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Books > Professional & Technical > Energy technology & engineering > Electrical engineering > Power generation & distribution
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Infinite Electrical Networks (Paperback)
Loot Price: R1,408
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Infinite Electrical Networks (Paperback)
Series: Cambridge Tracts in Mathematics
Expected to ship within 12 - 17 working days
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Over the past two decades a general mathematical theory of infinite
electrical networks has been developed. This is the first book to
present the salient features of this theory in a coherent
exposition. Using the basic tools of functional analysis and graph
theory, the author presents the fundamental developments of the
past two decades 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 recent 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 applications to exterior
problems of partial differential equations, random walks on
infinite graphs, and networks of operators on Hilbert spaces. The
jump in complexity from finite electrical networks to infinite ones
is comparable to the jump in complexity from finite-dimensional to
infinite-dimensional spaces. Many of the questions that are
conventionally asked about finite networks are presently
unanswerable for infinite networks, while questions that are
meaningless for finite networks crop up for infinite ones and lead
to surprising results, such as the occasional collapse of
Kirchoff's laws in infinite regimes. Some central concepts have no
counterpart in the finite case, as for example the extremities of
an infinite network, the perceptibility of infinity, and the
connections at infinity.
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