Lectures related to Optimization Theorem: Lagrange and Integrals

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

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

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

Change of Variables in Multiple Integrals

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

Multiple Integrals: Definitions and Properties

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

Techniques of Integration for Double Integrals

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

Generalized Integrals: Type 2

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

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Fundamental Theorem of Analysis: Integral (Part 2)

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

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Principal Value of an Integral: Examples

Covers examples of principal value of an integral with sin functions and singularities.

Integral Properties on Closed Pavés

Explores the integrability of continuous functions on closed pavés and the properties of their integrals, including boundedness and Darboux sums.

Multiple Integrals: Extension and Properties

Explores the extension and properties of multiple integrals for continuous functions on rectangles.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Generalized Integrals: Definition and Applications

Covers the definition and applications of generalized integrals in advanced analysis, including real functions, differential equations, and multiple integrals.

Essential Singularity and Residue Calculation

Explores essential singularities and residue calculation in complex analysis, emphasizing the significance of specific coefficients and the validity of integrals.

Multiple Integration: Part 2

Explores double integrals over unbounded domains and convergence of sequences.

Multiple Integration: Fubini Theorem

Explores multiple integration in R², focusing on double integrals over closed rectangles and the Fubini theorem.

Laplace Transform: Analytic Continuation

Covers the Laplace transform, its properties, and the concept of analytic continuation.

Advanced Analysis II: Double Integrals Techniques

Covers techniques for double integrals, emphasizing Fubini's Theorem and continuous functions.