Parametrized Curves in 2D

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Parametrized Curves in 2D: Examples and Properties

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

Regular Curves and Constant Speed

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

Surface of Revolution

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

Geometrical Aspects of Differential Operators

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

Curvature and Osculating Circle

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

Differential Geometry: Parametric Curves & Surfaces

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

Residue Theorem: Calculating Integrals on Closed Curves

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

Curves and Surfaces

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

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Derivatives and Functions: Definitions and Interpretations

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