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Monday, July 20, 2020 | History

1 edition of Differential and Difference Dimension Polynomials found in the catalog.

Differential and Difference Dimension Polynomials

by M. V. Kondratieva

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  • 0 Currently reading

Published by Springer Netherlands in Dordrecht .
Written in English

    Subjects:
  • Combinatorics,
  • Mathematics,
  • Differential equations, partial,
  • Algebra

  • About the Edition

    This book is the first monograph wholly devoted to the investigation of differential and difference dimension theory. The differential dimension polynomial describes in exact terms the degree of freedom of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. Difference algebra arises from the study of algebraic difference equations and therefore bears a considerable resemblance to its differential counterpart. Difference algebra was developed in the same period as differential algebra and it has the same founder, J. Ritt. It grew to a mathematical area with its own ideas and methods mainly due to the work of R. Cohn, who raised difference algebra to the same level as differential algebra. The relatively new science of computer algebra has given strong impulses to the theory of dimension polynomials, now that packages such as MAPLE enable the solution of many problems which cannot be solved otherwise. Applications of differential and difference dimension theory can be found in many fields of mathematics, as well as in theoretical physics, system theory and other areas of science. Audience: This book will be of interest to researchers and graduate students whose work involves differential and difference equations, algebra and number theory, partial differential equations, combinatorics and mathematical physics.

    Edition Notes

    Statementby M. V. Kondratieva, A. B. Levin, A. V. Mikhalev, E. V. Pankratiev
    SeriesMathematics and Its Applications -- 461, Mathematics and Its Applications -- 461
    ContributionsLevin, A. B., Mikhalev, A. V., Pankratiev, E. V.
    Classifications
    LC ClassificationsQA150-272
    The Physical Object
    Format[electronic resource] /
    Pagination1 online resource (xiii, 426 p.)
    Number of Pages426
    ID Numbers
    Open LibraryOL27032162M
    ISBN 109048151414, 9401712573
    ISBN 109789048151417, 9789401712576
    OCLC/WorldCa851367902

    Chapter 1 Differential and Difference Equations In this chapter we give a brief introduction to PDEs. In Section some simple prob-lems that arise in real-life phenomena are derived. (A more detailed derivation of such problems will follow in later chapters.) We show by a File Size: KB. An ordinary differential equation (ODE) is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of unknown function is generally represented by a variable (often denoted y), which, therefore, depends on x is often called the independent variable of the equation. The term "ordinary" is used in contrast with the term.

    This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. , starting with two-point boundary value problems in one dimension, followed. Zeros of Orthogonal Polynomials, Differentiation and Integration of Lagrange Interpolation Polynomials, Program Description, Discretization of Differential Equations in Terms of Ordinates, Exercises, References, 4. Solution of Linear Differential Equations By Collocation Introduction,

      In this paper, we deal with the zeros of the q-shift difference-differential polynomials and, where is a nonzero polynomial of degree n, () are constants, and is a small function of f. The results of this paper are an extension of the previous theorems given by Chen and Chen and by: 1.   Here is a set of assignement problems (for use by instructors) to accompany the Polynomials section of the Preliminaries chapter of the notes for Paul Dawkins Algebra course at Lamar University.


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Differential and Difference Dimension Polynomials by M. V. Kondratieva Download PDF EPUB FB2

A similar role in differential algebra is played by the differential dimension polynomials. The notion of differential dimension polynomial was introduced by E.

Kolchin in [KoI64]' but the problems and ideas that had led to this notion (and that are reflected in this book) have essentially more long history. "This book is the first monograph wholly devoted to the investigation of differential and difference dimension theory.

The differential dimension polynomial describes in exact terms the freedom degree of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations.".

This book is the first monograph wholly devoted to the investigation of differential and difference dimension theory. The differential dimension polynomial describes in exact terms the degree of freedom of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations.

Cite this chapter as: Kondratieva M.V., Levin A.B., Mikhalev A.V., Pankratiev E.V. () Differential Dimension Polynomials. In: Differential and Difference Cited by: 3. Levin() investigated the difference-differential dimension polynomials in two variables with characteristic set method.

The method of Levin is rather delicate but no general algorithm for. Multivariate Difference-Differential Dimension Polynomials and New Invariants of Difference-Differential Field Extensions Article (PDF Available). A new approach for investigating polynomial solutions of differential equations is proposed.

It is based on elementary linear algebra. Any differential operator of the form L (y) = ∑ k = 0 k = N a k (x) y (k), where a k is a polynomial of degree ≤ k, over an infinite field F has all eigenvalues in F in the space of polynomials of degree at most n, for all these eigenvalues are Cited by: Published 53 years ago, this book gives an overview of an area of mathematics that has found applications in algebraic, Diophantine, and differential geometry, model theory, Painleve theory, integrable systems, automatic theorem proving, combinatorics, difference equations, and 4/5(1).

In this paper we present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped Cited by: Direct application of difierence and difierential equations Sustainable harevesting Maximal concentration of a drug in an organ A nonlinear pendulum Equilibria of flrst order equations Equilibria for difierential equations Crystal growth{a case study Equilibrium points File Size: 1MB.

We give an algorithm which can be used to decompose the zero set for a finitely generated differential and difference polynomial sets into the union of the zero sets of regular and consistent ascending chains.

As a consequence, we solve the perfect ideal membership problem for Cited by: We give a positive answer in a strong form; that is, we compute a (lower and upper) bound for all the coefficients of the Kolchin polynomial of every such prime component.

We then show that, if we look at those components of a specified differential type, we can compute a significantly better bound for the typical differential dimension. Harry Bateman was a famous English mathematician.

In writing this book he had endeavoured to supply some elementary material suitable for the needs of students who are studying the subject for the first time, and also some more advanced work which may be useful to men who are interested more in physical mathematics than in the developments of differential geometry and the theory of functions.

Title Solving polynomial differential equations by transforming them to linear functional-differential equations John Michael Nahay Broadway Performance Systems, LLC Rosemere Ave., Silver Spring, MD Email: [email protected] Abstract We present a new approach to solving polynomial ordinary differential equationsAuthor: John Michael Nahay.

Also in [37–39], the authors derived new formulas using shifted Chebyshev polynomials and shifted Jacobi polynomials of any degree, respectively and applied them together with tau and collocation spectral methods for solving multiterm linear and nonlinear fractional differential by: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations.

starting with two-point boundary value problems in one dimension, followed. Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields. The first stage of this development of the theory is associated with its founder, J.F.

Ritt (), and R. Cohn, whose book Difference Algebra () remained the only. What is the practical difference, though. You'll probably be disappointed to hear "not much". Except one thing: when your functions represent actual quantities, rather than just formal manipulation of symbols, the derivative and the differential measure different things.

With its numerous pedagogical features that consistently engage readers, A Workbook for Differential Equations is an excellent book for introductory courses in differential equations and applied mathematics at the undergraduate level. It is also a suitable reference for professionals in all areas of science, physics, and engineering.

Definitely the best intro book on ODEs that I've read is Ordinary Differential Equations by Tenebaum and Pollard. Dover books has a reprint of the book for maybe dollars on Amazon, and considering it has answers to most of the problems found.

used textbook “Elementary differential equations and boundary value problems” by Boyce & DiPrima (John Wiley & Sons, Inc., Seventh Edition, c ).

Many of the examples presented in these notes may be found in this book. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven. Differential equation involves derivatives of function. Difference equation involves difference of terms in a sequence of numbers.

People sometimes construct difference equation to approximate differential equation so that they can write code to s.Joseph Fels Ritt (Aug – January 5, ) was an American mathematician at Columbia University in the early 20th century. He was born and died in New York. After beginning his undergraduate studies at City College of New York, Ritt received his B.A.

from George Washington University in He then earned a doctorate in mathematics from Columbia University in Fields: Mathematics.