Lectures related to Regular Curves: Parametrization and Tangent Vectors

Geometrical Aspects of Differential Operators

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

Vector Calculus: Line Integrals

Covers the concept of line integrals and their application in vector fields.

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.

Curvilinear Integrals

Covers curvilinear integrals in R^n, focusing on continuous functions and curves.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Curvilinear Integrals: Tangent Vectors and Oriented Arcs

Explains the tangent vectors and curvilinear integrals along oriented arcs.

Understanding Positive and Negative Orientation in Curves

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

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.

Curves: Parameterized Curves and Tangent Vectors

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Curve Integrals of Vector Fields

Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Surface Integrals: Regular Parametrization

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

Vector Fields Analysis

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

Regular Curves and Constant Speed

Covers regular curves and constant speed, with examples of circles and helices.

Curvilinear Integrals: Interpretation and Convexity

Explores the interpretation of curvilinear integrals in vector fields and the proof of potential fields.

Parametric Curves: Descartes' Folium

Covers Descartes' Folium, a parametric curve with specific equations and properties, including domain boundaries and tangent vector analysis.

Differential Geometry: Curves

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

Tangent Vectors and Bézier Curves

Explains tangent vectors of curves and the construction and applications of Bézier curves in computer graphics.

Surface Integrals: Implicit Surfaces

Covers implicit surfaces, parametric descriptions, regular parametrization, normal vectors, and orientable surfaces.

Surfaces in R^3: Curves and Regular Surfaces

Covers curves in R^2, regular surfaces in R^3, and geometric properties of edges.