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New Releases. Description 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.
Product details Format Hardback pages Dimensions x x Illustrations note 4 Tables, black and white; XIV, p. Other books in this series.
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Indispensable for mathematicians, physicists and engineers wishing to become acquainted with this topic. Read more Read less. No customer reviews. Share your thoughts with other customers.
Write a customer review. Most helpful customer reviews on Amazon. April 6, - Published on Amazon. This book, as usual by the excellent Springer publishers, continues the trend launched by the Clifford algebra people Lounesto, Chisholm, Baylis, Pezzaglia, Okubo, Benn, etc.
Both this book by Vein and Dale and the Clifford algebra books and papers use algebra in physics largely to replace hard to manipulate geometry and unwieldly matrices. A matrix is an algebraic quantity, but it is very hard to handle: it is essentially a table of numbers, for example a table of people's heights, or people's heights by weights. You add tables by adding corresponding positions in each table, and likewise for subtracting, while multiplication is much more complicated.
Applied Mathematical Sciences. Free Preview cover. © Determinants and Their Applications in Mathematical Physics. Authors: Vein, Robert, Dale, Paul. Buy Determinants and Their Applications in Mathematical Physics (Applied Mathematical Sciences) on elocusopcraf.ga ✓ FREE SHIPPING on qualified orders.
A determinant is a single number, typically, which is gotten by combining the numbers of the matrix table in a certain way given by a formula. Thus, replacing a matrix by a determinant means replacing a table by a single number. It turns out that the Einstein Equation s of general relativity can be solved in this way for the axially symmetric field , and likewise for equations involving solitary waves Kadomtsev-Petashvili equation , waves in a rotating fluid Benjamin-Ono equation , etc.
An important tool in this process is Backlund transformations, which are described in the appendix but are more thoroughly described in the book of Bluman and Kumei which together with their journal publications initiated much of the simplification of differential equations of the modern era.