Lectures related to Cartesian Equations: Lines in the Plane

Covers the parametrization of straight lines and their geometric interpretation.

Covers linear independence, bases, and coordinate systems with examples and theorems.

Explores the scalar product of vectors, including properties and calculation methods.

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

Explores vector geometry basics, historical perspectives, and practical applications.

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Covers translations, homotheties, and geometric transformations using vectors and matrices.

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.