Lectures related to Extrema: Local and Global

Rolle's Theorem: Applications and Examples

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

Covers the Mean Value Theorem in differential calculus, focusing on critical points and global extrema within intervals.

Extreme Values of Continuous Functions

Covers extreme values of continuous functions on compact sets and differentiability.

Derivability and Maximum Values

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

Properties of Continuous Functions: Maximum and Minimum

Explores the properties of continuous functions, including maximum and minimum values and intermediate values.

Continuous Functions: Derivability and Global Properties

Covers continuous functions, derivability, and global properties in differential calculus.

Fubini's Theorem: Multiple Integrals

Explores Fubini's Theorem for multiple integrals, emphasizing the n=2 case.

Analyse II: Theorems on Continuous Functions and Extremums

Covers the theorems on continuous functions and extremums in compact sets.

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.

Extrema and Implicit Functions

Explores conditions for local extrema in two and three variables, along with implicit functions and finding absolute minima and maxima.

Extreme Values Theorem

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

Max Local Exercise

Covers finding unique local maxima and functions oscillating infinitely.

Lagrange Method: 2 Constraints

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

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Bisection Method: Proposition and Demonstration

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

Continuous Functions on Compact Sets

Explores continuous functions on compact sets, discussing boundedness and extremum values.

Properties of Continuous Functions

Covers the properties of continuous functions and explores inverse and injective functions with examples.

Generalized Integrals: Type 2

Covers the integration of limit expansions and continuous functions by pieces.

Global and local extrema of functions

Explains global and local extrema of functions, including the possibility of functions having no maximum or minimum values.

Function Approximations

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.