Lectures related to Fundamental Theorem of Calculus Example

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

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 Change of Variable Formula

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

Fundamental Theorem of Integral Calculus

Explores the Fundamental Theorem of Analysis for continuous functions on closed intervals, illustrated with examples like integrating cos(x).

Differential Calculus: Theorem of Finite Increments

Explains how a function reaches its maximum and minimum values.

Divergence of Vector Fields

Explores divergence of vector fields, rotational definitions, and integral derivation applications.

Integrals of Type 1

Covers the definition of integrals of type 1 and the importance of continuity.

Fubini's Theorem: Multiple Integrals

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

The Intermediate Value Theorem

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

Integral: change of variable formula

Explores the change of variable formula for integrals and its applications.

Integral Calculus: Fundamentals and Applications

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

Fundamental Theorem Statement

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

Fundamentals of Digital Systems: Integral Theorems and Applications

Provides an overview of integral theorems and their applications in digital systems, focusing on iterated integrals and measure theory.

Fundamental Theorem of Analysis: Integral (Part 2)

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

Surjectivity of Derivative Application

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

Integration by Change of Variables

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

Extreme Values Theorem

Discusses the Extreme Values Theorem 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.

Fundamental Theorem of Calculus: Integrals and Primitives

Explains the Fundamental Theorem of Calculus, focusing on integrals and their relationship with primitives.