*Eine Einführung*

Author: Wolfgang Walter

Publisher: Springer-Verlag

ISBN: 364296317X

Category: Mathematics

Page: 232

View: 7701

*Eine Einführung*

Author: Wolfgang Walter

Publisher: Springer-Verlag

ISBN: 364296317X

Category: Mathematics

Page: 232

View: 7701

*Eine Einführung*

Author: Wolfgang Walter

Publisher: Springer-Verlag

ISBN: 3642961045

Category: Mathematics

Page: 232

View: 9033

*eine Einführung*

Author: Wolfgang Walter

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 229

View: 6918

Author: Vladimir I. Arnold

Publisher: Springer Science & Business Media

ISBN: 9783540548133

Category: Mathematics

Page: 338

View: 5764

Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation." --SIAM REVIEW

Author: Edward L. Ince

Publisher: Courier Corporation

ISBN: 0486158217

Category: Mathematics

Page: 576

View: 1169

Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. "Highly recommended" — Electronics Industries.

Author: V. DHARMAIAH

Publisher: PHI Learning Pvt. Ltd.

ISBN: 8120346661

Category: Mathematics

Page: 420

View: 855

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.*Second Edition*

Author: Philip Hartman

Publisher: SIAM

ISBN: 9780898719222

Category: Differential equations

Page: 612

View: 9169

Ordinary Differential Equations covers the fundamentals of the theory of ordinary differential equations (ODEs), including an extensive discussion of the integration of differential inequalities, on which this theory relies heavily. In addition to these results, the text illustrates techniques involving simple topological arguments, fixed point theorems, and basic facts of functional analysis. Unlike many texts, which supply only the standard simplified theorems, this book presents the basic theory of ODEs in a general way. This SIAM reissue of the 1982 second edition covers invariant manifolds, perturbations, and dichotomies, making the text relevant to current studies of geometrical theory of differential equations and dynamical systems. In particular, Ordinary Differential Equations includes the proof of the Hartman-Grobman theorem on the equivalence of a nonlinear to a linear flow in the neighborhood of a hyperbolic stationary point, as well as theorems on smooth equivalences, the smoothness of invariant manifolds, and the reduction of problems on ODEs to those on "maps" (Poincaré). Audience: readers should have knowledge of matrix theory and the ability to deal with functions of real variables.

Author: Wolfgang Walter

Publisher: Springer Science & Business Media

ISBN: 1461206014

Category: Mathematics

Page: 384

View: 6494

Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.*A First Course*

Author: D. Somasundaram

Publisher: CRC Press

ISBN: 9780849309885

Category: Mathematics

Page: 295

View: 8162

Though ordinary differential equations is taught as a core course to students in mathematics and applied mathematics, detailed coverage of the topics with sufficient examples is unique. Written by a mathematics professor and intended as a textbook for third- and fourth-year undergraduates, the five chapters of this publication give a precise account of higher order differential equations, power series solutions, special functions, existence and uniqueness of solutions, and systems of linear equations. Relevant motivation for different concepts in each chapter and discussion of theory and problems-without the omission of steps-sets Ordinary Differential Equations: A First Course apart from other texts on ODEs. Full of distinguishing examples and containing exercises at the end of each chapter, this lucid course book will promote self-study among students.*Methods and Applications*

Author: W. T. Ang,Y. S. Park

Publisher: Universal-Publishers

ISBN: 1599429756

Category: Mathematics

Page: 204

View: 4887

This introductory course in ordinary differential equations, intended for junior undergraduate students in applied mathematics, science and engineering, focuses on methods of solution and applications rather than theoretical analyses. Applications drawn mainly from dynamics, population biology and electric circuit theory are used to show how ordinary differential equations appear in the formulation of problems in science and engineering. The calculus required to comprehend this course is rather elementary, involving differentiation, integration and power series representation of only real functions of one variable. A basic knowledge of complex numbers and their arithmetic is also assumed, so that elementary complex functions which can be used for working out easily the general solutions of certain ordinary differential equations can be introduced. The pre-requisites just mentioned aside, the course is mainly self-contained. To promote the use of this course for self-study, suggested solutions are not only given to all set exercises, but they are also by and large complete with details.

Author: Wolfgang Wasow

Publisher: Courier Corporation

ISBN: 9780486495187

Category: Mathematics

Page: 374

View: 6675

"A book of great value . . . it should have a profound influence upon future research."--Mathematical Reviews. Hardcover edition. The foundations of the study of asymptotic series in the theory of differential equations were laid by Poincaré in the late 19th century, but it was not until the middle of this century that it became apparent how essential asymptotic series are to understanding the solutions of ordinary differential equations. Moreover, they have come to be seen as crucial to such areas of applied mathematics as quantum mechanics, viscous flows, elasticity, electromagnetic theory, electronics, and astrophysics. In this outstanding text, the first book devoted exclusively to the subject, the author concentrates on the mathematical ideas underlying the various asymptotic methods; however, asymptotic methods for differential equations are included only if they lead to full, infinite expansions. Unabridged Dover republication of the edition published by Robert E. Krieger Publishing Company, Huntington, N.Y., 1976, a corrected, slightly enlarged reprint of the original edition published by Interscience Publishers, New York, 1965. 12 illustrations. Preface. 2 bibliographies. Appendix. Index.

Author: Earl A. Coddington

Publisher: Courier Corporation

ISBN: 0486131831

Category: Mathematics

Page: 320

View: 6533

A thorough, systematic first course in elementary differential equations for undergraduates in mathematics and science, requiring only basic calculus for a background. Includes many exercises and problems, with answers. Index.

Author: Bindhyachal Rai,D. P. Choudhury,Herbert I. Freedman

Publisher: CRC Press

ISBN: 9780849309922

Category: Mathematics

Page: 463

View: 8629

Designed as a text for both under and postgraduate students of mathematics and engineering, A Course in Ordinary Differential Equations deals with theory and methods of solutions as well as applications of ordinary differential equations. The treatment is lucid and gives a detailed account of Laplace transforms and their applications, Legendre and Bessel functions, and covers all the important numerical methods for differential equations.

Author: Einar Hille

Publisher: Courier Corporation

ISBN: 9780486696201

Category: Mathematics

Page: 484

View: 5743

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.

Author: Kurt Otto Friedrichs

Publisher: CRC Press

ISBN: 9780677009650

Category: Mathematics

Page: 205

View: 2889

Author: Carmen Chicone

Publisher: Springer Science & Business Media

ISBN: 0387307699

Category: Mathematics

Page: 636

View: 1519

Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions.

Author: A. Canada,P. Drabek,A. Fonda

Publisher: Elsevier

ISBN: 9780080463810

Category: Mathematics

Page: 752

View: 4511

This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields

Author: C. R. MONDAL

Publisher: PHI Learning Pvt. Ltd.

ISBN: 9788120334670

Category: Mathematics

Page: 192

View: 506

Written in a clear, precise and readable manner, this textbook (now revised and corrected) is designed to provide postgraduate mathematics students with a sound and inspiring introduction to the main themes of ordinary differential equations. It is presented from the viewpoint of applied mathematics to treat differential equations both from the theoretical background and practical applications to scientific and engineering problems. Beginning with a comprehensive treatment of linear differential equations with variable coefficients, the text gives a detailed discussion on some well-known special functions which provide solutions of secondorder linear ordinary differential equations having several regular singular points. Many of the standard concepts and methods which are useful in the study of special functions are discussed. The properties of special functions are derived from their differential equations and boundary conditions. Finally, existence and uniqueness of solutions of differential equations are established. Worked-out examples are introduced throughout the text. End-of-chapter exercises further help understand the mathematical and physical structure of the subject.

Author: Ratan Prakash Agarwal,Ravi P. Agarwal,V. Lakshmikantham

Publisher: World Scientific

ISBN: 9789810213572

Category: Mathematics

Page: 312

View: 951

This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.

Author: Bhamra

Publisher: Allied Publishers

ISBN: 9788177644890

Category:

Page: N.A

View: 311