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Elementary Theory of Equations (Classic Reprint) - Softcover

 
9781332804023: Elementary Theory of Equations (Classic Reprint)

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Excerpt from Elementary Theory of Equations

The longer an engineer has been separated from his alma mater, the fewer mathematical formulas he uses and the more he relies upon tables and, when the latter fail, upon graphical methods. Although graphical methods have the advantage of being ocular, they frequently suffer from the fact that only what is seen is sensed. But this defect is due to the kind of graphics used. With the aid of the scientific art of graphing pre sented in Chapter I, one may not merely make better graphs in less time but actually draw correct negative conclusions from a graph so made, and therefore sense more than one sees. For instance, one may be sure that a given cubic equation has only the one real root seen in the graph, if the bend points lie on the same side of the x-axis. Emphasis is here placed upon Newton's method of solving numerical equations, both from the graphical and the numerical standpoint. One of several advantages (well recognized in Europe) of Newton's method over Homer's is that it applies as well to non-algebraic as to algebraic equations. In this elementary book, the author has of course omitted the difficult Galois theory of algebraic equations (certain texts on which are very erroneous) and has merely illustrated the subject of invariants by a few examples. It is surprising that the theorems of Descartes, Budan, and Sturm, on the real roots of an equation, are Often stated inaccurately. Nor are the texts in English on this subject more fortunate on the score of correct proofs; for these reasons, care has been taken in selecting the books to which the reader is referred in the present text. The material is here so arranged that, before an important general theorem is stated, the reader has had concrete illustrations and often also special cases. The exercises are so placed that a reasonably elegant and brief solution may be expected, without resort to tedious multiplications and similar manual labor. Very few Of the five hundred exercises are of the same nature.

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Leonard Eugene Dickson
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ISBN 10: 1332804020 ISBN 13: 9781332804023
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Paperback. Condition: New. Print on Demand. This book delves into the fascinating world of equations, exploring the historical development of methods for solving them. It takes a deep dive into the theory of equations, revealing the intricacies of algebraic and trigonometric solutions for cubic and quartic equations. The author skillfully presents complex numbers in a clear and logical manner, employing geometrical representations and demonstrating the application of these abstract concepts to real-world problems. The book goes further, exploring the concepts of multiple roots, bend points, and inflexion points, providing a comprehensive understanding of how the graphical representation of equations helps to analyze their solutions. The book's detailed treatment of equations, their roots, and their graphical interpretations offers invaluable insights into the fundamental principles of algebra, making it an essential resource for anyone seeking a deeper understanding of this fundamental branch of mathematics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332804023_0

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Condition: New. KlappentextrnrnExcerpt from Elementary Theory of EquationsThe longer an engineer has been separated from his alma mater, the fewer mathematical formulas he uses and the more he relies upon tables and, when the latter fail, upon graphical. Seller Inventory # 2147992462

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