Discontinuities in the Electromagnetic Field

A multifaceted approach to understanding, calculating, and managing electromagnetic discontinuities
Presenting new, innovative approaches alongside basic results, this text helps readers better understand, calculate, and manage the discontinuities that occur within the electromagnetic field. Among the electromagnetic discontinuities explored in this volume are:
Bounded jump discontinuities at the interfaces between two media or on the material sheets that model very thin layers
Unbounded values at the edges of wedge–type structures
Unbounded values at the tips of conical structures
The text examines all the key issues related to the bodies that carry the interfaces, edges, or tips, whether these bodies are at rest or in motion with respect to an observer. In addition to its clear explanations, the text offers plenty of step–by–step examples to clarify complex theory and calculations. Moreover, readers are encouraged to fine–tune their skills and knowledge by solving the text′s problem sets.
Three fundamental, classical theories serve as the foundation for this text: distributions, confluence, and the special theory of relativity. The text sets forth the fundamentals of all three of these theories for readers who are not fully familiar with them. Moreover, the author demonstrates how to solve electromagnetic discontinuity problems by seamlessly combining all three theories into a single approach.
With this text as their guide, readers can apply a unique philosophy and approach to the investigation and development of structures that have the potential to enhance the capabilities of electronics, antennas, microwaves, acoustics, medicine, and many more application areas.

Spis treści:
Preface.
Chapter 1. Introduction.
Chapter 2. Distributions and derivatives in the sense of distribution.
2.1 Functions and distributions.
2.2 Test func tions. The space C.
2.3 Convergence in C.
2.4 Distributions.
2.5 Some simple operations on distributions.
2.6 Order of a distribution.
2.7 The support of a distribution.
2.8 Some generalizations.
Chapter 3. Maxwell equations in the sense of distributions.
3.1 Maxwell equations reduced into the vacuum.
3.2 Universal boundary conditions and compatibility relations.
3.3 The concept of material sheet.
3.4 The case of monochromatic fields.
Chapter 4. Boundary conditions on material sheets at rest.
4.1 Universal boundary conditions and compatibility relations.
4.2 Some general results.
4.3 Some particular cases.
Chapter 5. Boundary conditions on a moving material sheet.
5.1 Boundary conditions on plane which moves in a direction normal to itself.
5.2 Derivation of the boundary conditions by the Special Theory of Relativity when the motion is uniform.
5.3 Boundary conditions on the interface of two simple media.
Chapter 6. Edge singularities on material wedges bounded by plane boundaries.
6.1 Introduction.
6.2 Singularities at the edges of material wedges.
6.3 The wedge with penetrable boundaries.
6.4 The wedge with impenetrable boundaries.
6.5 Examples. Application to half–planes.
6.6 Edge–conditions for the induced surface currents.
Chapter 7. Tip singularities at the apex of a material cone.
7.1 Introduction.
7.2 Algebraic singularities of an H–type field.
7.3 Algebraic singularities of an E–type field.
7.4 The case of impenetrable cones.
7.5 Confluence and logarithmic singularities.
7.6 Application to widely used actual boundary conditions.
7.7 Numerical solutions of the transcendental equations satisfied by the minimal exponent.
Chapter 8. Temporal discontinuities.
8.1 Universal initial conditions.
8.2 Linear mediums in the generalized sense.
8.3 An illustrative example.
References.
I ndex. 

Nota biograficzna:

M. Mithat Idemen, PhD, is Professor in the Mathematics Department of Yeditepe University (Istanbul, Turkey) and honorary member of the Turkish Academy of Sciences (TüBA). He has served as editor and associate editor for various scientific journals, including the International Series of Monographs on Advanced Electromagnetics.

Okładka tylna:

A multifaceted approach to understanding, calculating, and managing electromagnetic discontinuities
Presenting new, innovative approaches alongside basic results, this text helps readers better understand, calculate, and manage the discontinuities that occur within the electromagnetic field. Among the electromagnetic discontinuities explored in this volume are:
Bounded jump discontinuities at the interfaces between two media or on the material sheets that model very thin layers
Unbounded values at the edges of wedge–type structures
Unbounded values at the tips of conical structures
The text examines all the key issues related to the bodies that carry the interfaces, edges, or tips, whether these bodies are at rest or in motion with respect to an observer. In addition to its clear explanations, the text offers plenty of step–by–step examples to clarify complex theory and calculations. Moreover, readers are encouraged to fine–tune their skills and knowledge by solving the text′s problem sets.
Three fundamental, classical theories serve as the foundation for this text: distributions, confluence, and the special theory of relativity. The text sets forth the fundamentals of all three of these theories for readers who are not fully familiar with them. Moreover, the author demonstrates how to solve electromagnetic discontinuity problems by seamlessly combining all three theories into a single approach.
With this text as their guide, readers can apply a unique philosoph y and approach to the investigation and development of structures that have the potential to enhance the capabilities of electronics, antennas, microwaves, acoustics, medicine, and many more application areas.