Lectures related to Coordinate Vector Operations

Analytical Geometry: Rotation and Center

Explores rotation in analytical geometry, including center coordinates and fixed points.

Covers landmarks, coordinate systems, frames, and terminology in coordinates, emphasizing geometric angles and orthogonal vectors.

Translations and Homotheties

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.

Analytical Study of Plan: Points, Lines

Covers the analytical study of the plan, focusing on points and lines.

Analytical Geometry: Coordinates and Midpoints

Covers coordinates, midpoints, and abscissa in analytical geometry, providing practical problem-solving examples.

Tensor Analysis: Coordinate Systems

Covers tensor analysis for arbitrary coordinate systems and introduces Christoffel symbols.

Vectors: Coordinate Calculations

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Analytical Geometry: Lines Study

Covers the analytical study of lines in a plane, focusing on equations and geometric interpretations.

Analytical Geometry: Symmetry of Vectors

Explores the symmetry of vectors with respect to a line in Analytical Geometry.

Translations and Homotheties

Explores translations and homotheties, discussing their properties and practical applications in preserving geometric characteristics.

Linear Independence and Bases

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

Coordinate Systems: Polar, Cylindrical, Spherical

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

Analytical Study of Space

Covers the analytical study of space, focusing on points, lines, and planes.

Analytical Study of Space

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Vector Equations in Analytical Geometry

Explores vector equations for lines in the plane and the concept of 'observation points'.

Coordinate Systems and Vectors

Covers the concept of coordinate systems, landmarks, and vectors in space.

Rotating Vectors in Physics 1

Explores rotating vectors in physics, emphasizing the norm-angular speed relationship and various coordinate systems.

Vector Transformation and Tense

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.