Lectures related to Implicit curve

Implicit Curves: Analysis & Regular Points

Covers implicit curves, regular and critical points, convexity, concavity, and inflection points.

Regular Curves and Constant Speed

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

Kinematic Quantities and Linear Mass Density

Discusses kinematic quantities and linear mass density in examples of metal wires.

Implicit Functions: Tangent Plan Equation

Covers implicit functions of class C and the equation of the tangent plane.

Tangent Plane to Implicit Function

Explores the tangent plane to implicit functions, emphasizing equations and graphical representations.

Parametric Curves: Envelope and Caustics

Explores parametric curves, focusing on finding envelopes and caustics.

Implicit Functions Theorem

Discusses finding min and max of functions on compact sets and the theorem of implicit functions.

Implicit Function Theorem: Tangent Hyperplane

Explores the implicit function theorem for n=2 and n=3, focusing on tangent hyperplanes.

Geometrical Aspects of Differential Operators

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

Parametric Curves: Descartes' Folium

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

Optimality conditions: second order

Explores necessary and sufficient optimality conditions for local minima on manifolds, focusing on second-order critical points.

Regular Curves Analysis

Explores the analysis of regular curves, flow quantification, domain determination, and surface regularity.

Surface Integrals: Implicit Surfaces

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

Regular Curves and Bijectivity

Explores regular curves and their bijectivity properties in mathematical analysis.

Parametric Curves: Descartes' Folium

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

Green Theorem: Analyzing Potential Derivatives

Explores potential derivatives, Green theorem, simple curves, and adherence in open domains.

Regular Curves: Parametrization and Tangent Vectors

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

Vector Analysis: Scalar Fields

Covers the analysis of scalar fields, including divergence, gradient, and Laplacian.

Parametric Curves: Limaçon de Pascal

Introduces the Limaçon de Pascal, a parametric curve with unique properties.

Parametric Curves: Pascal's Limaçon

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