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Lecture
Differentiability: Functions and Matrices
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Related lectures (29)
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Differentiability: Functions and Matrices
Explores differentiability for functions and matrices, covering partial differentiability, the Jacobean matrix, and the chain rule.
Functions of LR: Differentiability
Explains differentiability in LR functions and introduces the Jacobian matrix.
Differentiability and Partial Derivatives
Explores differentiability in two variables and the chain rule for compositions.
Differentiability and Composition
Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.
Connections: motivation and definition
Explores the definition of connections for smooth vector fields on manifolds.
Local Invertibility: Vector Fields
Covers local invertibility of vector fields and the Inverse Function Theorem.
Derivability and Composition
Covers derivability, linear applications, composition of functions, and the gradient vector.
Differentiation and Coordinate Changes in Multivariable Functions
Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.
Linear Applications and Matrix Derivatives
Explores linear applications, derivatives, Jacobian matrix, composition of functions, and matrix products.
Local Invertibility: Vector Fields
Covers local invertibility of vector fields and the Inverse Function Theorem.
