Computation Of The Real And Complex Roots Of Algebraic And Transcendental Equations

Author

Beauregard Stubblefield, Prairie View State University

Date of Award

8-1945

Document Type

Thesis

Degree Name

Master of Science

Degree Discipline

Mathematics

Abstract

Origin and History of the Problem: The science of algebra arose In its effort to solve equations. Since the main objects in algebra have been the discussion of equalities and the transformation of forms into simpler equivalent ones, that science may well be called the Science of Equations. The solution of an equation containing one unknown quantity consists in the determination of Its value or values, these being called roots. An algebraic equation of degree n has n roots, while transcendental equations have an infinite number of roots. There has existed for years the problem of finding values, as exact as possible, or as close as one wishes of these roots. This problem still has not been satisfactorily solved. It is the object of researchers to continue work to the end of calculating all of the real and complex roots of algebraic and transcendental equations simultaneously by a single method. Thus, Lagrange, at the beginning of his manuscript on "The Solution of Numerical Equations" (1767), published his first memoirs which were followed by works of Harriot, Ougtred, Pell, and others. Descartes has assisted in these findings by his rule of signs, which though fundamentally important, lacks sufficient accuracy. The greatest analysis initiated by Newton and terminated by Lagrange made a decisive step from Descartes' theory by using "the squares of the differences." This method was simple in theory but necessitated tiring and sometimes indefinite conclusions. Fourier attained approximately the same conclusions in his efforts. In 1820, he published a rule which he had formulated and used for several years. Though his rule lacked satisfactory proof, his findings at least aided Sturm with his theories advanced several years later. This theorem concerns only a derivative and the function itself which is somewhat similar to the highest common factor.

Committee Chair/Advisor

A. W. Randall

Committee Member

C. P. Stephens

Committee Member

C. P. Stephens

Committee Member

J. S. Flipper

Publisher

Prairie View State University

Rights

Date of Digitization

11/10/2021

Contributing Institution

John B Coleman Library

City of Publication

Prairie View

MIME Type

Application/PDF

Recommended Citation

Stubblefield, B. (1945). Computation Of The Real And Complex Roots Of Algebraic And Transcendental Equations. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/703