Nonlinear Ordinary Differential Equations
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Author |
: R. Grimshaw |
Publisher |
: Routledge |
Total Pages |
: 342 |
Release |
: 2017-10-19 |
ISBN-10 |
: 9781351428088 |
ISBN-13 |
: 135142808X |
Rating |
: 4/5 (88 Downloads) |
Synopsis Nonlinear Ordinary Differential Equations by : R. Grimshaw
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.
Author |
: Dominic Jordan |
Publisher |
: Oxford University Press |
Total Pages |
: 541 |
Release |
: 2007-08-23 |
ISBN-10 |
: 9780199208241 |
ISBN-13 |
: 0199208247 |
Rating |
: 4/5 (41 Downloads) |
Synopsis Nonlinear Ordinary Differential Equations by : Dominic Jordan
This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinicbifurcation and Liapunov exponents.Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007).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.
Author |
: Dominic Jordan |
Publisher |
: Oxford University Press |
Total Pages |
: 594 |
Release |
: 2007-08-23 |
ISBN-10 |
: 9780199212033 |
ISBN-13 |
: 0199212031 |
Rating |
: 4/5 (33 Downloads) |
Synopsis Nonlinear Ordinary Differential Equations: Problems and Solutions by : Dominic Jordan
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, bifurcationsand 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.
Author |
: Donal O'Regan |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 207 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9789401715171 |
ISBN-13 |
: 9401715173 |
Rating |
: 4/5 (71 Downloads) |
Synopsis Existence Theory for Nonlinear Ordinary Differential Equations by : Donal O'Regan
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.
Author |
: Raimond A. Struble |
Publisher |
: Courier Dover Publications |
Total Pages |
: 289 |
Release |
: 2018-01-16 |
ISBN-10 |
: 9780486817545 |
ISBN-13 |
: 0486817547 |
Rating |
: 4/5 (45 Downloads) |
Synopsis Nonlinear Differential Equations by : Raimond A. Struble
Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.
Author |
: Ferdinand Verhulst |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 287 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642971495 |
ISBN-13 |
: 3642971490 |
Rating |
: 4/5 (95 Downloads) |
Synopsis Nonlinear Differential Equations and Dynamical Systems by : Ferdinand Verhulst
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.
Author |
: A. C. King |
Publisher |
: Cambridge University Press |
Total Pages |
: 554 |
Release |
: 2003-05-08 |
ISBN-10 |
: 0521816580 |
ISBN-13 |
: 9780521816588 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Differential Equations by : A. C. King
Differential equations are vital to science, engineering and mathematics, and this book enables the reader to develop the required skills needed to understand them thoroughly. The authors focus on constructing solutions analytically and interpreting their meaning and use MATLAB extensively to illustrate the material along with many examples based on interesting and unusual real world problems. A large selection of exercises is also provided.
Author |
: Harold Thayer Davis |
Publisher |
: |
Total Pages |
: 590 |
Release |
: 1960 |
ISBN-10 |
: MINN:31951D03527010I |
ISBN-13 |
: |
Rating |
: 4/5 (0I Downloads) |
Synopsis Introduction to Nonlinear Differential and Integral Equations by : Harold Thayer Davis
Author |
: P. L. Sachdev |
Publisher |
: Wiley-Interscience |
Total Pages |
: 944 |
Release |
: 1997 |
ISBN-10 |
: UOM:39015060105825 |
ISBN-13 |
: |
Rating |
: 4/5 (25 Downloads) |
Synopsis A Compendium on Nonlinear Ordinary Differential Equations by : P. L. Sachdev
This book offers a collection of approximately 2,500 nonlinear ordinary differential equations and includes the equation, the answer or important results, and references. Nonlinear phenomena have become a dominant theme in the sciences and this thoroughly up-to-date book is a useful research tool for applied mathematicians and engineers.
Author |
: Nw McLachlan |
Publisher |
: Franklin Classics |
Total Pages |
: 220 |
Release |
: 2018-10-15 |
ISBN-10 |
: 0343267098 |
ISBN-13 |
: 9780343267094 |
Rating |
: 4/5 (98 Downloads) |
Synopsis Ordinary Non Linear Differential Equationsin Engineering and Physical Sciences by : Nw McLachlan
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.