Multiple Integrals: Problematic Cases and Compact Domains

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Two-loop Computations: External Legs and Internal Propagators

Covers the computation of two-loop diagrams with external legs and internal propagators.

Unclosed Curves Integrals

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

Notation in Multivariable Calculus

Reviews the notation used in multivariable calculus, emphasizing accurate translation between different forms of integrals.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Integrals of Functions

Covers integrals as the reciprocal function of the derivative and explains displacement integral of velocity and variation of speed and acceleration in rectilinear motion.

Taylor Series and Definite Integrals

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

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Green's Functions in Laplace Equations

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

Integrals in Higher Dimensions

Explores integrals in higher dimensions, emphasizing the versatility of integration methods and the significance of changing the order of integration.

Geometric Examples: Triangles and Functions

Explores geometric examples of triangles and functions, demonstrating the variation of x and y within defined ranges.