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- DescriptionThis book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bezout presents his approach to solving systems of polymial equations in several variables and in great detail. He introduces the revolutionary tion of the polymial multiplier, which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, w kwn as Bezout's theorem, is stated as follows: The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unkwns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations. The book offers large numbers of results and insights about conditions for polymials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polymial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polymial equations or inequalities, and this translation offers a valuable historic perspective on this active research field.
- Author BiographyEtienne Bezout (1730-1783) is credited with the invention of the determinant (named Bezoutian by Sylvester) as well as several key innovations to solve simultaneous polynomial equations in many unknowns. By the time of his death, he was a member of the French Academy of Sciences and the Examiner of the Guards of the Navy and of the Corps of Artillery. Eric Feron Dutton/Ducoffe Professor of Aerospace Engineering at Georgia Institute of Technology, and Visiting Professor of Aerospace Engineering at Massachusetts Institute of Technology, where he is affiliated with the Laboratory for Information and Decision Systems and the Operations Research Center. He is also an Adviser to the French Academy of Technologies. His interests span numerical analysis, optimization, systems analysis, and their applications to aerospace engineering.
- Author(s)Etienne Bezout
- PublisherPrinceton University Press
- Date of Publication13/03/2006
- SubjectScience & Mathematics: Textbooks & Study Guides
- Place of PublicationNew Jersey
- Country of PublicationUnited States
- ImprintPrinceton University Press
- Content NoteIllustrations, facsim.
- Weight657 g
- Width152 mm
- Height229 mm
- Spine30 mm
- Translated byEric Feron
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