector Fields

Related lectures (28)

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Covers local invertibility of vector fields and the Inverse Function Theorem.

Explains differentiability in LR functions and introduces the Jacobian matrix.

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

Covers derivability, linear applications, composition of functions, and the gradient vector.

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

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

Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.

Discusses inverse functions and local invertibility based on the determinant of the Jacobian matrix.

Explores differentiable functions in R², including vector fields and coordinate transformations.

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