Introduction To Theory Of Ordinary Differential Equation

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Ordinary Differential Equations and Stability Theory:

Author : David A. Sanchez
Publisher : Courier Dover Publications
ISBN 13 : 0486837599
Total Pages : 179 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Ordinary Differential Equations and Stability Theory: by : David A. Sanchez

Download or read book Ordinary Differential Equations and Stability Theory: written by David A. Sanchez and published by Courier Dover Publications. This book was released on 2019-09-18 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.

The Qualitative Theory of Ordinary Differential Equations

Author : Fred Brauer
Publisher : Courier Corporation
ISBN 13 : 0486151514
Total Pages : 325 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis The Qualitative Theory of Ordinary Differential Equations by : Fred Brauer

Download or read book The Qualitative Theory of Ordinary Differential Equations written by Fred Brauer and published by Courier Corporation. This book was released on 2012-12-11 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ordinary Differential Equations

Author : Luis Barreira
Publisher : American Mathematical Society
ISBN 13 : 1470473860
Total Pages : 264 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ordinary Differential Equations by : Luis Barreira

Download or read book Ordinary Differential Equations written by Luis Barreira and published by American Mathematical Society. This book was released on 2023-05-17 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly. The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.

Introduction to the Theory of Linear Partial Differential Equations

Author : J. Chazarain
Publisher : Elsevier
ISBN 13 : 0080875351
Total Pages : 575 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Introduction to the Theory of Linear Partial Differential Equations by : J. Chazarain

Download or read book Introduction to the Theory of Linear Partial Differential Equations written by J. Chazarain and published by Elsevier. This book was released on 2011-08-18 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Theory of Linear Partial Differential Equations

An Introduction to Ordinary Differential Equations

Author : Ravi P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 0387712763
Total Pages : 333 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis An Introduction to Ordinary Differential Equations by : Ravi P. Agarwal

Download or read book An Introduction to Ordinary Differential Equations written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.

Ordinary Differential Equations

Author : Morris Tenenbaum
Publisher : Courier Corporation
ISBN 13 : 0486649407
Total Pages : 852 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Ordinary Differential Equations by : Morris Tenenbaum

Download or read book Ordinary Differential Equations written by Morris Tenenbaum and published by Courier Corporation. This book was released on 1985-10-01 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

Introduction to Ordinary Differential Equations

Author : Albert L. Rabenstein
Publisher : Academic Press
ISBN 13 : 1483226220
Total Pages : 444 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Introduction to Ordinary Differential Equations by : Albert L. Rabenstein

Download or read book Introduction to Ordinary Differential Equations written by Albert L. Rabenstein and published by Academic Press. This book was released on 2014-05-12 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutions, and that should be of interest to the mathematics major, such as the theorems about the existence and uniqueness of solutions. The final chapters discuss the stability of critical points of plane autonomous systems and the results about the existence of periodic solutions of nonlinear equations. This book is great use to mathematicians, physicists, and undergraduate students of engineering and the science who are interested in applications of differential equation.

Ordinary Differential Equations: Basics and Beyond

Author : David G. Schaeffer
Publisher : Springer
ISBN 13 : 1493963899
Total Pages : 565 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Ordinary Differential Equations: Basics and Beyond by : David G. Schaeffer

Download or read book Ordinary Differential Equations: Basics and Beyond written by David G. Schaeffer and published by Springer. This book was released on 2016-11-10 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text (www.math.duke.edu/ode-book). Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).

An Introduction to Ordinary Differential Equations

Author : Earl A. Coddington
Publisher :
ISBN 13 :
Total Pages : 292 pages
Book Rating : 4.:/5 (28 download)

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Book Synopsis An Introduction to Ordinary Differential Equations by : Earl A. Coddington

Download or read book An Introduction to Ordinary Differential Equations written by Earl A. Coddington and published by . This book was released on 1968 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Linear Ordinary Differential Equations

Author : Earl A. Coddington
Publisher : SIAM
ISBN 13 : 9781611971439
Total Pages : 353 pages
Book Rating : 4.9/5 (714 download)

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Book Synopsis Linear Ordinary Differential Equations by : Earl A. Coddington

Download or read book Linear Ordinary Differential Equations written by Earl A. Coddington and published by SIAM. This book was released on 1997-01-01 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions.

Ordinary Differential Equations in the Complex Domain

Author : Einar Hille
Publisher : Courier Corporation
ISBN 13 : 9780486696201
Total Pages : 514 pages
Book Rating : 4.6/5 (962 download)

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Book Synopsis Ordinary Differential Equations in the Complex Domain by : Einar Hille

Download or read book Ordinary Differential Equations in the Complex Domain written by Einar Hille and published by Courier Corporation. This book was released on 1997-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.

A Textbook on Ordinary Differential Equations

Author : Shair Ahmad
Publisher : Springer
ISBN 13 : 3319164082
Total Pages : 337 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis A Textbook on Ordinary Differential Equations by : Shair Ahmad

Download or read book A Textbook on Ordinary Differential Equations written by Shair Ahmad and published by Springer. This book was released on 2015-06-05 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.

Ordinary Differential Equations and Dynamical Systems

Author : Gerald Teschl
Publisher : American Mathematical Society
ISBN 13 : 147047641X
Total Pages : 370 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ordinary Differential Equations and Dynamical Systems by : Gerald Teschl

Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl and published by American Mathematical Society. This book was released on 2024-01-12 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION

Author : V. DHARMAIAH
Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 8120346661
Total Pages : 403 pages
Book Rating : 4.1/5 (23 download)

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Book Synopsis INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION by : V. DHARMAIAH

Download or read book INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATION written by V. DHARMAIAH and published by PHI Learning Pvt. Ltd.. This book was released on 2012-09-19 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematically-organized text on the theory of differential equations deals with the basic concepts and the methods of solving ordinary differential equations. Various existence theorems, properties of uniqueness, oscillation and stability theories, have all been explained with suitable examples to enhance students’ understanding of the subject. The book also discusses in sufficient detail the qualitative, the quantitative, and the approximation techniques, linear equations with variable and constants coefficients, regular singular points, and homogeneous equations with analytic coefficients. Finally, it explains Riccati equation, boundary value problems, the Sturm–Liouville problem, Green’s function, the Picard’s theorem, and the Sturm–Picone theorem. The text is supported by a number of worked-out examples to make the concepts clear, and it also provides a number of exercises help students test their knowledge and improve their skills in solving differential equations. The book is intended to serve as a text for the postgraduate students of mathematics and applied mathematics. It will also be useful to the candidates preparing to sit for the competitive examinations such as NET and GATE.

An Introduction to Ordinary Differential Equations

Author : James C. Robinson
Publisher : Cambridge University Press
ISBN 13 : 9780521533911
Total Pages : 416 pages
Book Rating : 4.5/5 (339 download)

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Book Synopsis An Introduction to Ordinary Differential Equations by : James C. Robinson

Download or read book An Introduction to Ordinary Differential Equations written by James C. Robinson and published by Cambridge University Press. This book was released on 2004-01-08 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A first course in ordinary differential equations for mathematicians, scientists and engineers. Solutions are provided.

Geometrical Methods in the Theory of Ordinary Differential Equations

Author : V.I. Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 1461210372
Total Pages : 366 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Geometrical Methods in the Theory of Ordinary Differential Equations by : V.I. Arnold

Download or read book Geometrical Methods in the Theory of Ordinary Differential Equations written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.

A Second Course in Elementary Differential Equations

Author : Paul Waltman
Publisher : Elsevier
ISBN 13 : 1483276600
Total Pages : 272 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis A Second Course in Elementary Differential Equations by : Paul Waltman

Download or read book A Second Course in Elementary Differential Equations written by Paul Waltman and published by Elsevier. This book was released on 2014-05-10 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.