Concept

Domain (mathematical analysis)

Related lectures (32)

Green Theorem: Analyzing Potential Derivatives

Explores potential derivatives, Green theorem, simple curves, and adherence in open domains.

Explores limits, continuity, and elementary functions' properties, emphasizing the importance of understanding continuous functions.

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Green's Theorem: Domain Analysis

Explores Green's Theorem application in domain analysis and potential functions.

Fubini Theorem: Double and Triple Integrals

Explores the Fubini theorem for double and triple integrals, focusing on regular domains and order of integration.

Advanced Analysis II: Differentiability and Continuity

Explores differentiability and continuity in advanced analysis, emphasizing the importance of continuity and demonstrating key concepts.

Regular Curves and Bijectivity

Explores regular curves and their bijectivity properties in mathematical analysis.

Derivatives and Local Extrema

Explores derivatives, local extrema, and function variation in mathematical analysis.

Semi-groups of Contractions

Explores semi-groups of contractions, discussing uniqueness theorems, maximum principles, and the infinitesimal generator.

Factorisation: Real Coefficients Examples

Covers the factorization of polynomials with real coefficients in the complex domain, demonstrating how to find complex roots and obtain irreducible factors.

FK-Percolation and the Six-Vertex Model: Critical Phenomena

Covers the transition from the six-vertex model to FK-percolation, focusing on critical phenomena and phase transitions in two-dimensional systems.

Continuous Functions: Theory and Applications

Explores continuous functions, Cauchy criterion, and function extension by continuity.