Lectures related to Local Invertibility: Vector Fields

Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Differentiability and Composition

Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.

Derivability and Composition

Covers derivability conditions, function composition, Jacobian matrix, and chain derivation.

Local Frames

Covers the concept of local frames, their construction, and limitations.

Differentiability and Tangent Planes in Multivariable Functions

Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.

Diffeomorphism and implicit functions

Explores diffeomorphisms, implicit functions, and coordinate transformations in advanced analysis.

Computing Derivatives: Derivatives and Algebraic Operations

Covers the computation of derivatives and the properties of differentiable functions.