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Coordinate Systems: Polar, Cylindrical, Spherical

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

Discusses the graph of a relation and the concept of separation.

Polar Coordinates: Position and Velocity

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

Kinematics: Position, Velocity, Acceleration, Trajectory

Covers the fundamental concepts of kinematics, including reference frames, position vectors, velocity, acceleration, and trajectories.

General Physics: Mechanics

Covers mechanics concepts in different coordinate systems, explaining position, velocity, and acceleration vectors.

Special Relativity

Covers the main points of special relativity, including symmetries, transformations, 4-vectors, Maxwell equations, and proper time.

Surfaces: The Torus

Explores the definition of surfaces, focusing on the torus and its construction through various examples and morphic images.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Optimization Problems: Algebra and Trinomial Equations

Explores optimization problems in algebra and trinomial equations, focusing on maximizing area with fixed perimeters.

Covariant Derivatives and Christoffel Symbols

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

Coordinate Systems: Applications and Transformations

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

Coordinate Systems: Cylindrical, Spherical, Rotations

Covers cylindrical and spherical coordinates, position, velocity, and acceleration vectors.

Relative Positions: Examples

Covers examples of relative positions in a 2D space, focusing on equations involving x and y coordinates.

Indicial Notation and Vectors

Explores indicial notation, vectors, and the transformation law in the context of mass flux density.

Consequences of TBS

Explores the consequences of the Total Bell System (TBS) in a commutative body.

Relations and Sequences

Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.

Introduction to Category Theory: Examples

Introduces the theory of categories through examples and discusses the product of categories.

Coordinate Systems and Rotations

Covers cylindrical and spherical coordinates, vector positions, velocities, accelerations, and rotations.

Homotopy: Fundamentals and Examples

Covers the fundamentals of homotopy and its applications in topology.

Differential Equations: Mathematical Complements Log in to Mediaspace to watch this video

Covers the definition of differential equations and their relation to functions and derivatives.