Methods of Demonstrations: Recurrence and Taylor Formula

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Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Polar Coordinates: Jacobian Matrix and Examples

Covers polar coordinates, the Jacobian matrix, and examples of calculating areas in polar coordinates.

Coordinate Systems: Polar, Cylindrical, Spherical

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

Taylor Polynomial: Order 2

Explores Taylor polynomials of order 2 and their applications in differential calculus and polar coordinates.

Coordinate Systems: Transformations and Applications

Covers the transformation and application of coordinate systems, focusing on cylindrical coordinates and Jacobian matrix.

Coordinate Changes: Spherical System

Explores differentiability, coordinate changes, Jacobian determinant, gradient transformation, and chain rule.

General Physics: Mechanics

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

Coordinate Systems: Applications and Transformations

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

Recurrence on Two Variables

Covers methods of proof, such as recurrence on two variables and the gradient.

Circular motion: Concepts and Calculations

Explores circular motion concepts, centripetal force, velocity, and acceleration in different coordinate systems, with a focus on auto racing and Formula 1 tire physics.