Discontinuities in the electromagnetic field / M. Mithat Idemen

Includes bibliographical references and index

Machine generated contents note: Preface. -- Chapter 1. Introduction. -- Chapter 2. Distributions and derivatives in the sense of distribution. -- 2.1 Functions and distributions. -- 2.2 Test functions. 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. -- Index

"This book presents some new approaches and basic results connected with the discontinuities of the electromagnetic field. The discontinuities in question may be (1) the bounded jump discontinuities on the interfaces between two media or on the material sheets which model very thin layers or (2) unbounded values at the edge of wedge type structures or (3) unbounded values at the tips of conical structures. The book involves may examples as well as problems (exercises) to be solved by the readers"-- Provided by publisher