Lectures related to Fundamental Theorem of Integral Calculus

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

Integral Calculus: Fundamentals and Applications

Explores integral calculus fundamentals, including antiderivatives, Riemann sums, and integrability criteria.

Rolle's Theorem: Applications and Examples

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

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

Integral Calculus: Introduction and Summary

Provides an overview of integral calculus, including Darboux sums, closed box subdivisions, and integrability of continuous functions.

Generalized Integrals: Type 2

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

Fundamental Theorem of Analysis: Integral (Part 2)

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

Differential Calculus: Theorem of Finite Increments

Explains how a function reaches its maximum and minimum values.

The Intermediate Value Theorem

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

Fundamental Theorem Statement

Explains the fundamental theorem of integral calculus and its implications for continuous functions on closed intervals.

Integral Calculus: Techniques and Applications

Explores integral calculus techniques, areas under graphs, Darboux sums, and the fundamental theorem of calculus.

Limits and Continuity: Analysis 1

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

Functions: Continuity and Derivability

Explores continuous and derivable functions on closed intervals.

Integration by Change of Variables

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

Integral Change of Variable Formula

Explores the integral change of variable formula and its applications in calculus.

Fields from Potential: Derivation and Curvilinear Integral

Explores deriving fields from a potential, curvilinear integrals, and necessary conditions for domains.

Intermediate Values Theorem

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

Bisection Method: Proposition and Demonstration

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

The Intermediate Value Theorem

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

Derivative of Integral with Parameter Dependency

Explores the derivative of an integral with parameter dependency and its continuity.