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Author: Edgar Dehn
Publisher: Courier Corporation
Published: 2012-09-05
Total Pages: 225
ISBN-13: 0486155102
DOWNLOAD EBOOK →Focusing on basics of algebraic theory, this text presents detailed explanations of integral functions, permutations, and groups as well as Lagrange and Galois theory. Many numerical examples with complete solutions. 1930 edition.
Author: Etienne Bézout
Publisher: Princeton University Press
Published: 2009-01-10
Total Pages: 363
ISBN-13: 1400826969
DOWNLOAD EBOOK →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: René Lamour
Publisher: Springer Science & Business Media
Published: 2013-01-19
Total Pages: 667
ISBN-13: 3642275559
DOWNLOAD EBOOK →Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In this relatively short time, DAEs have become a widely acknowledged tool to model processes subjected to constraints, in order to simulate and to control processes in various application fields such as network simulation, chemical kinematics, mechanical engineering, system biology. DAEs and their more abstract versions in infinite-dimensional spaces comprise a great potential for future mathematical modeling of complex coupled processes. The purpose of the book is to expose the impressive complexity of general DAEs from an analytical point of view, to describe the state of the art as well as open problems and so to motivate further research to this versatile, extra-ordinary topic from a broader mathematical perspective. The book elaborates a new general structural analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of special projector functions. Numerical integration issues and computational aspects are treated also in this context.
Author: Peter Kunkel
Publisher: European Mathematical Society
Published: 2006
Total Pages: 396
ISBN-13: 9783037190173
DOWNLOAD EBOOK →Differential-algebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many others. This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential-algebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differential-algebraic equations (Runge-Kutta and BDF methods) are discussed and analyzed with respect to convergence and order. A chapter is devoted to index reduction methods that allow the numerical treatment of general differential-algebraic equations. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differential-algebraic equations completes the text. The book is addressed to graduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry. A prerequisite is a standard course on the numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for self-study.
Author: Uri M. Ascher
Publisher: SIAM
Published: 1998-08-01
Total Pages: 304
ISBN-13: 0898714125
DOWNLOAD EBOOK →This book contains all the material necessary for a course on the numerical solution of differential equations.
Author: K. E. Brenan
Publisher: SIAM
Published: 1996-01-01
Total Pages: 268
ISBN-13: 9781611971224
DOWNLOAD EBOOK →Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date. The objective of this monograph is to advance and consolidate the existing research results for the numerical solution of DAE's. The authors present results on the analysis of numerical methods, and also show how these results are relevant for the solution of problems from applications. They develop guidelines for problem formulation and effective use of the available mathematical software and provide extensive references for further study.
Author: Jiri Herman
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 353
ISBN-13: 1461212707
DOWNLOAD EBOOK →A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.
Author: Speedy Publishing
Publisher: Speedy Publishing LLC
Published: 2015-01-21
Total Pages: 6
ISBN-13: 1681275422
DOWNLOAD EBOOK →Algebra is a complex form a math that has been known to baffle adults and students alike. However, many adults no longer have to deal with algebra but a lot of middle and high school students do. A study guide will help high school students to understand how do algebra. They can also use it to practice and to develop their skills in this area of math.
Author: BarCharts, Inc
Publisher:
Published: 2014-05-31
Total Pages: 0
ISBN-13: 9781423222668
DOWNLOAD EBOOK →This guide outlines basic algebraic equations, formulas, properties & operations.
Author: Robert Moses
Publisher: Beacon Press
Published: 2002-06-10
Total Pages: 260
ISBN-13: 0807031690
DOWNLOAD EBOOK →The remarkable story of the Algebra Project, a community-based effort to develop math-science literacy in disadvantaged schools—as told by the program’s founder “Bob Moses was a hero of mine. His quiet confidence helped shape the civil rights movement, and he inspired generations of young people looking to make a difference”—Barack Obama At a time when popular solutions to the educational plight of poor children of color are imposed from the outside—national standards, high-stakes tests, charismatic individual saviors—the acclaimed Algebra Project and its founder, Robert Moses, offer a vision of school reform based in the power of communities. Begun in 1982, the Algebra Project is transforming math education in twenty-five cities. Founded on the belief that math-science literacy is a prerequisite for full citizenship in society, the Project works with entire communities—parents, teachers, and especially students—to create a culture of literacy around algebra, a crucial stepping-stone to college math and opportunity. Telling the story of this remarkable program, Robert Moses draws on lessons from the 1960s Southern voter registration he famously helped organize: “Everyone said sharecroppers didn't want to vote. It wasn't until we got them demanding to vote that we got attention. Today, when kids are falling wholesale through the cracks, people say they don't want to learn. We have to get the kids themselves to demand what everyone says they don't want.” We see the Algebra Project organizing community by community. Older kids serve as coaches for younger students and build a self-sustained tradition of leadership. Teachers use innovative techniques. And we see the remarkable success stories of schools like the predominately poor Hart School in Bessemer, Alabama, which outscored the city's middle-class flagship school in just three years. Radical Equations provides a model for anyone looking for a community-based solution to the problems of our disadvantaged schools.
