Lectures related to Curve orientation

Geometrical Aspects of Differential Operators

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

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Circular Trigonometry: Understanding Geometric Angles

Explores the concept of angles in circular trigonometry, emphasizing geometric angles and their properties.

Geometric Transformations: Translation and Homothety

Explores geometric transformations like translation and homothety in the plane.

From STL to SLI and CLI

Explores the transformation process from .STL to .SLI and .CLI formats.

Analysis III: Third Class

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

Curve Parameterization

Explores curve parametrization, including setting curves, trace, and direction preservation.

Analytical Geometry: Oriented Angles

Explores oriented angles in analytical geometry, discussing unit vectors, trigonometric functions, matrix representations, and rotations.

Green's Theorem: Boundary and Normal Vectors

Explores boundaries, normal vectors, and Green's theorem application in transforming integrals.

Green Theorems: Divergence Theorem and Identities of Green

Explores the application of Green theorems in 2D and 3D spaces.

Understanding Positive and Negative Orientation in Curves

Explores positive and negative orientation in curves, emphasizing their impact on tangent and normal vectors.

Analytical Geometry: Rotation and Center

Explores rotation in analytical geometry, including center coordinates and fixed points.

Residues Theorem

Explores the Residues Theorem and the classification of holomorphic functions.

Parametric Curves: Envelope and Caustics

Explores parametric curves, focusing on finding envelopes and caustics.

Geometric Curve Reparameterization

Covers the reparameterization of geometric curves and the concept of 'same geometric curve'.

Divergence Theorem: Green Identities in R²

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

Surface Integrals: Regular Parametrization

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

Polymer Conformation: Beyond the Freely Jointed Chain

Explores polymer conformation beyond the Freely Jointed Chain model, emphasizing the importance of correlations and rigidity.

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.

Cauchy Integral Formula

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