Partial Derivatives: Matrices and Local Extrema

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Partial Derivatives and Differential Equations

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Mathematical Complements: df or δf

Explores mathematical tools for differentials of functions of multiple variables and their practical applications in thermodynamics and real-life scenarios.

Partial Derivatives: Definitions and Interpretations

Explores partial derivatives, their interpretations, and geometric applications in multivariable functions.

Partial Differentiation

Explores the process of partial differentiation through various examples in two dimensions, emphasizing the importance of treating each variable separately.

Linear Applications and Matrix Derivatives

Explores linear applications, derivatives, Jacobian matrix, composition of functions, and matrix products.

Optimization Techniques: Local and Global Extrema

Discusses optimization techniques, focusing on local and global extrema in functions.

Differentiability and Hessians

Explores functions of class C^p, Hessian matrices, and methods to verify differentiability at a point.

Advanced Analysis II: Local Extrema and Hessians

Covers the analysis of local extrema and Hessians, focusing on the development of limit notations.

Symmetric Matrices: Diagonalization

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Objective function, Differentiability, The second order

Explores the role of first and second derivatives in function curvature and convexity.