# Mathematical Foundations of Network Analysis

• Paul Slepian
Book

Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 16)

1. Front Matter
Pages I-XI
2. Paul Slepian
Pages 1-2
3. Paul Slepian
Pages 3-22
4. Paul Slepian
Pages 23-45
5. Paul Slepian
Pages 46-60
6. Paul Slepian
Pages 61-75
7. Paul Slepian
Pages 76-94
8. Paul Slepian
Pages 95-105
9. Paul Slepian
Pages 106-137
10. Paul Slepian
Pages 138-186
11. Back Matter
Pages 187-196

### Introduction

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.

### Keywords

Algebra Analysis Elektrisches Netzwerk calculus circuit electrical engineering graph theory linear algebra linearity network network analysis operator

#### Authors and affiliations

• Paul Slepian
• 1
1. 1.Department of MathematicsRensselaer Polytechnic InstituteTroyUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-87424-6
• Copyright Information Springer-Verlag Berlin Heidelberg 1968
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-642-87426-0
• Online ISBN 978-3-642-87424-6
• Series Print ISSN 0081-3877
• Buy this book on publisher's site