Lectures related to Integrals in Higher Dimensions

Improper Integrals: Convergence and Comparison

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

Green's Functions in Laplace Equations

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

Magnetostatics: Magnetic Field and Force

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

Multiple Integration: Fubini Theorem

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

Unclosed Curves Integrals

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Comparison Series and Integrals

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

Techniques of Integration for Double Integrals

Covers techniques for computing double integrals using Fubini's Theorem and examples.

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Fubini's Theorem: Multiple Integrals

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

Taylor Series and Definite Integrals

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

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.