Lectures related to Comparing Functions

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Power Functions: Properties and Derivatives

Covers properties of logarithms, power functions, and their derivatives, with examples illustrating key concepts.

Generalized Powers: Derivatives and Exponentials

Covers properties of logarithms, derivatives, exponentials, and sine-cosine functions.

Lagrange Method: 2 Constraints

Explains the Lagrange method with 2 constraints and composite functions' derivatives.

Continuous Functions and Derivatives

Covers the definitions of continuous functions and derivatives, emphasizing the concept of functions being continuous at a point and the notion of derivatives.

Intermediate Value Theorem

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

Rolle's Theorem: Applications and Examples

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

Derivatives Operations

Covers algebraic operations on derivatives and the concept of continuity and differentiability.

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Tangent to Graph of a Function

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

Differential Equations: Solutions and Derivatives

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

Derivatives: Definition and Properties

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Curve Length and Function Definition

Explores curve length, function definition, continuity, derivatives, integrals, and graphical representations of functions in two variables.

Surjectivity of Derivative Application

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

Directional Derivatives

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

Generalized Finite Increments

Explores generalized finite increments, derivatives, reciprocals, and Bernoulli-L'Hospital rule.

Closed Intervals: Definitions and Remarks

Explains definitions and remarks about closed intervals in functions.

Advanced Analysis II: March 23

Covers variable bounds, convergence of integrals, and homomorphisms in advanced analysis.

Derivability and Continuity

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