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| nonlinear ordinary differential equations jordan: Nonlinear Ordinary Differential Equations Dominic William Jordan, Peter Smith, 1999 This edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos. |
| nonlinear ordinary differential equations jordan: Nonlinear Ordinary Differential Equations Dominic Jordan, Peter Smith, 2007-08-23 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. |
| nonlinear ordinary differential equations jordan: Nonlinear Ordinary Differential Equations: Problems and Solutions Dominic Jordan, Peter Smith, 2007-08-23 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. |
| nonlinear ordinary differential equations jordan: Nonlinear Ordinary Differential Equations:An Introduction for Scientists and Engineers Dominic Jordan, Peter Smith, 2007-08-23 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. |
| nonlinear ordinary differential equations jordan: Nonlinear Ordinary Differential Equations Dominic William Jordan, Peter Smith, 1987 This new edition has been expanded to contain an introduction to areas of current importance such as bifurcation, structural stability and chaotic behavior. Other topics include linearization, perturbation theory, subharmonics, stability, the existence of limit cycles, and Poincar maps. The text is concerned with practical applications and includes over 400 examples and exercises. |
| nonlinear ordinary differential equations jordan: Ordinary Differential Equations and Dynamical Systems Gerald Teschl, 2024-01-12 This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations. |
| nonlinear ordinary differential equations jordan: Nonlinear Ordinary Differential Equations Dominic William Jordan, Peter Smith, 2023 An ideal companion to 'Nonlinear Ordinary Differential Equations, Fourth Edition', this text contains over 500 problems and solutions in nonlinear differential equations, many of which can be adapted for independent coursework and self-study. |
| nonlinear ordinary differential equations jordan: Finite Difference Methods for Ordinary and Partial Differential Equations Randall J. LeVeque, 2007-01-01 This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples. |
| nonlinear ordinary differential equations jordan: Nonlinear ordinary differential equations D. W. Jordan, 1979 |
| nonlinear ordinary differential equations jordan: Ordinary Differential Equations with Applications Carmen Chicone, 2008-04-08 This book is based on a two-semester course in ordinary di?erential eq- tions that I have taught to graduate students for two decades at the U- versity of Missouri. The scope of the narrative evolved over time from an embryonic collection of supplementary notes, through many classroom tested revisions, to a treatment of the subject that is suitable for a year (or more) of graduate study. If it is true that students of di?erential equations giveaway their point of viewbythewaytheydenotethederivativewith respecttotheindependent variable, then the initiated reader can turn to Chapter 1, note that I write x ?,not x , and thus correctly deduce that this book is written with an eye toward dynamical systems. Indeed, this book contains a thorough int- duction to the basic properties of di?erential equations that are needed to approach the modern theory of (nonlinear) dynamical systems. However, this is not the whole story. The book is also a product of my desire to demonstrate to my students that di?erential equations is the least insular of mathematical subjects, that it is strongly connected to almost all areas of mathematics, and it is an essential element of applied mathematics. |
| nonlinear ordinary differential equations jordan: Differential Equations A. C. King, 2003 The authors focus on constructing solutions analytically, and interpreting their meaning; MATLAB is used extensively to illustrate the material. The many worked examples, based on interesting real world problems, the large selection of exercises, including several lengthier projects, the broad coverage, and clear and concise presentation will appeal to undergraduates. |
| nonlinear ordinary differential equations jordan: Exploring ODEs Lloyd N.Trefethen, Asgeir Birkisson, Tobin A. Driscoll, 2017-12-21 Exploring ODEs is a textbook of ordinary differential equations for advanced undergraduates, graduate students, scientists, and engineers. It is unlike other books in this field in that each concept is illustrated numerically via a few lines of Chebfun code. There are about 400 computer-generated figures in all, and Appendix B presents 100 more examples as templates for further exploration. |
| nonlinear ordinary differential equations jordan: Stability and Stabilization William J. Terrell, 2009-02-15 Stability and Stabilization is the first intermediate-level textbook that covers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations. Designed for advanced undergraduates and beginning graduate students in the sciences, engineering, and mathematics, the book takes a unique modern approach that bridges the gap between linear and nonlinear systems. Presenting stability and stabilization of equilibria as a core problem of mathematical control theory, the book emphasizes the subject's mathematical coherence and unity, and it introduces and develops many of the core concepts of systems and control theory. There are five chapters on linear systems and nine chapters on nonlinear systems; an introductory chapter; a mathematical background chapter; a short final chapter on further reading; and appendixes on basic analysis, ordinary differential equations, manifolds and the Frobenius theorem, and comparison functions and their use in differential equations. The introduction to linear system theory presents the full framework of basic state-space theory, providing just enough detail to prepare students for the material on nonlinear systems. Focuses on stability and feedback stabilization Bridges the gap between linear and nonlinear systems for advanced undergraduates and beginning graduate students Balances coverage of linear and nonlinear systems Covers cascade systems Includes many examples and exercises |
| nonlinear ordinary differential equations jordan: The Qualitative Theory of Ordinary Differential Equations Fred Brauer, John A. Nohel, 2012-12-11 Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Focuses on stability theory and its applications to oscillation phenomena, self-excited oscillations, more. Includes exercises. |
| nonlinear ordinary differential equations jordan: Differential Dynamical Systems James D. Meiss, 2007-01-01 Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems conceptsflow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems. Audience This textbook is intended for senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with elementary differential equations and linear algebra and should have had exposure to advanced calculus. Contents List of Figures; Preface; Acknowledgments; Chapter 1: Introduction; Chapter 2: Linear Systems; Chapter 3: Existence and Uniqueness; Chapter 4: Dynamical Systems; Chapter 5: Invariant Manifolds; Chapter 6: The Phase Plane; Chapter 7: Chaotic Dynamics; Chapter 8: Bifurcation Theory; Chapter 9: Hamiltonian Dynamics; Appendix: Mathematical Software; Bibliography; Index |
| nonlinear ordinary differential equations jordan: Nonlinear Dynamics and Chaos Steven H. Strogatz, 2018-05-04 This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. |
| nonlinear ordinary differential equations jordan: Mathematical Techniques Dominic William Jordan, Peter Smith, 1997 Undergraduate students of engineering, science, and mathematics must quickly master a variety of mathematical methods, although many of these students do not have strong mathematics backgrounds. In this well-received book, now in its second edition, the authors use their extensive experience with diverse groups of students to provide an accessible introduction to mathematical techniques. They start at the elementary level and proceed to cover the full range of topics typically encountered by beginning students: BL Analytic geometry, vector algebra, vector fields (div and curl), differentiation, and integration. BL Complex numbers, matrix operations, and linear systems of equations. BL Differential equations and first-order linear systems, functions of more than one variable, double integrals, and line integrals. BL Laplace transforms, Fourier series and Fourier transforms. BL Probability and statistics. Incorporating many suggestions from readers, this new edition has expanded discussions of vectors and new chapters on Fourier series and on probability and statistics. The emphasis throughout is on understanding concepts through well-chosen examples, and the book includes over 500 fully worked problems. As far as is possible chapter topics are self-contained so that a student only needing to master certain techniques can omit others without trouble. The generously illustrated text also includes simple numerical processes which lead to examples and projects for computation (particularly with Mathematica), and contains a large number of exercises (with answers) to reinforce the material. These features combine to make this book an ideal starting point for students entering the sciences |
| nonlinear ordinary differential equations jordan: Asymptotic Expansions for Ordinary Differential Equations Wolfgang Wasow, 2018-03-21 This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. A book of great value. — Mathematical Reviews. 1976 revised edition. |
| nonlinear ordinary differential equations jordan: An Introduction to Dynamical Systems Rex Clark Robinson, 2012 This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course. The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimension. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where periodic orbits appear, and finally, chaotic systems of differential equations. The many different approaches are systematically introduced through examples and theorems. The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form. Chaotic systems are presented both mathematically and more computationally using Lyapunov exponents. With the one-dimensional maps as models, the multidimensional maps cover the same material in higher dimensions. This higher dimensional material is less computational and more conceptual and theoretical. The final chapter on fractals introduces various dimensions which is another computational tool for measuring the complexity of a system. It also treats iterated function systems which give examples of complicated sets. In the second edition of the book, much of the material has been rewritten to clarify the presentation. Also, some new material has been included in both parts of the book. This book can be used as a textbook for an advanced undergraduate course on ordinary differential equations and/or dynamical systems. Prerequisites are standard courses in calculus (single variable and multivariable), linear algebra, and introductory differential equations. |
| nonlinear ordinary differential equations jordan: Introduction to Differential Equations Michael Eugene Taylor, 2011 The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponential and trigonometric functions, which plays a central role in the subsequent development of this chapter. Chapter 2 provides a mini-course on linear algebra, giving detailed treatments of linear transformations, determinants and invertibility, eigenvalues and eigenvectors, and generalized eigenvectors. This treatment is more detailed than that in most differential equations texts, and provides a solid foundation for the next two chapters. Chapter 3 studies linear systems of differential equations. It starts with the matrix exponential, melding material from Chapters 1 and 2, and uses this exponential as a key tool in the linear theory. Chapter 4 deals with nonlinear systems of differential equations. This uses all the material developed in the first three chapters and moves it to a deeper level. The chapter includes theoretical studies, such as the fundamental existence and uniqueness theorem, but also has numerous examples, arising from Newtonian physics, mathematical biology, electrical circuits, and geometrical problems. These studies bring in variational methods, a fertile source of nonlinear systems of differential equations. The reader who works through this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations. |
| nonlinear ordinary differential equations jordan: Handbook of Exact Solutions for Ordinary Differential Equations Valentin F. Zaitsev, Andrei D. Polyanin, 2002-10-28 Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo |
| nonlinear ordinary differential equations jordan: Ordinary Differential Equations Bernd J. Schroers, 2011-09-29 Ordinary Differential Equations introduces key concepts and techniques in the field and shows how they are used in current mathematical research and modelling. It deals specifically with initial value problems, which play a fundamental role in a wide range of scientific disciplines, including mathematics, physics, computer science, statistics and biology. This practical book is ideal for students and beginning researchers working in any of these fields who need to understand the area of ordinary differential equations in a short time. |
| nonlinear ordinary differential equations jordan: Nonlinear Ordinary Differential Equations R. Grimshaw, 2017-10-19 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 jordan: Linear Ordinary Differential Equations Earl A. Coddington, Robert Carlson, 1997-01-01 A thorough development of the main topics in linear differential equations with applications, examples, and exercises illustrating each topic. |
| nonlinear ordinary differential equations jordan: Nonlinear Ordinary Differential Equations D. W. Jordan, 1979 |
| nonlinear ordinary differential equations jordan: Handbook of Exact Solutions to the Nonlinear Schrödinger Equations (Second Edition) USAMA. AL KHAWAJA, 2024-06-28 |
| nonlinear ordinary differential equations jordan: Ordinary Differential Equations Philip Hartman, 2002-01-01 Covers the fundamentals of the theory of ordinary differential equations. |
| nonlinear ordinary differential equations jordan: Introduction to Linear Algebra and Differential Equations John W. Dettman, 2012-10-05 Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index. |
| nonlinear ordinary differential equations jordan: Nonlinear Ordinary Differential Equations Martin Hermann, Masoud Saravi, 2016-05-09 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. |
| nonlinear ordinary differential equations jordan: Nonlinear Operators and Differential Equations in Banach Spaces Robert H. Martin, 1987 |
| nonlinear ordinary differential equations jordan: Introductory Differential Equations Martha L. Abell, James P. Braselton, 2009-09-09 This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, Fourier Series and Boundary Value Problems. The text is appropriate for two semester courses: the first typically emphasizes ordinary differential equations and their applications while the second emphasizes special techniques (like Laplace transforms) and partial differential equations. The texts follows a traditional curriculum and takes the traditional (rather than dynamical systems) approach. Introductory Differential Equations is a text that follows a traditional approach and is appropriate for a first course in ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. Note that some schools might prefer to move the Laplace transform material to the second course, which is why we have placed the chapter on Laplace transforms in its location in the text. Ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple would be recommended and/or required ancillaries depending on the school, course, or instructor. - Technology Icons - These icons highlight text that is intended to alert students that technology may be used intelligently to solve a problem, encouraging logical thinking and application - Think About It Icons and Examples - Examples that end in a question encourage students to think critically about what to do next, whether it is to use technology or focus on a graph to determine an outcome - Differential Equations at Work - These are projects requiring students to think critically by having students answer questions based on different conditions, thus engaging students |
| nonlinear ordinary differential equations jordan: Partial Differential Equations I Michael E. Taylor, 2010-10-29 The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. |
| nonlinear ordinary differential equations jordan: Introduction to Monte Carlo Methods for Transport and Diffusion Equations Bernard Lapeyre, Etienne Pardoux, Rémi Sentis, 2003 This text is used by for the resolution of partial differential equations, trasnport equations, the Boltzmann equation and the parabolic equations of diffusion. |
| nonlinear ordinary differential equations jordan: Functional Analysis, Sobolev Spaces and Partial Differential Equations Haim Brezis, 2010-11-10 This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list. |
| nonlinear ordinary differential equations jordan: Differential Equations for Engineers Wei-Chau Xie, 2010-04-26 Xie presents a systematic introduction to ordinary differential equations for engineering students and practitioners. Mathematical concepts and various techniques are presented in a clear, logical, and concise manner. Various visual features are used to highlight focus areas. Complete illustrative diagrams are used to facilitate mathematical modeling of application problems. Readers are motivated by a focus on the relevance of differential equations through their applications in various engineering disciplines. Studies of various types of differential equations are determined by engineering applications. Theory and techniques for solving differential equations are then applied to solve practical engineering problems. A step-by-step analysis is presented to model the engineering problems using differential equations from physical principles and to solve the differential equations using the easiest possible method. This book is suitable for undergraduate students in engineering. |
| nonlinear ordinary differential equations jordan: Differential Equations and Dynamical Systems Lawrence Perko, 2012-12-06 Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations. |
| nonlinear ordinary differential equations jordan: Lectures on Analytic Differential Equations I︠U︡. S. Ilʹi︠a︡shenko, S. Yakovenko, 2008 The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the mor The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. on several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area. |
| nonlinear ordinary differential equations jordan: A Second Course in Elementary Differential Equations Paul Waltman, 2014-05-10 A Second Course in Elementary Differential Equations deals with norms, metric spaces, completeness, inner products, and an asymptotic behavior in a natural setting for solving problems in differential equations. The book reviews linear algebra, constant coefficient case, repeated eigenvalues, and the employment of the Putzer algorithm for nondiagonalizable coefficient matrix. The text describes, in geometrical and in an intuitive approach, Liapunov stability, qualitative behavior, the phase plane concepts, polar coordinate techniques, limit cycles, the Poincaré-Bendixson theorem. The book explores, in an analytical procedure, the existence and uniqueness theorems, metric spaces, operators, contraction mapping theorem, and initial value problems. The contraction mapping theorem concerns operators that map a given metric space into itself, in which, where an element of the metric space M, an operator merely associates with it a unique element of M. The text also tackles inner products, orthogonality, bifurcation, as well as linear boundary value problems, (particularly the Sturm-Liouville problem). The book is intended for mathematics or physics students engaged in ordinary differential equations, and for biologists, engineers, economists, or chemists who need to master the prerequisites for a graduate course in mathematics. |
Home | Nonlinear Dynamics - Springer
Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The journal covers nonlinear dynamics …
Methods in Nonlinear Analysis - SpringerLink
Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials …
Nonlinear Acoustics - SpringerLink
Chapters 10 through 15 cover applications and additional methodologies encountered in nonlinear acoustics that include perturbation and numerical methods, ray theory for inhomogeneous …
Home | Journal of Nonlinear Science - Springer
The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. It features papers …
Nonlinear Systems: Analysis, Stability, and Control | SpringerLink
Coupled with this set of analytic advances has been the vast increase in computational power available for both the simulation and visualization of nonlinear systems as well as for the …
Articles | Nonlinear Dynamics - Springer
4 days ago · Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The ...
Nonlinear Dynamics: A Concise Introduction Interlaced with Code ...
This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at …
Data-driven nonlinear and stochastic dynamics with control
Dec 16, 2024 · The analysis is developed with reference to a nonlinear beam where the two boundary conditions have nonlinearities and masses, with the goal of identifying the uncertain …
Lectures on Nonlinear Dynamics - SpringerLink
This book presents a compilation of lectures delivered at the São Paulo School of Advanced Sciences on Nonlinear Dynamics, categorized into four groups: parametric resonance, …
Aims and scope | Nonlinear Dynamics - Springer
Nonlinear Dynamics provides a forum for the rapid publication of original research in the field of nonlinear dynamics. The scope of the journal encompasses all nonlinear dynamic phenomena …
Home | Nonlinear Dynamics - Springer
Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The journal covers nonlinear dynamics …
Methods in Nonlinear Analysis - SpringerLink
Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials …
Nonlinear Acoustics - SpringerLink
Chapters 10 through 15 cover applications and additional methodologies encountered in nonlinear acoustics that include perturbation and numerical methods, ray theory for inhomogeneous …
Home | Journal of Nonlinear Science - Springer
The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. It features papers …
Nonlinear Systems: Analysis, Stability, and Control | SpringerLink
Coupled with this set of analytic advances has been the vast increase in computational power available for both the simulation and visualization of nonlinear systems as well as for the …
Articles | Nonlinear Dynamics - Springer
4 days ago · Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The ...
Nonlinear Dynamics: A Concise Introduction Interlaced with Code ...
This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at …
Data-driven nonlinear and stochastic dynamics with control
Dec 16, 2024 · The analysis is developed with reference to a nonlinear beam where the two boundary conditions have nonlinearities and masses, with the goal of identifying the uncertain …
Lectures on Nonlinear Dynamics - SpringerLink
This book presents a compilation of lectures delivered at the São Paulo School of Advanced Sciences on Nonlinear Dynamics, categorized into four groups: parametric resonance, …
Aims and scope | Nonlinear Dynamics - Springer
Nonlinear Dynamics provides a forum for the rapid publication of original research in the field of nonlinear dynamics. The scope of the journal encompasses all nonlinear dynamic phenomena …
