Determinants and Their Applications in Mathematical Physics

Paul Dale

ISBN 10: 147577270X / ISBN 13: 9781475772708

Verlag: Springer New York, Springer New York Mär 2013, 2013

Beschreibung

Neuware -The last treatise on the theory of determinants, by T. Muir, revised and enlarged by W. H. Metzler, was published by Dover Publications Inc. in 1960. It is an unabridged and corrected republication of the edition ori- nally published by Longman, Green and Co. in 1933 and contains a preface by Metzler dated 1928. The Table of Contents of this treatise is given in Appendix 13. A small number of other books devoted entirely to determinants have been published in English, but they contain little if anything of importance that was not known to Muir and Metzler. A few have appeared in German and Japanese. In contrast, the shelves of every mathematics library groan under the weight of books on linear algebra, some of which contain short chapters on determinants but usually only on those aspects of the subject which are applicable to the chapters on matrices. There appears to be tacit agreement among authorities on linear algebra that determinant theory is important only as a branch of matrix theory. In sections devoted entirely to the establishment of a determinantal relation, many authors de ne a determinant by rst de ning a matrixM and then adding the words: ¿Let detM be the determinant of the matrix M¿ as though determinants have no separate existence. This belief has no basis in history.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 396 pp. Englisch.

Bestandsnummer des Verkäufers 9781475772708

Bibliografische Details

• Titel: Determinants and Their Applications in Mathematical Physics
• Verlag: Springer New York, Springer New York Mär 2013
• Erscheinungsjahr: 2013
• Sprache: Englisch
• ISBN-10: 147577270X
• ISBN-13: 9781475772708
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 155 H x 22 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 22 mm
• Gewicht: 598 Gramm

Über diesen Titel

Inhaltsangabe

This book is unique. It contains a detailed account of all important relations in the analytic theory of determinants from the classical work of Laplace, Cauchy and Jacobi in the 18th and 19th centuries, to the most recent 20th century developments. Several contributions have never been published before. Mathematicians, physicists and engineers who wish to becom acquainted with modern developments in the analytic theory of determinants will find this book indispensible.

Reseña del editor

A unique and detailed account of all important relations in the analytic theory of determinants, from the classical work of Laplace, Cauchy and Jacobi to the latest 20th century developments. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors. They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis. Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory. The solutions are verified by applying theorems established in earlier chapters, and the book ends with an extensive bibliography and index. Several contributions have never been published before. Indispensable for mathematicians, physicists and engineers wishing to become acquainted with this topic.