Integrals in Higher Dimensions

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Related lectures (30)

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Volume Calculation in R^3

Covers the calculation of volumes of subsets in R^3 using double integrals.

Functions xr, r>0, on 10,1

Covers the properties of functions xr, r>0, on 10,1, including limits and integrals.

Multiple Integrals: Defining Integrals of Functions in R^2

Covers the definition of double integrals for functions of two variables over a domain in the plane R^2.

Generalized Integrals: Definition and Applications

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

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Multiple Integrals: Definitions and Properties

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

Fubini Theorem on Closed Rectangles

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

Green's Theorem: Understanding Rotations and Closed Paths

Explores Green's Theorem, rotations, closed paths, and integral signs.

Integral Applications: Plan Region Areas

Covers the calculation of areas of regions in the plane using integrals and explores convex functions.

Change of Variables: Integrability and Fubini's Theorem

Explores changing variables in double integrals and applying Fubini's theorem in R² for simplifying calculations.