Tangent vector

Formal sciences
Mathematics
Geometry
Differential geometry

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Differential Geometry: Parametric Curves & Surfaces

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

Trigonometric Functions

Covers the concept of trigonometric functions and their applications in geometry.

Curves and Surfaces

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

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.

Curvilinear Integrals: Tangent Vectors and Oriented Arcs

Explains the tangent vectors and curvilinear integrals along oriented arcs.

Curves: Parameterized Curves and Tangent Vectors

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

Interpolation and Calculus

Covers revisions on calculus, derivation rules, interpolation, and tangent vectors.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Differential Geometry: Surfaces

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Tangent Vectors and Bézier Curves

Explains tangent vectors of curves and the construction and applications of Bézier curves in computer graphics.