This book examines the close relationship between the physical phenomena of electromagnetism and the geometry of space and time. It starts with the Faraday-Maxwell insight that in electromagnetism exists an interconnected dynamical system in which space and time are closely linked with the physical phenomena. An appropriate mathematical basis is given by differential geometry to describe local relationships and topology to describe the system. These tools are introduced in the context of Maxwell's equations in the familiar vector notation, which are greatly simplified by the geometrical approach. Moreover, the geometrical idea of symmetry unifies the various conservation laws. Overall, the book clarifies the relationship between fields, potentials, and sources. Links between macroscopic and quantum phenomena are explored from a geometrical angle, and there is a simple discussion of superconductivity. This book is addressed to engineers, applied mathematicians, physicists, and students involved in the design and analysis of electromagnetic systems.
... it is written in a style which is accessible to those who are familiar with electromagnetism from an engineering standpoint.
.... the electromagnetic analyst will find Baldomir and Hammond's book useful and helpful in relation to some of the literature now appearing. It also can be enjoyed in its own right for the challenging intellectual exercise with respect to electromagnetism which it represents. International Compumag Society Newsletter, July 1996
1: The historical development of electromagnetism
2: A geometrical approach to Maxwell's equations
3: Variational methods
4: Coordinates and coordinate transformations
5: Symmetries of space and time
6: Electromagnetic radiation
7: The relationship between electricity and magnetism in electrodynamics
8: Electrodynamics and conductivity
9: The inner geometry of electrodynamics