Author : Edgar Dehn
Publisher : Courier Corporation
Page : 225 pages
File Size : 13,94 MB
Release : 2012-09-05
Category : Mathematics
ISBN : 0486155102
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 : Peter Kunkel
Publisher : European Mathematical Society
Page : 396 pages
File Size : 47,64 MB
Release : 2006
Category : Boundary value problems
ISBN : 9783037190173
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
Page : 304 pages
File Size : 14,73 MB
Release : 1998-08-01
Category : Mathematics
ISBN : 0898714125
This book contains all the material necessary for a course on the numerical solution of differential equations.
Author : Etienne Bézout
Publisher : Princeton University Press
Page : 363 pages
File Size : 12,50 MB
Release : 2009-01-10
Category : Mathematics
ISBN : 1400826969
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
Page : 667 pages
File Size : 21,49 MB
Release : 2013-01-19
Category : Mathematics
ISBN : 3642275559
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 : K. E. Brenan
Publisher : SIAM
Page : 268 pages
File Size : 16,91 MB
Release : 1996-01-01
Category : Mathematics
ISBN : 9781611971224
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 : George Ballard Mathews
Publisher :
Page : 76 pages
File Size : 33,92 MB
Release : 1907
Category : Equations, Theory of
ISBN :
Author : Demetrios P. Kanoussis
Publisher : Golden Ratio Publications
Page : 46 pages
File Size : 43,95 MB
Release : 2015-02-24
Category : Education
ISBN : 1310146195
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.
Author : Jiri Herman
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 24,70 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461212707
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
Page : 6 pages
File Size : 29,6 MB
Release : 2014-09-23
Category : Mathematics
ISBN : 1680321617
One exceptionally important part of knowing how to do algebra is knowing all of the equations. This can be very difficult for a student who is first learning how to do algebra, and it can be very difficult for one to sit down to learn them. One great way for persons to avoid simply starring at the equation for hours is to use an algebra equation study guide. The guide contains useful exercises a student can do in order to learn the problems.
