Coordinate Changes: Polar and Spherical

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Explores examples of applying the change of variable formula to simplify integrals over different regions.

Explores diffeomorphisms, implicit functions, and coordinate transformations in advanced analysis.

Covers derivability conditions, function composition, Jacobian matrix, and chain derivation.

Explores cylindrical and spherical coordinates with visual aids and practical experiments.

Covers cylindrical and spherical coordinate systems and their applications in 3D space.

Covers rotations around fixed points and spherical coordinates, discussing cinematic moments and angular velocity.

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

Covers the fundamental concepts of kinematics, including position, velocity, and acceleration in different coordinate systems.

Explores local diffeomorphisms and their properties, including local inverses and neighborhood mappings.

Introduces the basics of kinematics, covering reference frames, trajectories, and coordinate systems.