Read more
Informationen zum Autor 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. Klappentext A multifaceted approach to understanding, calculating, and managing electromagnetic discontinuitiesPresenting 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 structuresThe 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. Zusammenfassung Filled with new approaches and basic results connected with the discontinuities of the electromagnetic field, this new book offers an important resource for graduate and undergraduate students. Inhaltsverzeichnis Preface ix 1. Introduction 1 2. Distributions and Derivatives in the Sense of Distribution 7 2.1 Functions and Distributions, 7 2.2 Test Functions. The Space C¿ 0 , 9 2.3 Convergence in D , 14 2.4 Distribution, 16 2.5 Some Simple Operations in D , 21 2.5.1 Multiplication by a Real Number or a Function, 21 2.5.2 Translation and Rescaling, 21 2.5.3 Derivation of a Distribution, 22 2.6 Order of a Distribution, 26 2.7 The Support of a Distribution, 31 2.8 Some Generalizations, 33 2.8.1 Distributions on Multidimensional Spaces, 33 2.8.2 Vector-Valued Distributions, 38 3. Maxwell Equations in the Sense of Distribution 49 3.1 Maxwell Equations Reduced into the Vacuum, 49 3.1.1 Some Simple Examples, 53 3.2 Universal Boundary Conditions and Compatibility Relations, 54 3.2.1 An Example. Discontinuities on a Combined Sheet, 57 3.3 The Concept of Material Sheet, 59 3.4 The Case of Monochromatic Fields, 62 3.4.1 Discontinuities on the Interface Between Two Simple Media that Are at Rest, 64 4. Boundary Conditions on Material Sheets at Rest 67 4.1 Universal Boundary Conditions and Compatibility Relations for a Fixed Material Sheet, 67 4.2 Some General Results, 69 4.3 Some Particular Cases, 70 4.3.1 Planar Material Sheet Between Two Simple Media, 70 4.3.2 Cylindrically or Spherically Curved Material Sheet Located Between Two Simple Media, 91 4.3.3 Conical Material Sheet Located Between T...
