Lectures related to Properties of the Integral

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

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

Generalized Integrals: Type 2

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

Change of Variables in Multiple Integrals

Explores changing variables in multiple integrals, with a focus on polar transformations and their applications in calculating areas.

Definite Integral: Riemann Sum

Introduces Riemann sums as approximations of the area under a function's graph.

Integral Change of Variable Formula

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

Multiple Integration: Part 2

Explores double integrals over unbounded domains and convergence of sequences.

Properties of the Integral

Explores properties of the integral, including summation, continuous functions, and proofs related to partitions and interval points.

Fundamental Theorem of Analysis: Integral (Part 2)

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

Fundamental Theorem of Calculus Example

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

Generalized Integrals: Bounded Interval

Introduces generalized integrals on a bounded interval, discussing convergence, divergence, comparison criteria, variable substitution, and corollaries.

Techniques of Integration for Double Integrals

Covers techniques for computing double integrals using Fubini's Theorem and examples.

Calculating Integrals in Multiple Dimensions

Explores the method of calculating integrals in multiple dimensions using a step-by-step approach and examples.

Exposition des trois types

Covers the exposition of the three types of generalized integrals and their combinations.

Divergence of Vector Fields

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

Analysis II: Abstract Integration

Explores the extension of functions and the conditions for continuity.

Integral Calculus: Fundamentals and Applications

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

Analysis II: Abstract Integration

Explores abstract integration of functions and the need for stronger conditions beyond continuity.

Integral: change of variable formula

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

Bisection Method: Proposition and Demonstration

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