Advanced analysis II: jordan-measurable sets

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Multiple Integrals: Extension and Properties

Explores the extension and properties of multiple integrals for continuous functions on rectangles.

Multiple Integration: Fubini Theorem

Explores multiple integration in R², focusing on double integrals over closed rectangles and the Fubini theorem.

Generalized Integrals: Definition and Applications

Covers the definition and applications of generalized integrals in advanced analysis, including real functions, differential equations, and multiple integrals.

Differentiation under Integral Sign

Explores differentiation under the integral sign, comparing it with the Riemann integral and discussing key assumptions and theorems.

Riemann Integral: Construction and Properties

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

Taylor Series and Riemann Integral

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

Magnetostatics: Magnetic Field and Force

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Lagrangian Multipliers: Extrema and Constraints

Covers Lagrangian multipliers, extrema with constraints, multiple integrals, and Darboux sums.

Riemann Sums and Definite Integrals

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.