by M Cessenat (CEA/DAM, France)

This book provides the reader with basic tools to solve problems of electromagnetism in their natural functional frameworks thanks to modern mathematical methods: integral surface methods, and also semigroups, variational methods, etc., well adapted to a numerical approach.

As examples of applications of these tools and concepts, we solve several fundamental problems of electromagnetism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propagation in a waveguide, with junctions and cascades. We hope that mathematical notions will allow a better understanding of modelization in electromagnetism and emphasize the essential features related to the geometry and nature of materials.

• Mathematical Modelling of the Electromagnetic Field in Continuous Media: Maxwell Equations and Constitutive Relations
• Mathematical Framework for Electromagnetism
• Stationary Scattering Problems with Bounded Obstacles
• Waveguide Problems
• Stationary Scattering Problems on Unbounded Obstacles
• Evolution Problems
• Appendix — Differential Geometry for Electromagnetism
• References
• Index
• Notations