Lectures related to Integration by Change of Variables

Rolle's Theorem: Applications and Examples

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

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

Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Bisection Method: Proposition and Demonstration

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

Differential Calculus: Theorem of Finite Increments

Explains how a function reaches its maximum and minimum values.

The Intermediate Value Theorem

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

Surjectivity of Derivative Application

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

Functions: Continuity and Derivability

Explores continuous and derivable functions on closed intervals.

Derivability and Maximum Values

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

Uniform Continuity: Proof and Theorem

Covers the concept of uniform continuity and a theorem on continuous functions.

Derivability on an Interval: Rolle's Theorem

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

Extreme Values Theorem

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

Rolle's Theorem and Mean Value Theorem

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

Fundamental Theorem of Calculus Example

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

Intermediate Values Theorem

Explores the Intermediate Values Theorem for continuous functions on closed intervals.

Fundamental Theorem of Analysis: Integral (Part 2)

Explores the integral part of the Fundamental Theorem of Analysis with examples like y = cos(x).

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Continuous Functions: Definitions and Criteria

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

Properties of Continuous Functions

Explores the continuity of elementary functions and the properties of continuous functions on closed intervals.

Advanced Analysis I: Continuous Functions on Compact Sets

Explores the necessity of uniform continuity for continuous functions on compact sets.