Advanced Studies in the Mathematical Theory of Scattering (Introduction chapter/excerpt)

We present here the contents and the introduction chapter of our book, 'Advanced Studies in the Mathematical Theory of Scattering', recently published. This book is a collection of independent mathematical studies, describing the analytical reduction of complex generic problems in the theory of scattering and propagation of electromagnetic waves in the presence of imperfectly conducting objects. Their subjects are as follows: – a global method for the scattering by a multimode plane; – diffraction by an impedance curved wedge; – scattering by impedance polygons; – advanced properties of spectral functions in frequency and time domains; – bianisotropic media and related coupling expressions; – exact and asymptotic reductions of surface radiation integrals. Each of our approaches can be qualified as analytical, when it leads to exact explicit expressions, or, as semi-analytical, when it drastically reduces the mathematical complexity of studied problems. Therefore, they can be used in mathematical physics and engineering, to analyze and model, as well as in applied mathematics, to calculate for a low computational cost, the scattered fields in electromagnetism.