Curves in Space: Singularities and Developments

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Covers the mechanics of slender structures, focusing on exact kinematics and equilibrium equations of rods.

Explores spatial curves, singularities, and mechanisms, analyzing their geometric properties and applications.

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

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

Explores the Frenet-Serret formulas for curvature and torsion in three-dimensional space.

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

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

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

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

Examines geometric singularities in architectural design through the analysis of spatial intersections.