Lectures related to Unit interval

Explores Taylor's theorem for functions on open intervals, focusing on nth derivatives.

Covers derivability on an interval, including Rolle's Theorem and practical applications in function analysis.

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

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Explores the theorems on maximum and minimum values of functions and their relation to continuity.

Explores continuity on a compact interval and its implications in limit calculations.

Covers the demonstration of the BH theorem and the continuity of functions.

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

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

Explains how a function reaches its maximum and minimum values.

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

Focuses on Theorem 2 for functions of class Cn and their Taylor expansion around a.

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

Explains the definition and uniqueness of developments limites for continuous functions on open intervals.

Covers Taylor series with integral remainder for open intervals and their applications in mathematical analysis.

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

Covers the properties of definite integrals and their implications through examples.

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

Explores continuous and derivable functions on closed intervals.

Covers the development of Taylor polynomials of order p around a point x.