Lectures related to Parametrized Curves in 2D: Examples and Properties

Parametrized Curves in 2D

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

Regular Curves and Constant Speed

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

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Curvature and Osculating Circle

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

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Surface of Revolution

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

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Derivatives and Functions: Definitions and Interpretations

Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.

Arc Length Approximation

Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.

Symmetries of Trigonometric Functions

Explores the symmetries of trigonometric functions, periodicity, and properties of even and odd functions.

Trigonometric Equations: Sinus and Cosinus

Covers the resolution of simple trigonometric equations involving sinus and cosinus functions.

Geometrical Aspects of Differential Operators

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

Continuity: Examples and Definitions

Covers the concept of continuity, providing examples and definitions of continuous functions.

Graphical Definition: Level Sets and Domains

Covers the graphical definition of functions, focusing on level sets and domains.

Integration Techniques: Part 2

Explores integration techniques, including indefinite integrals and variable changes, through trigonometric functions.

Limites en un point: définition et exemples

Covers the definition and examples of limits at a point in calculus.

Mathematics: Analysis and Algebra Overview

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Differential Geometry: Parametric Curves & Surfaces

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

Derivatives and Continuity

Explores derivatives, reciprocal functions, and continuity of functions with examples and formulas.

Limit of the Quotient and Periodicity

Explores the limit of the quotient for sequences and the periodicity of functions.