"Mathematical Methods in Electromagnetism: Linear Theory and Applications" by Michel Cessenat

This book provides the reader with basic tools to solve problems of electromagnetism in thier 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 electromagentism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propogation in a waveguide, with junctions and cascades.
It is the aim to present mathematical notions that will allow a better understanding of modelization in electromagnetism and emphasize the essentail features related to the geometery and nature of materials.

Contents
Acknowledgements
Preface
CHAPTER 1 MATHEMATICAL MODELLING OF THE ELECTROMAGNETIC FIELD IN CONTINUOUS MEDIA MAXWELL EQUATIONS AND CONSTITUTIVE RELATIONS
CHAPTER 2 MATHEMATICAL FRAMEWORK FOR ELECTROMAGNETISM
CHAPTER 3 STATIONARY SCATTERING PROBLEMS WITH BOUNDED OBSTACLE
CHAPTER 4 WAVEGUIDE PROBLEMS
CHAPTER 5 STATIONARY SCATTERING PROBLEMS ON UNBOUNDED OBSTACLES
CHAPTER 6 EVOLUTION PROBLEMS
APPENDIX DIFFERENTIAL GEOMETRY FOR ELECTROMAGNETISM
References
Notations
Series on Advances in Mathematics for Applied Sciences