Differential Calculation: Notion of Derivative

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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.