Curves in Space: Singularities and Developments

Related lectures (30)

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Covers the residual theorem from Cauchy, focusing on simple closed curves and holomorphic functions.

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

Explores spatial curves, focusing on intersections and singularities in architectural contexts.

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Covers the calculation of areas using integrals for geometric regions defined by curves and parametric equations.

Explains vector fields, Frenet frame, and local curve behavior using Frenet-Serret formulas.

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

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

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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