Lectures related to Intermediate Value Theorem

Rolle's Theorem: Applications and Examples

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

Continuous Functions: Definitions and Criteria

Covers the definition and criteria for continuous functions and explores the intermediate value theorem.

Geometric Interpretation of Derivatives

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

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Surjectivity of Derivative Application

Covers the surjectivity of the derivative application for continuous functions on closed intervals.

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Continuous Functions: Theory and Applications

Explores continuous functions, Cauchy criterion, and function extension by continuity.

Advanced Analysis: Differential Equations Overview

Covers the fundamentals of differential equations, their properties, and methods for finding solutions through various examples.

Differential Equations: Solutions and Derivatives

Explores differential equations solutions, derivatives, differentiability, composite functions, and continuous functions.

Partial Derivatives: Derivability

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

Differentiability of Functions of Several Variables

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

Advanced Analysis: Differential Equations Overview

Provides an overview of differential equations, their properties, and methods for finding solutions through various examples and graphical representations.

Derivatives and Tangent Planes

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Differential Equations: Solutions and Functions

Explores solutions of differential equations and properties of functions.

Derivatives and Local Extrema

Explores derivatives, local extrema, and function variation in mathematical analysis.

Directional Derivatives

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

Partial Derivatives and Differential Equations

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

Rolle's Theorem and Mean Value Theorem

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

Existence and Uniqueness of Local Solutions

Explores the proof of existence and uniqueness of local solutions for a Cauchy problem with separable variables.