Tangent Vectors and Bézier Curves

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Tangent vectors without embedding space: Making tangent spaces linear

Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.

Curves in Space: Parametric Equations and Surfaces

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

Geometrical Aspects of Differential Operators

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

Parametric Curves: Analysis and Applications

Covers the analysis of parametric curves and their tangent vectors, focusing on applications and geometric interpretations.

Length of Curves and Tangent Vectors

Covers the calculation of the length of curves and the properties of tangent vectors.

Parametric Curves: Lissajous and Folium

Explores parametric curves like Lissajous and the Folium of Descartes, discussing tangents, periodicity, and symmetry.

Topology of Riemann Surfaces

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

Projective Geometry: Tangent Lines

Discusses the correction of tangent lines and projective plane curves, exploring topological applications and curve structure.

Surfaces in Space

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Advanced Analysis II: Isoclines Method

Explores the Isoclines Method and solutions of differential equations with tangents.