Concept

Jordan curve theorem

Related lectures (27)

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Residues Theorem

Explores the Residues Theorem and the classification of holomorphic functions.

Residues Theorem Applications

Explores applications of the residues theorem in various scenarios, with a focus on Laurent series development.

Green Theorem: Analyzing Potential Derivatives

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

Analysis III: Third Class

Covers the correction of the simple curve definition and the importance of orientation in mathematical analysis.

Divergence Theorem: Green Identities in R²

Explores the divergence theorem and corollaries related to Green identities in the plane, demonstrating their application through examples.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Cauchy Integral Formula

Covers the Cauchy Integral Formula, Morera's Theorem, Liouville's Theorem, and the Fundamental Theorem of Algebra.

Laurent Series: Definition and Properties

Covers the definition and properties of Laurent series, including convergence and function expansion.

Field Derivation: Potential and Convexity

Covers the derivation of a field from a potential and explores convexity.

Residual Theorem: Cauchy

Covers the residual theorem from Cauchy, focusing on simple closed curves and holomorphic functions.

Convex Functions: Analytical Definition and Geometric Interpretation

Explores convex functions, including properties, definitions, and analytical interpretations, demonstrating how to determine convexity and evaluate limits for different types of functions.

Tangent and Normal Vectors: Curves in R^2

Covers the parameterization of curves, tangent and normal vectors, simple closed curves, exterior normal, regular curves, and domains in R^2.

The Jordan Curve Theorem

Explores the Jordan Curve Theorem, illustrating the division of a plane by a simple closed curve into two regions.

Cauchy Theorem and Laurent Series

Covers the Cauchy theorem, the conditions to apply it, and the Laurent series.

Green-Riemann Formula: Curvilinear Integrals

Covers the Green-Riemann formula, connectedness by arcs, parametrization of curves, and open simply connected domains in the Oxy plane.

Descriptive Geometry: Cones and Cylinders

Explains the definitions of cones and cylinders as ruled surfaces and how to find tangent planes to them.

Vector Fields Analysis

Explores vector fields analysis, covering curvilinear integrals, potential fields, and field connectivity conditions.

Fixed-Point Method: Example

Covers the fixed-point method with an example and its convergence criteria.

Surface Integrals: Regular Parametrization

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.