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The Sum Of No Equation

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General Theory Of Algebraic Equations

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Author : Etienne Bézout
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10

General Theory Of Algebraic Equations written by Etienne Bézout and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-10 with Mathematics categories.

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.

A Solution To The Reaction Rate Equations In The Atmosphere Below 150 Kilometers

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Author : Thomas J. Keneshea
language : en
Publisher:
Release Date : 1963

A Solution To The Reaction Rate Equations In The Atmosphere Below 150 Kilometers written by Thomas J. Keneshea and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Chemical kinetics categories.

One way to acquire a better understanding of the formation and destruction of ionization in the atmosphere is through the solution of the system of time-dependent reaction rate equations. These ordinary differential equations form a simultaneous set each question of which describes the time rate of change of a particular atmospheric constituent. In the general problem, all the molecules and atoms whether neutral, charged, or excited, as well as the free electrons would be included. A computer program is presented for developing the numerical solution to this problem. The method of solution of the set of equations uses a fourth order Runge Kutta integration with a variable mesh. When a species enters its quasi-equilibrium state, its differential equation is removed from the set and its equilibrium equation is inserted into the simultaneous algebraic set. The algebraic set is solved by the method of successive substitutions. The over-all solution is obtained by iteration between the differential and the algebraic sets. The ability of the computer program to develop extensive solutions is demonstrated by several examples taken under different conditions.

Pantologia

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Author : John Mason Good
language : en
Publisher:
Release Date : 1813

Pantologia written by John Mason Good and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1813 with Encyclopedias and dictionaries categories.

Proceedings Of The Ninth International Colloquium On Differential Equations

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Author : D. Bainov
language : en
Publisher: VSP
Release Date : 1999

Proceedings Of The Ninth International Colloquium On Differential Equations written by D. Bainov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

The Ninth International Colloquium on Differential Equations was organized by the Institute for Basic Science of Inha University, the International Federation of Nonlinear Analysts, the Mathematical Society of Japan, Pharmaceutical Faculty of the Medical University of Sofia, the University of Catania and UNESCO, with the cooperation of a number of international mathematical organizations, and was held at the Technical University of Plovdiv, Bulgaria, August 18-23, 1998. This proceedings volume contains selected talks which deal with various aspects of differential equations and applications

Non Linear Differential Equations And Dynamical Systems

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Author : Luis Manuel Braga da Costa Campos
language : en
Publisher: CRC Press
Release Date : 2019-11-05

Non Linear Differential Equations And Dynamical Systems written by Luis Manuel Braga da Costa Campos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-05 with Mathematics categories.

Non-Linear Differential Equations and Dynamical Systems is the second book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This second book consists of two chapters (chapters 3 and 4 of the set). The first chapter considers non-linear differential equations of first order, including variable coefficients. A first-order differential equation is equivalent to a first-order differential in two variables. The differentials of order higher than the first and with more than two variables are also considered. The applications include the representation of vector fields by potentials. The second chapter in the book starts with linear oscillators with coefficients varying with time, including parametric resonance. It proceeds to non-linear oscillators including non-linear resonance, amplitude jumps, and hysteresis. The non-linear restoring and friction forces also apply to electromechanical dynamos. These are examples of dynamical systems with bifurcations that may lead to chaotic motions. Presents general first-order differential equations including non-linear like the Ricatti equation Discusses differentials of the first or higher order in two or more variables Includes discretization of differential equations as finite difference equations Describes parametric resonance of linear time dependent oscillators specified by the Mathieu functions and other methods Examines non-linear oscillations and damping of dynamical systems including bifurcations and chaotic motions

Ganit Mathematics 6

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Author : Lata Wishram
language : en
Publisher: Vikas Publishing House
Release Date :

Ganit Mathematics 6 written by Lata Wishram and has been published by Vikas Publishing House this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

GANIT MATHEMATICS series consists of ten textbooks; two textbooks for Primer A and B, eight textbooks for classes 1-8. This series is strictly bases on the syllabus prescribed by the Council for the Indian School Certificate. The series has been developed to guide the young minds to observe and experience mathematics all around them. Each concept has been related to everyday life in order to develop a spirit of curiosity and discovery. Concepts are gradually built up with easy-to-follow steps and plenty of examples.

Polynomial Diophantine Equations

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Author : Bogdan Grechuk
language : en
Publisher: Springer Nature
Release Date : 2024-09-01

Polynomial Diophantine Equations written by Bogdan Grechuk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-01 with Mathematics categories.

This book proposes a novel approach to the study of Diophantine equations: define an appropriate version of the equation’s size, order all polynomial Diophantine equations by size, and then solve the equations in order. Natural questions about the solution set of Diophantine equations are studied in this book using this approach. Is the set empty? Is it finite or infinite? Can all integer solutions be parametrized? By ordering equations by size, the book attempts to answer these questions in a systematic manner. When the size grows, the difficulty of finding solutions increases and the methods required to determine solutions become more advanced. Along the way, the reader will learn dozens of methods for solving Diophantine equations, each of which is illustrated by worked examples and exercises. The book ends with solutions to exercises and a large collection of open problems, often simple to write down yet still unsolved. The original approach pursued in this book makes it widely accessible. Many equations require only high school mathematics and creativity to be solved, so a large part of the book is accessible to high school students, especially those interested in mathematical competitions such as olympiads. The main intended audience is undergraduate students, for whom the book will serve as an unusually rich introduction to the topic of Diophantine equations. Many methods from the book will be useful for graduate students, while Ph.D. students and researchers may use it as a source of fascinating open questions of varying levels of difficulty.