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Lecture
Partial Differentiation
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Partial Differentiation
Explores simple examples of partial differentiation, demonstrating how to calculate partial derivatives and gradients in various scenarios.
Differentiability: Partial Derivatives and Hessiennes
Explains partial derivatives, Hessienne matrix, and their properties.
Partial Derivatives and Matrix Hessians
Covers partial derivatives, Hessian matrices, and their importance for functions with multiple variables.
Differentiability and Partial Derivatives
Explores differentiability in two variables and the chain rule for compositions.
Partial Derivatives: Matrices and Local Extrema
Covers hessian matrices, positive definite matrices, and local extrema of functions.
Second Order Approximations: The Hessian Matrix
Explores second order approximations for twice differentiable functions using the Hessian matrix.
Differentiability and Hessians
Explores functions of class C^p, Hessian matrices, and methods to verify differentiability at a point.
Derivatives and Tangent Planes
Covers derivatives, differentiability, and tangent planes for functions of one and two variables.
Derivatives of Functions: Differentiability and Matrices
Explores differentiability, matrices, and composite functions through examples and mathematical notations.
Differentiability: Theorem and Mean Value Theorem
Explores differentiability, gradients, and the Mean Value Theorem in open sets.