Description
Book SynopsisAn introduction to multivectors, dyadics, and differential forms for electrical engineers While physicists have long applied differential forms to various areas of theoretical analysis, dyadic algebra is also the most natural language for expressing electromagnetic phenomena mathematically.
Trade Review“…a modern, clear and well-organised account…in an easily mastered notation…” (
Ultramicroscopy, Vol 104, 2005)
Table of ContentsPreface. 1 Multivectors.
1.1 The Grassmann algebra.
1.2 Vectors and dual vectors.
1.3 Bivectors.
1.4 Multivectors.
1.5 Geometric interpretation.
2 Dyadic Algebra.
2.1 Products of dyadics.
2.2 Dyadic identities.
2.3 Eigenproblems.
2.4 Inverse dyadic.
2.5 Metric dyadics.
2.6 Hodge dyadics.
3 Differential Forms.
3.1 Differentiation.
3.2 Differentiation theorems.
3.3 Integration.
3.4 Affine transformations.
4 Electromagnetic Fields and Sources.
4.1 Basic electromagnetic quantities.
4.2 Maxwell equations in three dimensions.
4.3 Maxwell equations in four dimensions.
4.4 Transformations.
4.5 Super forms.
5 Medium, Boundary, and Power Conditions.
5.1 Medium conditions.
5.2 Conditions on boundaries and interfaces.
5.3 Power conditions.
5.4 The Lorentz force law.
5.5 Stress dyadic.
6 Theorems and Transformations.
6.1 Duality transformation.
6.2 Reciprocity.
6.3 Equivalence of sources.
7 Electromagnetic Waves.
7.1 Wave equation for potentials.
7.2 Wave equation for fields.
7.3 Plane waves.
7.4 TE and TM polarized waves.
7.5 Green functions.
References.
Appendix A: Multivector and Dyadic Identities.
Appendix B: Solutions to Selected Problems.
Index.
About the Author.
