Lectures related to Surjectivity of Derivative Application

Rolle's Theorem: Applications and Examples

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

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

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Rolle's Theorem and Mean Value Theorem

Covers Rolle's Theorem and the Mean Value Theorem, demonstrating their applications through examples.

Rolle's Theorem and Mean Value Theorem

Covers Rolle's Theorem and the Mean Value Theorem with illustrative examples.

Closed Intervals: Definitions and Remarks

Explains definitions and remarks about closed intervals in functions.

Rolle's Theorem

Explores Rolle's Theorem for continuous and differentiable functions on closed intervals.

Differential Calculus: Theorem of Finite Increments

Explains how a function reaches its maximum and minimum values.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Integration by Change of Variables

Covers integration by change of variables and the derivation in chain rule.

The Intermediate Value Theorem

Explains the Intermediate Value Theorem for continuous functions on closed intervals.

Bisection Method: Proposition and Demonstration

Covers the bisection method proposition and its demonstration for finding roots.

Derivability and Maximum Values

Covers the theorem of intermediate values and finding maximum and minimum values of functions on closed intervals.

Directional Derivatives

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

Continuous Derivatives

Covers the concept of continuous derivatives and their application in analyzing functions and determining critical points.

Objective function, Differentiability, the first order

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

Fundamental Theorem of Calculus Example

Demonstrates the practical importance of the fundamental theorem of calculus through a detailed example.

Extreme Values Theorem

Discusses the Extreme Values Theorem for continuous functions on closed intervals.

Functions: Continuity and Derivability

Explores continuous and derivable functions on closed intervals.

Functions Reciprocal and Monotone: Advanced Analysis II

Explores reciprocal functions, strict monotonicity, and continuity in advanced analysis.