Differential Equations And Dynamical Systems

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Differential Equations and Dynamical Systems

Lawrence Perko
Differential Equations and Dynamical Systems Book PDF

Author : Lawrence Perko
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468402490

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Differential Equations and Dynamical Systems by Lawrence Perko Pdf

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.

Ordinary Differential Equations and Dynamical Systems

Gerald Teschl
Ordinary Differential Equations and Dynamical Systems Book PDF

Author : Gerald Teschl
Publisher : American Mathematical Society
Page : 370 pages
File Size : 46,6 Mb
Release : 2024-01-12
Category : Mathematics
ISBN : 9781470476410

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Ordinary Differential Equations and Dynamical Systems by Gerald Teschl Pdf

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 Differential Equations and Dynamical Systems

Ferdinand Verhulst
Nonlinear Differential Equations and Dynamical Systems Book PDF

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642971495

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Nonlinear Differential Equations and Dynamical Systems by Ferdinand Verhulst Pdf

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.

Ordinary Differential Equations and Dynamical Systems

Thomas C. Sideris
Ordinary Differential Equations and Dynamical Systems Book PDF

Author : Thomas C. Sideris
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 42,8 Mb
Release : 2013-10-17
Category : Mathematics
ISBN : 9789462390218

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Ordinary Differential Equations and Dynamical Systems by Thomas C. Sideris Pdf

This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.

Introduction to Differential Equations with Dynamical Systems

Stephen L. Campbell,Richard Haberman
Introduction to Differential Equations with Dynamical Systems Book PDF

Author : Stephen L. Campbell,Richard Haberman
Publisher : Princeton University Press
Page : 445 pages
File Size : 48,5 Mb
Release : 2011-10-14
Category : Mathematics
ISBN : 9781400841325

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Introduction to Differential Equations with Dynamical Systems by Stephen L. Campbell,Richard Haberman Pdf

Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Differential Equations Dynamical Systems and an Introduction to Chaos Book PDF

Author : Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Publisher : Academic Press
Page : 433 pages
File Size : 45,6 Mb
Release : 2004
Category : Business & Economics
ISBN : 9780123497031

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Differential Equations, Dynamical Systems, and an Introduction to Chaos by Morris W. Hirsch,Stephen Smale,Robert L. Devaney Pdf

Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.

Differential Equations, Dynamical Systems, and Linear Algebra

Morris W. Hirsch,Robert L. Devaney,Stephen Smale
Differential Equations Dynamical Systems and Linear Algebra Book PDF

Author : Morris W. Hirsch,Robert L. Devaney,Stephen Smale
Publisher : Academic Press
Page : 358 pages
File Size : 51,7 Mb
Release : 1974-06-28
Category : Mathematics
ISBN : 9780080873763

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Differential Equations, Dynamical Systems, and Linear Algebra by Morris W. Hirsch,Robert L. Devaney,Stephen Smale Pdf

This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

Differential Dynamical Systems, Revised Edition

James D. Meiss
Differential Dynamical Systems Revised Edition Book PDF

Author : James D. Meiss
Publisher : SIAM
Page : 392 pages
File Size : 49,8 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9781611974645

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Differential Dynamical Systems, Revised Edition by James D. Meiss Pdf

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 concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. 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.

Non-Linear Differential Equations and Dynamical Systems

LUIS MANUEL. BRAGA DA COSTA CAMPOS
Non Linear Differential Equations and Dynamical Systems Book PDF

Author : LUIS MANUEL. BRAGA DA COSTA CAMPOS
Publisher : Unknown
Page : 0 pages
File Size : 43,6 Mb
Release : 2024-06-25
Category : Electronic
ISBN : 1032653728

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Non-Linear Differential Equations and Dynamical Systems by LUIS MANUEL. BRAGA DA COSTA CAMPOS Pdf

This the second book of Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-Volume Set, in the Mathematics and Physics for Science and Technology series. This book considers general first-order differential equations, including non-linear and with variable coefficients.

Differential Equations: From Calculus to Dynamical Systems: Second Edition

Virginia W. Noonburg
Differential Equations From Calculus to Dynamical Systems Second Edition Book PDF

Author : Virginia W. Noonburg
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 49,9 Mb
Release : 2020-08-28
Category : Education
ISBN : 9781470463298

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Differential Equations: From Calculus to Dynamical Systems: Second Edition by Virginia W. Noonburg Pdf

A thoroughly modern textbook for the sophomore-level differential equations course. The examples and exercises emphasize modeling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems. Bifurcations and analysis of parameter variation is a persistent theme. Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. The exposition is very clear and inviting. The book would serve well for use in a flipped-classroom pedagogical approach or for self-study for an advanced undergraduate or beginning graduate student. This second edition of Noonburg's best-selling textbook includes two new chapters on partial differential equations, making the book usable for a two-semester sequence in differential equations. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature.

Differential Equations and Dynamical Systems

D. Bahuguna
Differential Equations and Dynamical Systems Book PDF

Author : D. Bahuguna
Publisher : Alpha Science Int'l Ltd.
Page : 246 pages
File Size : 43,6 Mb
Release : 2005
Category : Mathematics
ISBN : 8173195889

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Differential Equations and Dynamical Systems by D. Bahuguna Pdf

Fifteen chapters from eminent researchers working in the area of differential equations and dynamical systems covering all relevant subjects, ranging from wavelets and their applications, to second order evolution equations.

Differential Equations and Dynamical Systems

Antonio Galves
Differential Equations and Dynamical Systems Book PDF

Author : Antonio Galves
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 46,5 Mb
Release : 2002
Category : Differentiable dynamical systems
ISBN : 9780821828601

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Differential Equations and Dynamical Systems by Antonio Galves Pdf

This volume contains contributed papers authored by participants of a Conference on Differential Equations and Dynamical Systems which was held at the Instituto Superior Tecnico (Lisbon, Portugal). The conference brought together a large number of specialists in the area of differential equations and dynamical systems and provided an opportunity to celebrate Professor Waldyr Oliva's 70th birthday, honoring his fundamental contributions to the field. The volume constitutes anoverview of the current research over a wide range of topics, extending from qualitative theory for (ordinary, partial or functional) differential equations to hyperbolic dynamics and ergodic theory.

Nonlinear Differential Equations and Dynamical Systems

Feliz Manuel Minhós,João Fialho
Nonlinear Differential Equations and Dynamical Systems Book PDF

Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 54,5 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101

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Nonlinear Differential Equations and Dynamical Systems by Feliz Manuel Minhós,João Fialho Pdf

This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Ordinary Differential Equations and Dynamical Systems

Gerald Teschl
Ordinary Differential Equations and Dynamical Systems Book PDF

Author : Gerald Teschl
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 44,5 Mb
Release : 2012-08-30
Category : Mathematics
ISBN : 9780821883280

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Ordinary Differential Equations and Dynamical Systems by Gerald Teschl Pdf

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 Poincare-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.

Partial Differential Equations and Dynamical Systems

William Edward Fitzgibbon
Partial Differential Equations and Dynamical Systems Book PDF

Author : William Edward Fitzgibbon
Publisher : Pitman Advanced Publishing Program
Page : 388 pages
File Size : 44,9 Mb
Release : 1984
Category : Mathematics
ISBN : UOM:39015049315677

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Partial Differential Equations and Dynamical Systems by William Edward Fitzgibbon Pdf

There has recently been a great amount of activity and a rapid growth in the areas of partial differential equations and dynamical systems. This interest has been encouraged by the development of powerful new techniques in nonlinear analysis and a renewed scientific interest in applied mathematical analysis. This book has been designed to make the reader aware of progress and current problems in this exciting and useful area. The book consists of articles by internationally known mathematical scientists, based on lectures given during a year-long program at the University of Houston.