Functional integral equations constitute a broad class of problems in which an unknown function appears under an integral sign. These equations play a pivotal role in modelling complex phenomena in ...

Electromagnetic integral equations offer a powerful framework for modelling wave propagation and scattering phenomena by recasting Maxwell’s equations into formulations involving integrals over ...

SIAM Journal on Applied Mathematics, Vol. 75, No. 3 (2015), pp. 929-952 (24 pages) We present a new class of well-conditioned integral equations for the solution of two and three dimensional ...

SIAM Journal on Applied Mathematics, Vol. 73, No. 5 (2013), pp. 1811-1829 (19 pages) This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally ...

Engineers have designed a metamaterial device that can solve integral equations. The device works by encoding parameters into the properties of an incoming electromagnetic wave; once inside, the ...

Analogue computer: Brian Edwards (left), Nader Engheta (centre) and Nasim Mohammadi Estakhri show-off their microwave protoype. (Courtesy: Eric Sucar/University of Pennsylvania) Metamaterials have ...

Integral equations in various scientific theories and their relation to differential equations. Methods of solving linear problems with Hilbert Schmidt, Cauchy, and Wiener-Hopf type kernels; ...

Glenn Bruda, a 17-year-old high school student, is credited with the discovery of a novel calculus formula that he has named the Maclaurin Integration technique. (Photo courtesy of Jennifer Bruda) ...

Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion ...