Lectures related to Equations in Space: Cartesian Equations of Planes

Rectilinear Movement: Vectors and Scalars

Explores rectilinear movement, vector algebra, scalar products, and vector decomposition in a three-dimensional space.

Continuity Equations: Internal Entropy Production

Explores continuity equations and internal entropy production in various coordinate systems, emphasizing scalar functions and vector quantities.

Canonical Analysis: Quadratic Geometry

Explores canonical analysis of quadratic functions to identify conic shapes in planes.

Kinematics: Deformation and Expansion

Explores kinematics of deformation, focusing on radial and linear expansion, torsion, and rotation by an angle.

Tensor Analysis: Coordinate Systems

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

Covariant Derivatives and Christoffel Symbols

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

Vectors: Basic Concepts and Operations

Covers the basics of vectors, including properties, operations, and graphical representation.

Coordinate Systems and Vectors

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