Algebraic Equations

Algebraic Equations PDF Author: Edgar Dehn
Publisher: Courier Corporation
ISBN: 0486155102
Category : Mathematics
Languages : en
Pages : 225

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Book Description
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.

Algebraic Equations

Algebraic Equations PDF Author: Edgar Dehn
Publisher: Courier Corporation
ISBN: 0486155102
Category : Mathematics
Languages : en
Pages : 225

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Book Description
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.

Differential-Algebraic Equations: A Projector Based Analysis

Differential-Algebraic Equations: A Projector Based Analysis PDF Author: René Lamour
Publisher: Springer Science & Business Media
ISBN: 3642275559
Category : Mathematics
Languages : en
Pages : 667

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Book Description
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.

General Theory of Algebraic Equations

General Theory of Algebraic Equations PDF Author: Etienne Bézout
Publisher: Princeton University Press
ISBN: 1400826969
Category : Mathematics
Languages : en
Pages : 363

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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.

Differential-algebraic Equations

Differential-algebraic Equations PDF Author: Peter Kunkel
Publisher: European Mathematical Society
ISBN: 9783037190173
Category : Boundary value problems
Languages : en
Pages : 396

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Book Description
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.

Equations and Inequalities

Equations and Inequalities PDF Author: Jiri Herman
Publisher: Springer Science & Business Media
ISBN: 1461212707
Category : Mathematics
Languages : en
Pages : 353

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Book Description
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.

Algebraic Equations

Algebraic Equations PDF Author: George Ballard Mathews
Publisher:
ISBN:
Category : Equations, Theory of
Languages : en
Pages : 76

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Book Description


Programming for Computations - MATLAB/Octave

Programming for Computations - MATLAB/Octave PDF Author: Svein Linge
Publisher: Springer
ISBN: 3319324527
Category : Computers
Languages : en
Pages : 228

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Book Description
This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations

Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations PDF Author: Uri M. Ascher
Publisher: SIAM
ISBN: 0898714125
Category : Mathematics
Languages : en
Pages : 304

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Book Description
This book contains all the material necessary for a course on the numerical solution of differential equations.

Algebraic Equations (Speedy Study Guides)

Algebraic Equations (Speedy Study Guides) PDF Author: Speedy Publishing
Publisher: Speedy Publishing LLC
ISBN: 1633839702
Category : Mathematics
Languages : en
Pages : 4

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Book Description
Algebraic equations are a great tool for rationalizing almost any relationship in the real and unreal worlds. The incorporation of algebra allows anyone to relate any one thing to another using a defined and constant standard. Any question about the value of an object or idea can be assigned a variable title. This variable is inserted into a directed algebraic equation with the goal of ascertaining certain values. With algebraic equations, it is possible to compare "oranges to apples" as long as certain constant properties are defined. If "X" is the universe, Algebra can help anyone compare the universe to an infinite pool of values with any number of goals in mind.

Algebraic Equations

Algebraic Equations PDF Author: Demetrios P. Kanoussis
Publisher: Golden Ratio Publications
ISBN: 1310146195
Category : Education
Languages : en
Pages : 46

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Book Description
This concise and to-the-point ebook presents the fundamental Theorems and main techniques to solve Algebraic Equations. Through the precise and illustrative presentation, the wide variety of characteristic solved examples and challenging problems, the reader will grasp the essential concepts of Algebraic Equations and advance to a higher level of understanding.