Regular Curves and Bijectivity

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Related lectures (26)

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Curvilinear Coordinates: Calculations and Examples

Covers curvilinear coordinates and area calculations using double integrals with examples of different curves.

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.

Analysis III: Third Class

Covers the correction of the simple curve definition and the importance of orientation in mathematical analysis.

Curves: Parameterized Curves and Tangent Vectors

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

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.

Curves in Space: Parametric Equations and Surfaces

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Curvature and Inflection Points

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.