By Jean van Bladel
Второе издание книги включает в себя новейшие методы, теоретические формулировки и приложения, имеющие непосредственное отношение к современным технологиям. Опираясь на основные принципы электромагнитной теории и анализа, в книге дается детальное обсуждение электростатических полей, теории потенциала, распространения волн высоких и низких частот в волноводах и свободном пространстве, рассеяния волн на препятствиях, прохождения волн через ограниченные апертуры и др.
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Djordjevic and E. Arvas, On the choice of expansions and weighting functions with numerical solution of operator equations, IEEE Trans. AP-33, 988–996 (1985). 6. O. Toeplitz, Zur Theorie der quadratischen Formen von unendlichvielen Veränderlichen, Nachrichten K. 7. 8. 9. 10. 11. Ges. d. Wiss. Göttingen, Klasse Math-phys. 5, 489–506 (1910). D. H. Preis, The Toeplitz matrix: Its occurrence in antenna problems and a rapid inversion algorithm, IEEE Trans. AP-20, 204–206 (1972). G. A. Watson, An algorithm for the inversion of block matrices of Toeplitz form, J.
11 (a) The evolution of a temperature disturbance. (b) The birth of an oscillation. 42 Chapter 1 Linear Analysis 3. 164) ∇2φ = 2 2 . c ∂t This solution is fundamentally oscillatory, as shown by the following simple argument. At t = 0 (Fig. 11b), we start with a positive ∇ 2 φ, which implies a positive ∂ 2 φ/∂t 2 , and therefore an upward curvature. The situation remains so until the curves cross each other at t1 , upon which the curvature turns downward. The oscillatory tendency is evident. 4. The last example concerns the Helmholtz equation in a source-free region, viz.
A band matrix is characterized by elements that are clustered in a narrow band containing the main diagonal. 36 Chapter 1 Linear Analysis 9. A lower triangular matrix is a square matrix having zero elements above the leading diagonal. Similarly, an upper triangular matrix has zero elements below the leading diagonal. 123), it is important first to investigate the existence and uniqueness of the solution. 132) plays a decisive role here. 123) unless† g, y0 = 0. 131), but a core solution may be introduced to ensure uniqueness.