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

Campbell, Rev. Eugene

9781451001464: First Course in the Theory of Equations (Classic Reprint)

Softcover

ISBN 10: 1451001460 ISBN 13: 9781451001464

Verlag: Forgotten Books, 2018

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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.

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Verlag: Forgotten Books
Erscheinungsdatum: 2018
Sprache: Englisch
ISBN 10: 1451001460
ISBN 13: 9781451001464
Einband: Taschenbuch
Anzahl der Seiten: 176
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First Course in the Theory of Equations (Classic Reprint)

Leonard Eugene Dickson

Verlag: Forgotten Books, 2018

ISBN 10: 1451001460 ISBN 13: 9781451001464

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Paperback. Zustand: 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 bookâ� �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. Bestandsnummer des Verk�ufers 9781451001464_0

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