Advanced Analysis II: Jordan-Measurable Functions

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

Clarifies the use of Jacobian, normal vectors in surfaces, and arccos(z) constraints.

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

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

Explores the Fubini theorem on closed rectangles in R², discussing integrability, iterated integrals, and compact sets.

Explores central force dynamics, conservation laws, and conic sections properties.

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

Explores Riemann integrability and Jordan measure, discussing the conditions for a set to be negligible.

Explores the change of variables theorem in the plane, emphasizing boundedness and continuity of functions.

Explores circular motion, friction, and Newton's laws in various coordinate systems.