Lectures related to Parametric Curves and Derivatives

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

Explores polynomial operations, properties, and subspaces in vector spaces.

Explores the definition of connections for smooth vector fields on manifolds.

Polar Coordinates: Position and Velocity

Explores polar coordinates, position, velocity, and acceleration vectors in Cartesian and polar systems, including cylindrical and spherical coordinates.

Differential Geometry: Parametric Curves & Surfaces

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

Geometric Areas: Integrals and Regions

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

Parametric Curves: Pascal's Limaçon

Introduces the Limaçon de Pascal, a curve described by a moving point on a circle.

Parametric Curves: Limaçon de Pascal

Introduces the Limaçon de Pascal, a parametric curve with unique properties.