Advanced analysis II: properties and applications

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Related lectures (32)

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Advanced analysis II: jordan-measurable sets

Explores Jordan-measurable sets and their properties, including volume calculations and change of variables in integrals.

Advanced Analysis II: Jordan-Measurable Functions

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

Fubini's Theorem: Multiple Integrals

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

Fubini Theorem on Closed Rectangles

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

Riemann Integral: Properties and Characterization

Explores the properties and characterization of the Riemann integral on different sets and measurable sets.

Multiple Integrals: Definitions and Properties

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

Riemann Integral: Construction and Properties

Explores the construction and properties of the Riemann integral, including integral properties and mean value theorem.

Lebesgue Integral: Comparison with Riemann

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

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Taylor Series and Riemann Integral

Explores Taylor series expansions and Riemann integrals, including limits, convergence, subdivisions, and sums.