Mathematical Foundations of Network Analysis (Springer Tracts in Natural Philosophy)

Paul Slepian

ISBN 10: 3642874266 / ISBN 13: 9783642874260

Published by Springer-Verlag New York Inc. 1968-01-01, 1968

About this Item

Seller Inventory # 6666-IUK-9783642874260

Bibliographic Details

• Title: Mathematical Foundations of Network Analysis (Springer Tracts in Natural Philosophy)
• Publisher: Springer-Verlag New York Inc. 1968-01-01
• Publication Date: 1968
• Language: English
• ISBN 10: 3642874266
• ISBN 13: 9783642874260
• Binding: Paperback
• Condition: New

About this title

Synopsis

In this book we attempt to develop the fundamental results of resistive network analysis, based upon a sound mathematical structure. The axioms upon which our development is based are Ohm's Law, Kirchhoff's Voltage Law, and Kirchhoff's Current Law. In order to state these axioms precisely, and use them in the development of our network analysis, an elaborate mathematical structure is introduced, involving concepts of graph theory, linear algebra, and one dimensional algebraic topology. The graph theory and one dimensional algebraic topology used are developed from first principles; the reader needs no background in these subjects. However, we do assume that the reader has some familiarity with elementary linear algebra. It is now stylish to teach elementary linear algebra at the sophomore college level, and we feel that the require­ ment that the reader should be familiar with elementary linear algebra is no more demanding than the usual requirement in most electrical engineering texts that the reader should be familiar with calculus. In this book, however, no calculus is needed. Although no formal training in circuit theory is needed for an understanding of the book, such experience would certainly help the reader by presenting him with familiar examples relevant to the mathematical abstractions introduced. It is our intention in this book to exhibit the effect of the topological properties of the network upon the branch voltages and branch currents, the objects of interest in network analysis.