Nonlinear Ordinary Differential Equations
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Nonlinear Ordinary Differential Equations
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Author : R. Grimshaw
language : en
Publisher: Routledge
Release Date : 2017-10-19
Nonlinear Ordinary Differential Equations written by R. Grimshaw and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.
Nonlinear Ordinary Differential Equations In Transport Processes
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Author : W. F. Ames
language : en
Publisher: Academic Press
Release Date : 1968
Nonlinear Ordinary Differential Equations In Transport Processes written by W. F. Ames and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Computers categories.
Nonlinear Ordinary Differential Equations in Transport Processes
Nonlinear Ordinary Differential Equations Problems And Solutions
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Author : Dominic Jordan
language : en
Publisher: OUP Oxford
Release Date : 2007-08-23
Nonlinear Ordinary Differential Equations Problems And Solutions written by Dominic Jordan and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-23 with Mathematics categories.
An ideal companion to the new 4th Edition of Nonlinear Ordinary Differential Equations by Jordan and Smith (OUP, 2007), this text contains over 500 problems and fully-worked solutions in nonlinear differential equations. With 272 figures and diagrams, subjects covered include phase diagrams in the plane, classification of equilibrium points, geometry of the phase plane, perturbation methods, forced oscillations, stability, Mathieu's equation, Liapunov methods, bifurcations and manifolds, homoclinic bifurcation, and Melnikov's method. The problems are of variable difficulty; some are routine questions, others are longer and expand on concepts discussed in Nonlinear Ordinary Differential Equations 4th Edition, and in most cases can be adapted for coursework or self-study. Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.
Nonlinear Ordinary Differential Equations
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Author : Dominic William Jordan
language : en
Publisher: Oxford University Press, USA
Release Date : 1987
Nonlinear Ordinary Differential Equations written by Dominic William Jordan and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Differential equations, Nonlinear categories.
The new edition has been significantly revised in line with current thinking on the subject. There is a new chapter on bifurcations, structural stability, and chaotic motion, and a more algebraic approach has been adopted to the linear treatment of linearized systems.
Nonlinear Ordinary Differential Equations
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Author : Dominic Jordan
language : en
Publisher: Oxford University Press on Demand
Release Date : 2007-08-23
Nonlinear Ordinary Differential Equations written by Dominic Jordan and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-23 with Language Arts & Disciplines categories.
Thoroughly updated and expanded 4th edition of the classic text, including numerous worked examples, diagrams and exercises. An ideal resource for students and lecturers in engineering, mathematics and the sciences it is published alongside a separate Problems and Solutions Sourcebook containing over 500 problems and fully-worked solutions.
Introduction To Nonlinear Differential And Integral Equations
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Author : Harold Thayer Davis
language : en
Publisher: Courier Corporation
Release Date : 1962-01-01
Introduction To Nonlinear Differential And Integral Equations written by Harold Thayer Davis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962-01-01 with Mathematics categories.
Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.
Nonlinear Ordinary Differential Equations
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Author : Dominic William Jordan
language : en
Publisher: Oxford University Press, USA
Release Date : 1999
Nonlinear Ordinary Differential Equations written by Dominic William Jordan and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos.
Existence Theory For Nonlinear Ordinary Differential Equations
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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Existence Theory For Nonlinear Ordinary Differential Equations written by Donal O'Regan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.
Nonlinear Differential Equations And Dynamical Systems
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Differential Equations And Dynamical Systems written by Ferdinand Verhulst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.
Nonlinear Ordinary Differential Equations
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Author : Martin Hermann
language : en
Publisher: Springer
Release Date : 2016-05-09
Nonlinear Ordinary Differential Equations written by Martin Hermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-09 with Mathematics categories.
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march method. This book comprehensively investigates various new analytical and numerical approximation techniques that are used in solving nonlinear-oscillator and structural-system problems. Students often rely on the finite element method to such an extent that on graduation they have little or no knowledge of alternative methods of solving problems. To rectify this, the book introduces several new approximation techniques.