First Course in the Theory of Equations (Classic Reprint) - Couverture souple

Campbell, Rev. Eugene

Couverture souple

ISBN 10 : 1451001460 ISBN 13 : 9781451001464

Editeur : Forgotten Books, 2018

Synopsis

Master Descartes’ rule of signs and Sturm’s method for isolating real roots. This edition guides you through the key ideas and practical steps used to count and locate real roots of real-coefficient polynomials, with clear explanations and worked examples.

The discussion translates abstract ideas into a concrete process you can apply. It covers how sign changes relate to roots, how to handle multiple roots, and how to use Sturm’s sequence to bracket roots exactly. The material includes exercises that reinforce the methods and show how they fit into broader algebra study.

• Understand variations of sign and how they constrain positive and negative roots.


• Follow step-by-step Sturm’s method to isolate real roots between intervals.


• Learn practical strategies to simplify and apply the Sturm sequence in exercises.


• See how these tools connect to broader strategies in solving real-coefficient polynomials.

Ideal for readers of introductory algebra and those preparing for more advanced polynomial theory.

A propos du livre

Présentation de l'éditeur

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
(Typographical errors above are due to OCR software and don't occur in the book.)

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1451001460
• ISBN 13: 9781451001464
• Reliure: Broché
• Nombre de pages: 178
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