Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.

Part 1. MODELLING AND MATHEMATICAL PRELIMINARIES

Chapter 1. Complex Media

Chapter 2. The Maxwell Equations and Constitutive Relations

Chapter 3. Space and Operators

Part 2. TIME-HARMONIC DETERMINISTIC PROBLEMS

Chapter 4. Well Posedness

Chapter 5. Scattering Problems: Beltrami Fields and Solvability

Chapter 6. Scattering Problems: A Variety of Topics

Part 3. TIME-DEPENDENT DETERMINISTIC PROBLEMS

Chapter 7. Well Posedness

Chapter 8. Controllability

Chapter 9. Homogenisation

Chapter 10. Towards a Scattering Theory

Chapter 11. Nonlinear Problems

Chapter 12. Well Posedness

Chapter 13. Controllability

Chapter 14. Homogenisation

Part 5. APPENDICES

Appendix A. Some Facts from Functional Analysis

Appendix B. Some Facts from Stochastic Analysis

Appendix C. Some Facts from Elliptic Homogenisation Theory

Appendix D. Some Facts form Dyadic Analysis

Appendix E. Notation and abbreviations

Bibliography

Index