Differentiable curve

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Related lectures (30)

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Derivatives and Functions: Definitions and Interpretations

Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.

Frenet-Serret Formulas: Curvature and Torsion

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

Differential Geometry: Parametric Curves & Surfaces

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

Curve Integrals: Properties and Applications

Explores curve integrals, demonstrating properties and real-life applications, including tunnel excavation and safety assessment based on crime density.

Interpolation and Calculus

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

Regular Curves and Bijectivity

Explores regular curves and their bijectivity properties in mathematical analysis.

Parametrized Curves in 2D

Covers the concept of parametrized curves in 2D and their properties.

Stereographic Projection and Metric Tensors

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.

Arc Length Approximation

Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.

Surfaces in R^3: Curves and Regular Surfaces

Covers curves in R^2, regular surfaces in R^3, and geometric properties of edges.