Regular Curves and Constant Speed

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Parametrized Curves in 2D

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

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.

Curves and Surfaces

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

Differential Geometry: Parametric Curves & Surfaces

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

Curvature and Osculating Circle

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

Parametrized Curves in 2D: Examples and Properties

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

Vector Calculus: Line Integrals

Covers the concept of line integrals and their application in vector fields.

Kinematic Quantities and Linear Mass Density

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

Residue Theorem: Calculating Integrals on Closed Curves

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