Mathematical Methods for Wave Propagation in Science and Engineering

Mathematical Methods for Wave Propagation in Science and Engineering

Volume 1: Fundamentals 

Mario Durán Toro, Ricardo Hein Hoernig & Jean-Claude Nédélec

Abstract

This series of books deals with the mathematical modeling and computational simulation of complex wave propagation phenomena in science and engineering. This first volume of the series introduces the basic mathematical and physical fundamentals, and it is mainly intended as a reference guide and a general survey for scientists and engineers. It presents a broad and practical overview of the involved foundations, being useful as much in industrial research, development, and innovation activities, as in academic labors.

The subjects are classified in terms of independent chapters or groups of chapters, so that specific topics of interest may be pursued at will without difficulty. Starting from the foundations of mathematics, logic and set theory, the book describes systematically and in a synthetic manner the most important notions of abstract mathematical spaces, functional analysis, measure and integration theory, vector analysis, special functions, Sobolev spaces, theory of distributions, Fourier transforms, linear wave propagation, and Green’s functions.

Biografía de los autores

Mario Durán Toro (born in 1966, Santiago de Chile) is Civil Mathematical Engineer of the Universidad de Chile, Doctor in Applied Mathematics of the École Polytechnique, and is currently Professor at the Faculty of Engineering of the Pontificia Universidad Católica de Chile. He was granted the honorary title of Chevalier de l’Ordre National du Mérite by the French government in 2007, in recognition of his contributions to science, technology, and student formation.

Ricardo Hein Hoernig (born in 1979, Santiago de Chile) is Civil Industrial Engineer with Academic Diploma in Electrical Engineering of the Pontificia Universidad Católica de Chile, Doctor in Applied Mathematics of the École Polytechnique, Doctor in Engineering Sciences of the Pontificia Universidad Católica de Chile, and is currently Research Engineer in the technological management company Ingenieros Matemáticos Consultores Asociados Sociedad Anónima (INGMAT) and Project Manager in the engineering company Oryxeio Ingeniería Limitada.

Jean-Claude Nédélec (born in 1943, Briec de l’Odet, France) is Engineer of the École Polytechnique, Doctor of State in Mathematics of the Sorbonne University, and is currently Research Director at the Center for Applied Mathematics of the École Polytechnique and Professor Emeritus in Mathematics at the University of Rennes. His contributions in the field of applied mathematics are numerous, being the most famous one the formulation of integral representations for Maxwell’s equations and their treatment by the boundary element method, universally known as the Nédélec finite element.