Nonlinear Ordinary Differential Equations PDF Download
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Author | : R. Grimshaw |
Publisher | : Routledge |
Total Pages | : 276 |
Release | : 2017-10-19 |
Genre | : Mathematics |
ISBN | : 135142808X |
Download Nonlinear Ordinary Differential Equations Book in PDF, ePub and Kindle
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 | : OUP Oxford |
Total Pages | : 540 |
Release | : 2007-08-24 |
Genre | : Mathematics |
ISBN | : 0191525995 |
Download Nonlinear Ordinary Differential Equations Book in PDF, ePub and Kindle
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, homoclinic bifurcation 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 | : Raimond A. Struble |
Publisher | : Courier Dover Publications |
Total Pages | : 289 |
Release | : 2018-01-16 |
Genre | : Mathematics |
ISBN | : 0486817547 |
Download Nonlinear Differential Equations Book in PDF, ePub and Kindle
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 |
Genre | : Mathematics |
ISBN | : 3642971490 |
Download Nonlinear Differential Equations and Dynamical Systems Book in PDF, ePub and Kindle
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 | : Dominic Jordan |
Publisher | : Oxford University Press |
Total Pages | : 594 |
Release | : 2007-08-23 |
Genre | : Mathematics |
ISBN | : 0199212031 |
Download Nonlinear Ordinary Differential Equations: Problems and Solutions Book in PDF, ePub and Kindle
An ideal companion to the student textbook Nonlinear Ordinary Differential Equations 4th Edition (OUP, 2007) this text contains over 500 problems and solutions in nonlinear differential equations, many of which can be adapted for independent coursework and self-study.
Author | : Donal O'Regan |
Publisher | : Springer Science & Business Media |
Total Pages | : 207 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 9401715173 |
Download Existence Theory for Nonlinear Ordinary Differential Equations Book in PDF, ePub and Kindle
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 | : Harold Thayer Davis |
Publisher | : |
Total Pages | : 590 |
Release | : 1960 |
Genre | : Calculus |
ISBN | : |
Download Introduction to Nonlinear Differential and Integral Equations Book in PDF, ePub and Kindle
Author | : A. C. King |
Publisher | : Cambridge University Press |
Total Pages | : 554 |
Release | : 2003-05-08 |
Genre | : Mathematics |
ISBN | : 9780521816588 |
Download Differential Equations Book in PDF, ePub and Kindle
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 | : Andrei D. Polyanin |
Publisher | : CRC Press |
Total Pages | : 835 |
Release | : 2004-06-02 |
Genre | : Mathematics |
ISBN | : 1135440816 |
Download Handbook of Nonlinear Partial Differential Equations Book in PDF, ePub and Kindle
The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
Author | : R. E. Gaines |
Publisher | : Springer |
Total Pages | : 267 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540375015 |
Download Coincidence Degree and Nonlinear Differential Equations Book in PDF, ePub and Kindle