Lectures related to Parametric Curves Study Elements

Parametric Curves: Descartes' Folium

Covers Descartes' Folium, a parametric curve with specific equations and properties, including 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.

Parametric Curves: Infinite Branches

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

Asymptotes in Parametric Curves

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

Parametric Curves: Descartes' Folium

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

Parametric Curves: Analysis and Applications

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

Interpolation and Calculus

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

Curves and Surfaces

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

Parametric Curves: Introduction

Covers parametric curves, including examples, symmetry, tangent vectors, and derivative signs.

Tangent Vectors and Bézier Curves

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

Differential Geometry: Surfaces

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

Curves: Parameterized Curves and Tangent Vectors

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

Geometry of Hyperbolas and Ellipses

Explores the construction of hyperbolas and ellipses, along with geometry properties and exercises on circles.

Differential Geometry: Curves

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

Parametric Curves - Introduction

Introduces parametric curves and discusses tangent vectors and symmetry properties.

Analysis Reminder: Open Sets and Denseness

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

Parametric Curves: Lissajous and Folium

Explores parametric curves like Lissajous and the Folium of Descartes, discussing tangents, periodicity, and symmetry.

Surfaces in R^3: Curves and Regular Surfaces

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

Tangent vectors without embedding space: Making tangent spaces linear

Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.

Curvilinear Integrals: Tangent Vectors and Oriented Arcs

Explains the tangent vectors and curvilinear integrals along oriented arcs.