Multiforms, Dyadics, and Electromagnetic Media [Hardcover]

• End-of-chapter exercises

• Formalism allows readers to find novel classes of media

• Covers various properties of electromagnetic media in terms of which they can be set in different classes

Preface xi

1 Multivectors and Multiforms 1

1.1 Vectors and One-Forms, 1

1.1.1 Bar Product | 1

1.1.2 Basis Expansions 2

1.2 Bivectors and Two-Forms, 3

1.2.1 Wedge Product ' 3

1.2.2 Basis Expansions 4

1.2.3 Bar Product 5

1.2.4 Contraction Products  and 6

1.2.5 Decomposition of Vectors and One-Forms 8

1.3 Multivectors and Multiforms, 8

1.3.1 Basis of Multivectors 9

1.3.2 Bar Product of Multivectors and Multiforms 10

1.3.3 Contraction of Trivectors and Three-Forms 11

1.3.4 Contraction of Quadrivectors and Four-Forms 12

1.3.5 Construction of Reciprocal Basis 13

1.3.6 Contraction of Quintivector 14

1.3.7 Generalized Bac-Cab Rules 14

1.4 Some Properties of Bivectors and Two-Forms, 16

1.4.1 Bivector Invariant 16

1.4.2 Natural Dot Product 17

1.4.3 Bivector as Mapping 17

Problems, 18

2 Dyadics 21

2.1 Mapping Vectors and One-Forms, 21

2.1.1 Dyadics 21

2.1.2 Double-Bar Product & 23l3I