Introduction To Differential Equations With Dynamical Systems

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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 : 54,5 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.

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 : 46,7 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.

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 : 45,5 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 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 : 49,9 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.

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 : 41,9 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.

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 : 225 pages
File Size : 51,8 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 and Dynamical Systems

Richard E. Williamson
Introduction to Differential Equations and Dynamical Systems Book PDF

Author : Richard E. Williamson
Publisher : McGraw-Hill Science, Engineering & Mathematics
Page : 712 pages
File Size : 41,5 Mb
Release : 1997
Category : Differentiable dynamical systems
ISBN : UOM:39076001878920

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Introduction to Differential Equations and Dynamical Systems by Richard E. Williamson Pdf

This textbook offers a foundation for a first course in differential equations, covering traditional areas in addition to topics such as dynamical systems. Numerical methods and problem-solving techniques are emphasized throughout the text. Discussion of computer use (Mathematica and Maple) is also included where appropriate, and where individual exercises are marked with an icon, they are best solved with the help of a computer or calculator.

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 : 42,7 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.

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 : 446 pages
File Size : 45,9 Mb
Release : 2008-04-21
Category : Mathematics
ISBN : 9780691124742

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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.

An Introduction to Dynamical Systems

Rex Clark Robinson
An Introduction to Dynamical Systems Book PDF

Author : Rex Clark Robinson
Publisher : American Mathematical Soc.
Page : 763 pages
File Size : 41,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891353

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An Introduction to Dynamical Systems by Rex Clark Robinson Pdf

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.

Chaos

Kathleen Alligood,Tim Sauer,J.A. Yorke
Chaos Book PDF

Author : Kathleen Alligood,Tim Sauer,J.A. Yorke
Publisher : Springer
Page : 620 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642592812

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Chaos by Kathleen Alligood,Tim Sauer,J.A. Yorke Pdf

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

Data-Driven Science and Engineering

Steven L. Brunton,J. Nathan Kutz
Data Driven Science and Engineering Book PDF

Author : Steven L. Brunton,J. Nathan Kutz
Publisher : Cambridge University Press
Page : 615 pages
File Size : 44,5 Mb
Release : 2022-05-05
Category : Computers
ISBN : 9781009098489

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Data-Driven Science and Engineering by Steven L. Brunton,J. Nathan Kutz Pdf

A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

An Introduction to Symbolic Dynamics and Coding

Douglas Lind,Brian Marcus
An Introduction to Symbolic Dynamics and Coding Book PDF

Author : Douglas Lind,Brian Marcus
Publisher : Cambridge University Press
Page : 571 pages
File Size : 47,6 Mb
Release : 2021-01-21
Category : Language Arts & Disciplines
ISBN : 9781108820288

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An Introduction to Symbolic Dynamics and Coding by Douglas Lind,Brian Marcus Pdf

Elementary introduction to symbolic dynamics, updated to describe the main advances in the subject since the original publication in 1995.

Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

Kenneth R. Meyer,Daniel C. Offin
Introduction to Hamiltonian Dynamical Systems and the N Body Problem Book PDF

Author : Kenneth R. Meyer,Daniel C. Offin
Publisher : Springer
Page : 384 pages
File Size : 54,6 Mb
Release : 2017-05-04
Category : Mathematics
ISBN : 9783319536910

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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Kenneth R. Meyer,Daniel C. Offin Pdf

This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)