Last edited by Melmaran
Friday, October 16, 2020 | History

4 edition of inverse problem of the calculus of variations for ordinary differential equations found in the catalog.

inverse problem of the calculus of variations for ordinary differential equations

by Anderson, Ian

  • 223 Want to read
  • 8 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Calculus of variations.,
  • Inverse problems (Differential equations),
  • Perturbation (Mathematics)

  • Edition Notes

    Includes bibliographical references (p. 108-110).

    StatementIan Anderson, Gerard Thompson.
    SeriesMemoirs of the American Mathematical Society,, no. 473
    ContributionsThompson, Gerard, 1955-
    Classifications
    LC ClassificationsQA3 .A57 no. 473, QA315 .A57 no. 473
    The Physical Object
    Paginationvi, 110 p. ;
    Number of Pages110
    ID Numbers
    Open LibraryOL1708974M
    ISBN 10082182533X
    LC Control Number92010610

    Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book . Abstract: A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and sufficient algebraic and differential conditions for the existence of a variational multiplier are : Matt Biesecker.

    Calculus of Variations and Differential Equations - CRC Press Book The calculus of variations is a classical area of mathematical analysis years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. Keywords: Calculus of variations; Inverse problem 1. Introduction The Inverse Problem of the Calculus of Variations is to determine whether a given system of differential equations may be derived from a variational principle. This paper concerns an aspect of the Inverse Problem for higher-order ordinary differential equations, where the.

    The Inverse Problem of the Calculus of Variations for Scalar Fourth Order Ordinary Deferential Equations, M.E. Fels, Trans. Amer. Math Soc., (12), , Cited by: Second Order Ordinary Differential Equations in Jet Bundles and the Inverse Problem of the Calculus of Variations Chapter. View record in Web of Science ® International Standard Book Number (ISBN) Additional Document Info. Publisher.


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Inverse problem of the calculus of variations for ordinary differential equations by Anderson, Ian Download PDF EPUB FB2

This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centers on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coincides with a given system of ordinary differential equations.

The inverse problem of the calculus of variations is the problem of finding variational principles for systems of differential equations. By using the general theory of the variational bicomplex, it is shown that the inverse problem for ordinary differential equations is equivalent to the problem of finding differential two forms, with certain prescribed algebraic properties, which are closed.

The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e.

how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange. Buy The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations (Memoirs of the American Mathematical Society) on FREE SHIPPING on qualified orders.

Destination page number Search scope Search Text Search scope Search Text. Introduction 2. The variational bicomplex for ordinary differential equations 3.

First integrals and the inverse problem for second order ordinary differential equations 4. The inverse problem for fourth order ordinary differential equations 5.

Exterior differential systems and the inverse problem for second order ordinary differential. The second part, the calculus of variations, is not commontly bundled together with a differential equations course.

It can be read independently if the reader is acquainted with the basic facts of the theory of differential equations.

From the start, the author draws a parallel between optimization of functions of a single real variable Cited by: : The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations (Memoirs of the American Mathematical Society) () by Ian Anderson; Gerard Thompson and a great selection of similar New, Used and Collectible Books available now at great : Paperback.

Numerous papers have been dedicated to the solution of the inverse problem of calculus of variations, namely finding a Lagrangian of differential equations. Some of these acknowledge the seminal work of Jacobi (see references in Nucci () and Nucci & Leach ()), but most failed to do by:   The inverse problem of the calculus of variations for scalar fourth-order ordinary differential equations, Trans.

Amer. Math. Soc. (), Cited by: This represents a subcase of Fels'conditions [M. Fels, The inverse problem of the calculus of variations for scalar fourth-order ordinary differential equations, Trans. Amer. Math. Soc. The calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.

Functionals are often expressed as definite integrals involving functions and their ons that maximize or minimize functionals may be found. Crampin M. () On the Inverse Problem of the Calculus of Variations for Systems of Second-Order Ordinary Differential Equations.

In: Antonelli P.L. (eds) Finslerian Geometries. Fundamental Theories of Physics (An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application), vol Cited by: 3. Inverse Problems in Ordinary Differential Equations and Applications / This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties.

The Nambu bracket. Numerous papers have been dedicated to the solution of the inverse problem of calculus of variations, namely finding a Lagrangian of differential equations. Some of these acknowledge the seminal work of Jacobi (see references in Nucci () and Nucci & Leach ()), but most failed to do so.

The Inverse Problem Of The Calculus Of Variations For Scalar Fourth-Order Ordinary Differential Equations Article (PDF Available) in Transactions of the American Mathematical Society ( As a consequence, one version of the inverse problem in the calculus of variations may be solved in the following way: given a differential equation ~ written as a source form if H(~) =°then there is a local Lagrangian A= L dx 1 /\ ••• /\ dx" with ~ = e(A+ Div 1)) for any current 1).Cited by: In mathematics, the inverse problem for Lagrangian mechanics is the problem of determining whether a given system of ordinary differential equations can arise as the Euler–Lagrange equations for some Lagrangian function.

There has been a great deal of activity in the study of this problem since the early 20th century. A notable advance in this field was a paper by the American. This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations.

While this course is usually required for engineering students the material is attractive to students in any field of applied science, including those in the biological standard analytic methods for solving first and second-order differential 1/5(2).

Please provide a summary of the answer (for the PDE case) and suggest books where I can learn about this subject of inverse problems in calculus of variations for ODE's and PDE's. real-analysis functional-analysis ordinary-differential-equations reference-request calculus-of-variations.

Book 3a Calculus and differential equations John Avery H. C. Ørsted Institute University of Copenhagen (Denmark) Books in the Series are available –freeofcharge–from the websites (see ‘Basic Books in Science’) (see ‘For the Love of Science’)File Size: KB.Using this strategy we can also discuss the inverse problem of fractional calculus of variations for classical partial differential equations, like the diffusion equation or Stokes equations, in order to obtain a Lagrangian representation of such PDEs.

The interest of such results is at least twofold:Cited by: Purchase Calculus and Ordinary Differential Equations - 1st Edition. Print Book & E-Book. ISBN