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Author: Dominic Jordan Publisher: Oxford University Press ISBN: 0199212031 Category : Mathematics Languages : en Pages : 594
Book Description
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: Dominic Jordan Publisher: Oxford University Press ISBN: 0199212031 Category : Mathematics Languages : en Pages : 594
Book Description
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: Mi-Ho Giga Publisher: Springer Science & Business Media ISBN: 0817646515 Category : Mathematics Languages : en Pages : 307
Book Description
This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.
Author: Donal O'Regan Publisher: Springer Science & Business Media ISBN: 9401715173 Category : Mathematics Languages : en Pages : 207
Book Description
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 ISBN: 0486817547 Category : Mathematics Languages : en Pages : 289
Book Description
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: W. Richard Kolk Publisher: Springer ISBN: Category : Science Languages : en Pages : 368
Book Description
Engineers, scientists, and applied mathematicians are habitually curious about behavior of physical systems. More often than not they will model the system and then analyze the model, hoping to expose the system's dynamic secrets. Traditionally, linear methods have been the norm and nonlinear effects were only added peripherally. This bias for linear techniques arises from the consum mate beauty and order in linear subs paces and the elegance of linear indepen dence is too compelling to be denied. And the bias has been, in the past, for tified by the dearth of nonlinear procedures, rendering the study of nonlinear dynamics untidy. But now a new attractiveness is being conferred on that non descript patchwork, and the virtue of the hidden surprises is gaining deserved respect. With a wide variety of individual techniques available, the student and the engineer as well as the scientist and researcher, are faced with an almost overwhelming task of which to use to help achieve an understanding sufficient to reach a satisfying result. If linear analysis predicts system behavior suffi ciently close to reality, that is delightful. In the more likely case where nonlin ear analysis is required, we believe this text fills an important void. We have tried to compile and bring some order to a large amount of information and techniques, that although well known, is scattered. We have also extended this knowledge base with new material not previously published.
Author: Dominic Jordan Publisher: Oxford University Press ISBN: 0199208247 Category : Mathematics Languages : en Pages : 541
Book Description
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: Andrei D. Polyanin Publisher: CRC Press ISBN: 1135440816 Category : Mathematics Languages : en Pages : 835
Book Description
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: Krzysztof A. Sikorski Publisher: Oxford University Press ISBN: 0198026676 Category : Computers Languages : en Pages : 253
Book Description
Optimal Solution of Nonlinear Equations is a text/monograph designed to provide an overview of optimal computational methods for the solution of nonlinear equations, fixed points of contractive and noncontractive mapping, and for the computation of the topological degree. It is of interest to any reader working in the area of Information-Based Complexity. The worst-case settings are analyzed here. Several classes of functions are studied with special emphasis on tight complexity bounds and methods which are close to or achieve these bounds. Each chapter ends with exercises, including companies and open-ended research based exercises.
Author: Dominic Jordan
Author: Dominic Jordan
Author: Mi-Ho Giga
Author: Donal O'Regan
Author: Raimond A. Struble
Author: Harold Thayer Davis
Author: W. Richard Kolk
Author: Dominic Jordan
Author: Andrei D. Polyanin
Author: Ferdinand Verhulst
Author: Krzysztof A. Sikorski