Symmetry of second derivatives

Formal sciences
Mathematics
Analysis
Vector analysis

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Partial Derivatives: Generalization and Order 2

Explains partial derivatives, generalization, and second order derivatives with examples and mathematical notations.

Differentiability in Analysis

Explores differentiability in analysis, discussing conditions for functions to be differentiable and continuous.

Differentiability and Hessians

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

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Partial Differential Equations

Introduces partial differential equations, covering derivatives, special cases, transformations, and the Jacobian matrix.

Differentiability Analysis

Explores differentiability, partial derivatives, Schwarz's theorem, and function continuity in mathematical analysis.

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.

Surface Integrals: Change of Variables

Explores surface integrals, change of variables, and properties of regular surfaces.

Functions of LR: Differentiability

Explains differentiability in LR functions and introduces the Jacobian matrix.

Partial Derivatives: Derivability

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.