Lectures related to Parametric Curves: Limaçon de Pascal

Introduces the Limaçon de Pascal, a curve described by a moving point on a circle.

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

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.

Ellipse and Circle: Geometric Analysis

Covers the geometric analysis of ellipses and circles, including foci, center, and symmetry.

Parametrized Curves in 2D

Covers the concept of parametrized curves in 2D and their properties.

Parametric Curves - Introduction

Introduces parametric curves and discusses tangent vectors and symmetry properties.

Regular Curves and Constant Speed

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

Parametric Curves: Introduction

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

Descriptive Geometry: The Sphere

Explores the properties and sections of a sphere, including symmetry, tangent planes, and circle projections.

Parametric Curves and Derivatives

Explores parametric curves, derivatives, equivalence of paths, and local behavior of functions.

Surfaces in Space

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Parametric Curves: Analysis and Applications

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

Differential Geometry: Parametric Curves & Surfaces

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

General Conics: Symmetry and Elimination

Covers the concepts of mixed product, cross product, homo coordinates, and general conics.

Residue Theorem: Calculating Integrals on Closed Curves

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

Differential Geometry: Curves

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

Parametrized Curves in 2D: Examples and Properties

Explores parametrized curves in 2D, including segments, straight lines, and circles with trigonometric functions.

Isometries & Orientation in Modern Geometry

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Parametric Curves: Lissajous and Folium

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