Sinossi
The theonof equations is not only a necessity in the subsequent mathematical courses and their apphcations, but furnishes an illuminating sequel to geometry-, algebra and analytic geometn .M oreover, it develops anew and in greater detail various fundamental ideas of calculus for the simple, but important, case of poh-nomials. The theon, of equations therefore affords a useful supplement to differential calculus whether taken subsequentlj or simultaneoush .I twas to meet the numerous needs of the student in regard to his earU er and future mathematical courses that the present book was planned with great care and after wide consultation. It differs essentially from the authors Elementary Theory of Equations, both in regard to omissions and additions, and since it is addressed to younger students and Tna.y be used parallel with a course in differential calculus. Simpler and more detailed proofs are now emplo ed. The exercises are simpler, more numerous, of greater variety, and involve more practical apphcations. This book throws important Ught on various elementarjtopics. For example, an alert student of geometrj who has learned how to bisect any angle is apt to ask if everjangle can be trisected with ruler and compasses and if not, whj not. After learning how to construct regular polygons of 3, 4, 5, 6, 8and 10 sides, he wiU be inquisitive about the missing ones of 7and 9sides. The teacher will be in a comfortable position if he knows the facts and what is involved in the simplest discussion to date of these questions, as given inC hapter III. Other chapters throw needed hght on various topics of algebra. In particular, the theory of graphs is presented inC hapter Vin a more scientific and practical manner than was possible in algebra and anah tic geometry. There is developed a method of computing a real root of an equation with minimum labor and with certai
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First Course in the Theory of Equations (Classic Reprint)
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Paperback. Condizione: New. Print on Demand. This book provides a comprehensive exploration of the theory of equations, a fundamental subject in mathematics that underpins many subsequent courses and applications. It serves as a natural continuation of geometry, algebra, and analytic geometry, and offers a detailed analysis of key calculus concepts through the lens of polynomial functions. The author aims to meet the diverse needs of students by providing simplified and detailed proofs, alongside an abundance of varied exercises, including practical applications. The book delves into classic problems that have captivated mathematicians for centuries, such as the trisection of an angle and the construction of regular polygons, offering insights into why certain constructions are impossible with only a ruler and compass. The text also examines the theory of graphs in a rigorous and practical manner, presenting a method for calculating real roots of equations with a high degree of accuracy. By exploring the works of mathematicians like Descartes, Sturm, and Budan, the author sheds light on techniques for isolating real roots, and introduces powerful tools such as determinants and matrices for solving systems of linear equations. The bookââ â¢s exploration of these fundamental mathematical topics provides a valuable resource for students seeking a deeper understanding of the theory of equations and its applications. 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. Codice articolo 9781451001464_0
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