Advanced analysis II: jordan-measurable sets

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Explores Fubini's Theorem for multiple integrals, emphasizing the n=2 case.

Explores properties and applications of Riemann integrals, Jordan-measurable sets, and continuity in advanced analysis.

Covers the definition and properties of multiple integrals, including double and triple integrals.

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

Covers the definitions and properties of double integrals over compact regions.

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Explores Jordan-measurable functions and double integrals for volume calculations in 3D space.

Covers the calculation of minimum points and the concept of definite integrals.

Explores Taylor series for function approximation and properties of definite integrals, including linearity and symmetry.

Explores the comparison between Lebesgue and Riemann integrals, demonstrating their equivalence when the Riemann integral exists.