Lectures related to Parametric Curves: Descartes' Folium

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

Differential Geometry: Parametric Curves & Surfaces

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

Curves: Parameterized Curves and Tangent Vectors

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

Curves and Surfaces

Covers the representation of plane curves and the nature of obtained curves.

Tangent Vectors and Bézier Curves

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

Parametric Curves Study Elements

Covers the study of parametric curves and tangent vectors.

Analysis Reminder: Open Sets and Denseness

Reviews open sets, denseness, real numbers, convergence, curves, continuity, and derivatives in analysis.

Parametric Curves: Analysis and Applications

Covers the analysis of parametric curves and their tangent vectors, focusing on applications and geometric interpretations.

Surfaces in R^3: Curves and Regular Surfaces

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

Parametric Curves: Infinite Branches

Discusses parametric curves with infinite branches and the behavior of functions near asymptotes.

Differential Geometry: Curves

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

Asymptotes in Parametric Curves

Explores asymptotes in parametric curves, symmetries, tangent vectors, and qualitative studies near stationary points.

Interpolation and Calculus

Covers revisions on calculus, derivation rules, interpolation, and tangent vectors.

Vector Calculus: Line Integrals

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

Differential Geometry: Surfaces

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Regular Curves and Constant Speed

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

Regular Curves: Parametrization and Tangent Vectors

Explores regular curves, examples like segments and functions, and curvilinear integrals along regular curves.

Geometrical Aspects of Differential Operators

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

Surface of Revolution

Explains the parametric equations of surfaces of revolution generated by curves in space.

Parametric Curves: Envelope and Caustics

Explores parametric curves, focusing on finding envelopes and caustics.