Multiforms, Dyadics, and Electromagnetic Media -- Contents -- Preface -- 1 Multivectors and Multiforms -- 1.1 Vectors and One-Forms -- 1.1.1 Bar Product -- 1.1.2 Basis Expansions -- 1.2 Bivectors and Two-Forms -- 1.2.1 Wedge Product -- 1.2.2 Basis Expansions -- 1.2.3 Bar Product -- 1.2.4 Contraction Products and -- 1.2.5 Decomposition of Vectors and One-Forms -- 1.3 Multivectors and Multiforms -- 1.3.1 Basis of Multivectors -- 1.3.2 Bar Product of Multivectors and Multiforms -- 1.3.3 Contraction of Trivectors and Three-Forms -- 1.3.4 Contraction of Quadrivectors and Four-Forms -- 1.3.5 Construction of Reciprocal Basis -- 1.3.6 Contraction of Quintivector -- 1.3.7 Generalized Bac-Cab Rules -- 1.4 Some Properties of Bivectors and Two-Forms -- 1.4.1 Bivector Invariant -- 1.4.2 Natural Dot Product -- 1.4.3 Bivector as Mapping -- Problems -- 2 Dyadics -- 2.1 Mapping Vectors and One-Forms -- 2.1.1 Dyadics -- 2.1.2 Double-Bar Product -- 2.1.3 Metric Dyadics -- 2.2 Mapping Multivectors and Multiforms -- 2.2.1 Bidyadics -- 2.2.2 Double-Wedge Product -- 2.2.3 Double-Wedge Powers -- 2.2.4 Double Contractions and -- 2.2.5 Natural Dot Product for Bidyadics -- 2.3 Dyadic Identities -- 2.3.1 Contraction Identities -- 2.3.2 Special Cases -- 2.3.3 More General Rules -- 2.3.4 Cayley-Hamilton Equation -- 2.3.5 Inverse Dyadics -- 2.4 Rank of Dyadics -- 2.5 Eigenproblems -- 2.5.1 Eigenvectors and Eigen One-Forms -- 2.5.2 Reduced Cayley-Hamilton Equations -- 2.5.3 Construction of Eigenvectors -- 2.6 Metric Dyadics -- 2.6.1 Symmetric Dyadics -- 2.6.2 Antisymmetric Dyadics -- 2.6.3 Inverse Rules for Metric Dyadics -- Problems -- 3 Bidyadics -- 3.1 Cayley-Hamilton Equation -- 3.1.1 Coefficient Functions -- 3.1.2 Determinant of a Bidyadic -- 3.1.3 Antisymmetric Bidyadic -- 3.2 Bidyadic Eigenproblem -- 3.2.1 Eigenbidyadic -- 3.2.2 Eigenbidyadic.

3.3 Hehl-Obukhov Decomposition -- 3.4 Example: Simple Antisymmetric Bidyadic -- 3.5 Inverse Rules for Bidyadics -- 3.5.1 Skewon Bidyadic -- 3.5.2 Extended Bidyadics -- 3.5.3 3D Expansions -- Problems -- 4 Special Dyadics and Bidyadics -- 4.1 Orthogonality Conditions -- 4.1.1 Orthogonality of Dyadics -- 4.1.2 Orthogonality of Bidyadics -- 4.2 Nilpotent Dyadics and Bidyadics -- 4.3 Projection Dyadics and Bidyadics -- 4.4 Unipotent Dyadics and Bidyadics -- 4.5 Almost-Complex Dyadics -- 4.5.1 Two-Dimensional AC Dyadics -- 4.5.2 Four-Dimensional AC Dyadics -- 4.6 Almost-Complex Bidyadics -- 4.7 Modified Closure Relation -- 4.7.1 Equivalent Conditions -- 4.7.2 Solutions -- 4.7.3 Testing the Two Solutions -- Problems -- 5 Electromagnetic Fields -- 5.1 Field Equations -- 5.1.1 Differentiation Operator -- 5.1.2 Maxwell Equations -- 5.1.3 Potential One-Form -- 5.2 Medium Equations -- 5.2.1 Medium Bidyadics -- 5.2.2 Potential Equation -- 5.2.3 Expansions of Medium Bidyadics -- 5.2.4 Gibbsian Representation -- 5.3 Basic Classes of Media -- 5.3.1 Hehl-Obukhov Decomposition -- 5.3.2 3D Expansions -- 5.3.3 Simple Principal Medium -- 5.4 Interfaces and Boundaries -- 5.4.1 Interface Conditions -- 5.4.2 Boundary Conditions -- 5.5 Power and Energy -- 5.5.1 Bilinear Invariants -- 5.5.2 The Stress-Energy Dyadic -- 5.5.3 Differentiation Rule -- 5.6 Plane Waves -- 5.6.1 Basic Equations -- 5.6.2 Dispersion Equation -- 5.6.3 Special Cases -- 5.6.4 Plane-Wave Fields -- 5.6.5 Simple Principal Medium -- 5.6.6 Handedness of Plane Wave -- Problems -- 6 Transformation of Fields and Media -- 6.1 Affine Transformation -- 6.1.1 Transformation of Fields -- 6.1.2 Transformation of Media -- 6.1.3 Dispersion Equation -- 6.1.4 Simple Principal Medium -- 6.2 Duality Transformation -- 6.2.1 Transformation of Fields -- 6.2.2 Involutionary Duality Transformation.

6.2.3 Transformation of Media -- 6.3 Transformation of Boundary conditions -- 6.3.1 Simple Principal Medium -- 6.3.2 Plane Wave -- 6.4 Reciprocity Transformation -- 6.4.1 Medium Transformation -- 6.4.2 Reciprocity Conditions -- 6.4.3 Field Relations -- 6.4.4 Time-Harmonic Fields -- 6.5 Conformal Transformation -- 6.5.1 Properties of the Conformal Transformation -- 6.5.2 Field Transformation -- 6.5.3 Medium Transformation -- Problems -- 7 Basic Classes of Electromagnetic Media -- 7.1 Gibbsian Isotropy -- 7.1.1 Gibbsian Isotropic Medium -- 7.1.2 Gibbsian Bi-isotropic Medium -- 7.1.3 Decomposition of GBI Medium -- 7.1.4 Affine Transformation -- 7.1.5 Eigenfields in GBI Medium -- 7.1.6 Plane Wave in GBI Medium -- 7.2 The Axion Medium -- 7.2.1 Perfect Electromagnetic Conductor -- 7.2.2 PEMC as Limiting Case of GBI Medium -- 7.2.3 PEMC Boundary Problems -- 7.3 Skewon-Axion Media -- 7.3.1 Plane Wave in Skewon-Axion Medium -- 7.3.2 Gibbsian Representation -- 7.3.3 Boundary Conditions -- 7.4 Extended Skewon-Axion Media -- Problems -- 8 Quadratic Media -- 8.1 P Media and Q Media -- 8.2 Transformations -- 8.3 Spatial Expansions -- 8.3.1 Spatial Expansion of Q Media -- 8.3.2 Spatial Expansion of P Media -- 8.3.3 Relation Between P Media and Q Media -- 8.4 Plane Waves -- 8.4.1 Plane Waves in Q Media -- 8.4.2 Plane Waves in P Media -- 8.4.3 P Medium as Boundary Material -- 8.5 P-Axion and Q-Axion Media -- 8.6 Extended Q Media -- 8.6.1 Gibbsian Representation -- 8.6.2 Field Decomposition -- 8.6.3 Transformations -- 8.6.4 Plane Waves in Extended Q Media -- 8.7 Extended P Media -- 8.7.1 Medium Conditions -- 8.7.2 Plane Waves in Extended P Media -- 8.7.3 Field Conditions -- Problems -- 9 Media Defined by Bidyadic Equations -- 9.1 QUADRATIC EQUATION -- 9.1.1 SD Media -- 9.1.2 Eigenexpansions -- 9.1.3 Duality Transformation -- 9.1.4 3D Representations -- 9.1.5 SDN Media.

9.2 CUBIC EQUATION -- 9.2.1 CU Media -- 9.2.2 Eigenexpansions -- 9.2.3 Examples of CU Media -- 9.3 BI-QUADRATIC EQUATION -- 9.3.1 BQ Media -- 9.3.2 Eigenexpansions -- 9.3.3 3D Representation -- 9.3.4 Special Case -- Problems -- 10 Media Defined by Plane-Wave Properties -- 10.1 Media With No Dispersion Equation (NDE Media) -- 10.1.1 Two Cases of Solutions -- 10.1.2 Plane-Wave Fields in NDE Media -- 10.1.3 Other Possible NDE Media -- 10.2 Decomposable Media -- 10.2.1 Special Cases -- 10.2.2 DC-Medium Subclasses -- 10.2.3 Plane-Wave Properties -- Problems -- Appendix A Solutions to Problems -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Chapter 9 -- Chapter 10 -- Appendix B Transformation to Gibbsian Formalism -- Vector and one-form -- Bivector and two-form -- Trivector and three-form -- Bar product -- Wedge product -- Contraction products -- Bac-cab rule -- Cross product of two Gibbsian two-forms -- Appendix C Multivector and Dyadic Identities -- Notation -- Multivectors and multiforms -- Dyadics -- Metric dyadics -- Electromagnetics -- References -- Index -- IEEE PRESS SERIES ON ELECTROMAGNETIC WAVE THEORY -- EULA.