Lectures related to Differential Calculation: Notion of Derivative

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Directional Derivatives

Explores directional derivatives, their calculation, examples, and cases of lack of continuity.

Geometric Interpretation of Derivatives

Explores the geometric interpretation of derivatives and properties of derivable functions.

Differential Functions: Derivability and Gradient

Explores differentiability in functions and the role of gradients in directional derivatives.

Partial Derivatives and Gradient

Explores partial derivatives, gradient, directional derivatives, and differentiability in determining slopes.

Directional Derivatives

Explores directional derivatives, showcasing scenarios where they exist but the function is not differentiable.

Methods of Demonstrations: Recurrence and Differential Calculus

Covers methods of demonstrations and differential calculus of functions of several variables.

Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Partial Derivatives and Derivability Theorems

Introduces partial derivatives, directional derivatives, and differentiability of functions with examples and the Schwartz theorem.

Directional Derivatives and Tangent Planes

Explores directional derivatives, tangent planes, and function differentiability in multivariable calculus.

Objective function, Differentiability, the first order

Covers directional derivative, differentiability, and gradient matrices, emphasizing the first order.

Functions with Multiple Variables

Covers functions with values in R^m, discussing limits, partial derivatives, and differentiability.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Intermediate Value Theorem

Covers the Intermediate Value Theorem and its applications in finding solutions of equations and understanding the properties of continuous functions.

Partial Derivatives and Derivability

Explains partial and directional derivatives, and functions' derivability.

Partial Derivatives and Gradient

Covers partial derivatives, gradient, and second partial derivatives with their applications.

Derivability and Continuity

Explores derivability, continuity, and composite functions with illustrative examples.

Advanced Analysis II: Hessians and Directional Derivatives

Explores Hessians, directional derivatives, and function continuity in advanced analysis.

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Advanced Analysis II: Differentiable Functions

Explores differentiable functions, Taylor approximations, and directional derivatives in open sets.