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Author: Florian Cajori
Publisher:
ISBN:
Category : Equations
Languages : en
Pages : 192
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Book Description
Author: Florian Cajori
Publisher:
ISBN:
Category : Equations
Languages : en
Pages : 192
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Book Description
Author: George Ballard Mathews
Publisher:
ISBN:
Category : Equations, Theory of
Languages : en
Pages : 76
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Book Description
Author: Leonard Eugene Dickson
Publisher:
ISBN:
Category : Equations, Theory of
Languages : en
Pages : 142
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Book Description
Author: Etienne Bézout
Publisher: Princeton University Press
ISBN: 9780691114323
Category : Mathematics
Languages : en
Pages : 378
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Book Description
This 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, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial 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, now known as "Bézout'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 unknowns 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 polynomials 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. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field.
Author:
Publisher:
ISBN:
Category : Classification
Languages : en
Pages : 206
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 346
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Book Description
Author: Teo Mora
Publisher: Cambridge University Press
ISBN: 1316297969
Category : Mathematics
Languages : en
Pages : 332
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Book Description
This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner bases, which allow one to manipulate the roots of the equation rather than just compute them. The book begins with the 'standard' solutions (Gianni–Kalkbrener Theorem, Stetter Algorithm, Cardinal–Mourrain result) and then moves on to more innovative methods (Lazard triangular sets, Rouillier's Rational Univariate Representation, the TERA Kronecker package). The author also looks at classical results, such as Macaulay's Matrix, and provides a historical survey of elimination, from Bézout to Cayley. This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Author: Felix Klein
Publisher: Courier Corporation
ISBN: 9780486495286
Category : Mathematics
Languages : en
Pages : 312
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Book Description
This well-known work covers the solution of quintics in terms of the rotations of a regular icosahedron around the axes of its symmetry. Its two-part presentation begins with discussions of the theory of the icosahedron itself; regular solids and theory of groups; introductions of (x + iy); a statement and examination of the fundamental problem, with a view of its algebraic character; and general theorems and a survey of the subject. The second part explores the theory of equations of the fifth degree and their historical development; introduces geometrical material; and covers canonical equations of the fifth degree, the problem of A's and Jacobian equations of the sixth degree, and the general equation of the fifth degree. Second revised edition with additional corrections.
Author:
Publisher: CUP Archive
ISBN:
Category :
Languages : en
Pages : 84
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Book Description
Author: Philip Hartman
Publisher: SIAM
ISBN: 0898715105
Category : Mathematics
Languages : en
Pages : 643
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Book Description
Covers the fundamentals of the theory of ordinary differential equations.
