Infinite Electrical Networks

This book presents the salient features of the general theory of infinite electrical networks in a coherent exposition.

Armen H. Zemanian (Author)

9780521063395, Cambridge University Press

Paperback / softback, published 29 May 2008

324 pages, 93 b/w illus.
22.8 x 15.2 x 1.8 cm, 0.48 kg

"...The book would make a fine Graduate level text for Electrical Engineers; it would also be useful for students in applied mathematics as a guide to possible research topics." Andrew Booth, Physics in Canada

This book presents the salient features of the general theory of infinite electrical networks in a coherent exposition. Using the basic tools of functional analysis and graph theory, the author examines the fundamental developments in the field and discusses applications to other areas of mathematics. The first half of the book presents existence and uniqueness theorems for both infinite-power and finite-power voltage-current regimes, and the second half discusses methods for solving problems in infinite cascades and grids. A notable feature is the invention of transfinite networks, roughly analogous to Cantor's extension of the natural numbers to the transfinite ordinals. The last chapter is a survey of application to exterior problems of partial differential equations, random walks on infinite graphs, and networks of operators on Hilbert spaces.

1. Introduction
2. Infinite-power regimes
3. Finite-power regimes: the linear case
4. Finite-power regimes: the nonlinear case
5. Transfinite electrical networks
6. Cascades
7. Grids
8. Applications.

Subject Areas: Combinatorics & graph theory [PBV], Geometry [PBM]