Lectures related to Integral: change of variable formula

Integral Change of Variable Formula

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

Generalized Integrals: Type 2

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

Fubini's Theorem: Multiple Integrals

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

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.

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Integral Calculus: Fundamentals and Applications

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

Fundamental Theorem of Calculus: Integrability, Anti-derivatives, Integration by Parts

Covers integrability, anti-derivatives, and integration by parts in calculus.

Fundamental Theorem Statement

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

Taylor Series and Definite Integrals

Explores Taylor series for function approximation and properties of definite integrals, including linearity and symmetry.

Fundamental Theorem of Calculus Example

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

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.

Techniques of Integration for Double Integrals

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

Derivative of an Integral

Covers the derivative of an integral dependent on a parameter and its fundamental properties.

Fundamental Theorem of Calculus: Integrals and Primitives

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

Divergence of Vector Fields

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

Multiple Integrals: Definitions and Properties

Covers the definition and properties of multiple integrals, including double and triple integrals.

Calculus Foundations: Taylor Series and Integrals

Introduces calculus concepts, focusing on Taylor series and integrals, including their applications and significance in mathematical analysis.

Magnetostatics: Magnetic Field and Force

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Multiple Integration: Part 2

Explores double integrals over unbounded domains and convergence of sequences.