Mathematical foundations of network analysis
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 grap…
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- Full title :Mathematical foundations of network analysis.
Summary
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.
Read More ↓Edition Statements
- Publication Date:©1968
Publication Statements
- Publisher(s):Springer
- Place of Publication:Berlin
- Language:eng
- Publication Date:©1968
The Physical Object
- Description:1 online resource (xi, 195 pages)
Edition Identifiers
- ISBN:9783642874246, 364287424X, 9783540043447, 3540043446
- DOI:10.1007/978-3-642-87424-6
- oclc:ocn610578478
- LC Classification:Q111
- Dewey Decimal:621.319/2
Table of Contents
1. Connected Networks -- 1.0 Introduction -- 1.1 Set Theory -- 1.2 Sets with Two or Less Elements -- 1.3 Generalized Union -- 1.4 Relations and Functions -- 1.5 Superpositions and Inverses -- 1.6 Restrictions -- 1.7 Cartesian Products -- 1.8 Some Special Symbols -- 1.9 Finite Sequences -- 1.10 Networks -- 1.11 Geometrical Realization of a Network -- 1.12 Subnetworks -- 1.13 Degree of a Vertex -- 1.14 Path in a Network -- 1.15 Proper Path in a Network -- 1.16 Reduction of a Path to a Proper Path -- 1.17 Connected Networks -- 1.18 Isolated Vertices -- 1.19 Connected Sets of Branches -- 1.20 Path Connected Set of Branches -- 1.21 Union of Connected Sets of Branches -- 1.22 Connectedness of Paths -- 1.23 Component of a Set of Branches -- 1.24 Existence of Components -- 1.25 Partition into Components -- 1.26 Removal of a Branch -- 2. Loops, Trees, and Cut Sets -- 2.0 Introduction -- 2.1 Loop in a Network -- 2.2 Loops -- 2.3 Subloops of a Loop -- 2.4 Branches and Vertices of a Loop -- 2.5 Paths in a Loop -- 2.6 Removal of a Branch from a Loop -- 2.7 Tree in a Network -- 2.8 Trees -- 2.9 Connected Subset of a Tree -- 2.10 Branches and Vertices of a Tree -- 2.11 Number of Vertices of a Co…
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