# Ordinary Differential Equations

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## Ordinary Differential Equations

Author | : Walter Wolfgang,Wolfgang Walter,Wolfgang Ludwig Walter |

Publsiher | : Springer Science & Business Media |

Total Pages | : 408 |

Release | : 1998-07 |

ISBN | : 9780387984599 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

This unique treatment of ODEs emphasizes subjects outside of the mainstream and presents material in a carefully organized fashion with clear explanations and consistent motivation. It includes material seldom found in other books, including new proofs for basic theorems. Exercises as well as applications in varying fields are dispersed throughout.

## Ordinary Differential Equations

Author | : Edward L. Ince |

Publsiher | : Courier Corporation |

Total Pages | : 580 |

Release | : 1956-01-01 |

ISBN | : 0486603490 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

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; further developments in the theory of boundary problems; existence theorems, equations of first order; nonlinear equations of higher order; more. "Highly recommended" — Electronics Industries.

## Solving Ordinary Differential Equations I

Author | : Ernst Hairer,Syvert P. Nørsett,Gerhard Wanner |

Publsiher | : Springer Science & Business Media |

Total Pages | : 540 |

Release | : 2008-04-16 |

ISBN | : 3540566708 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Solving Ordinary Differential Equations I Book Excerpt:**

This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been rewritten and new material has been included.

## Elements Of Ordinary Differential Equations And Special Functions

Author | : A. Chakrabarti |

Publsiher | : New Age International |

Total Pages | : 172 |

Release | : 2006 |

ISBN | : 9788122408805 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Elements Of Ordinary Differential Equations And Special Functions Book Excerpt:**

Ordinary Differential Equations And Special Functions Form A Central Part In Many Branches Of Physics And Engineering. A Large Number Of Books Already Exist In These Areas And Informations Are Therefore Available In A Scattered Form. The Present Book Tries To Bring Out Some Of The Most Important Concepts Associated With Linear Ordinary Differential Equations And The Special Functions Of Frequent Occurrence, In A Rather Elementary Form.The Methods Of Obtaining Series Solution Of Second Order Linear Ordinary Differential Equations Near An Ordinary Point As Well As Near A Regular Singular Point Have Been Explained In An Elegant Manner And, As Applications Of These Methods, The Special Functions Of Hermite And Bessel Have Been Dealt With.The Special Functions Of Legendre And Laguerre Have Also Been Discussed Briefly. An Appendix Is Prepared To Deal With Other Special Functions Such As The Beta Function, The Gamma Function, The Hypergeometric Functions And The Chebyshev Polynomials In A Short Form.The Topics Involving The Existence Theory And The Eigenvalue Problems Have Also Been Discussed In The Book To Create Motivation For Further Studies In The Subject.Each Chapter Is Supplemented With A Number Of Worked Out Examples As Well As A Number Of Problems To Be Handled For Better Understanding Of The Subject. R Contains A List Of Sixteen Important Books Forming The Bibliography.In This Second Edition The Text Has Been Thoroughly Revised.

## Ordinary Differential Equations

Author | : George F. Carrier,Carl E. Pearson |

Publsiher | : SIAM |

Total Pages | : 230 |

Release | : 1968-01-01 |

ISBN | : 0898712653 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

Teaches techniques for constructing solutions of differential equations in a novel way, often giving readers opportunity for ingenuity.

## An Introduction to Ordinary Differential Equations

Author | : Earl A. Coddington |

Publsiher | : Courier Corporation |

Total Pages | : 308 |

Release | : 1989-01-01 |

ISBN | : 9780486659428 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**An Introduction to Ordinary Differential Equations Book Excerpt:**

A thorough and systematic first course in elementary differential equations for undergraduates in mathematics and science, with many exercises and problems (with answers).

## Ordinary Differential Equations and Their Solutions

Author | : George Moseley Murphy |

Publsiher | : Courier Corporation |

Total Pages | : 466 |

Release | : 2011-01-01 |

ISBN | : 0486485919 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations and Their Solutions Book Excerpt:**

This treatment presents most of the methods for solving ordinary differential equations and systematic arrangements of more than 2,000 equations and their solutions. The material is organized so that standard equations can be easily found. Plus, the substantial number and variety of equations promises an exact equation or a sufficiently similar one. 1960 edition.

## Ordinary Differential Equations

Author | : Vladimir I. Arnold |

Publsiher | : Springer Science & Business Media |

Total Pages | : 346 |

Release | : 1992-05-08 |

ISBN | : 9783540548133 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

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

## Ordinary and Partial Differential Equations

Author | : Victor Henner,Tatyana Belozerova,Mikhail Khenner |

Publsiher | : CRC Press |

Total Pages | : 647 |

Release | : 2013-01-29 |

ISBN | : 1466515007 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary and Partial Differential Equations Book Excerpt:**

Covers ODEs and PDEs—in One Textbook Until now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn’t exist. Fulfilling this need, Ordinary and Partial Differential Equations provides a complete and accessible course on ODEs and PDEs using many examples and exercises as well as intuitive, easy-to-use software. Teaches the Key Topics in Differential Equations The text includes all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations. It also discusses other optional but important topics such as integral equations, Fourier series, and special functions. Numerous carefully chosen examples offer practical guidance on the concepts and techniques. Guides Students through the Problem-Solving Process Requiring no user programming, the accompanying computer software allows students to fully investigate problems, thus enabling a deeper study into the role of boundary and initial conditions, the dependence of the solution on the parameters, the accuracy of the solution, the speed of a series convergence, and related questions. The ODE module compares students’ analytical solutions to the results of computations while the PDE module demonstrates the sequence of all necessary analytical solution steps.

## Handbook of Ordinary Differential Equations

Author | : Andrei D. Polyanin,Valentin F. Zaitsev |

Publsiher | : CRC Press |

Total Pages | : 1767 |

Release | : 2017-11-15 |

ISBN | : 1351643916 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Handbook of Ordinary Differential Equations Book Excerpt:**

The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.

## Ordinary Differential Equations

Author | : Otto Plaat |

Publsiher | : Unknown |

Total Pages | : 295 |

Release | : 1971 |

ISBN | : 1928374650XXX |

Category | : Analysis |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

## Ordinary Differential Equations

Author | : Hartmut Logemann,Eugene P Ryan |

Publsiher | : Springer |

Total Pages | : 333 |

Release | : 2014-03-19 |

ISBN | : 9781447163978 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature. The following topics are particularly emphasised: • existence, uniqueness and continuation of solutions, • continuous dependence on initial data, • flows, • qualitative behaviour of solutions, • limit sets, • stability theory, • invariance principles, • introductory control theory, • feedback and stabilization. The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability. Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.

## Ordinary Differential Equations with Applications

Author | : Carmen Chicone |

Publsiher | : Springer Science & Business Media |

Total Pages | : 652 |

Release | : 2006-05-18 |

ISBN | : 0387307699 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations with Applications Book Excerpt:**

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.

## Ordinary Differential Equations

Author | : Raza Tahir-Kheli |

Publsiher | : Springer |

Total Pages | : 408 |

Release | : 2019-02-05 |

ISBN | : 3319764063 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

This textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE). The book provides a detailed theoretical and numerical description of ODE. It presents a large variety of ODE and the chosen groups are used to solve a host of physical problems. Solving these problems is of interest primarily to students of science, such as physics, engineering, biology and chemistry. Scientists are greatly assisted by using the DO obeying several simple algebraic rules. The book describes these rules and, to help the reader, the vocabulary and the definitions used throughout the text are provided. A thorough description of the relatively straightforward methodology for solving ODE is given. The book provides solutions to a large number of associated problems. ODE that are integrable, or those that have one of the two variables missing in any explicit form are also treated with solved problems. The physics and applicable mathematics are explained and many associated problems are analyzed and solved in detail. Numerical solutions are analyzed and the level of exactness obtained under various approximations is discussed in detail.

## An Introduction to Ordinary Differential Equations

Author | : James C. Robinson |

Publsiher | : Cambridge University Press |

Total Pages | : 416 |

Release | : 2004-01-08 |

ISBN | : 9780521533911 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**An Introduction to Ordinary Differential Equations Book Excerpt:**

A first course in ordinary differential equations for mathematicians, scientists and engineers. Solutions are provided.

## Ordinary Differential Equations

Author | : Refaat El Attar |

Publsiher | : Lulu.com |

Total Pages | : 186 |

Release | : 2006-07-21 |

ISBN | : 1411639200 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

An extended introduction to ordinary differential equations. This book can be used as self study material. It contains a little bit of theory and lot of solved examples as well as tons of exercises to test your ability to solve problems using the techniques presented in the text.

## Ordinary Differential Equations

Author | : William Cox |

Publsiher | : Elsevier |

Total Pages | : 232 |

Release | : 1995-12-22 |

ISBN | : 0080928676 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required. The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further study of partial differential equations.

## Ordinary Differential Equations

Author | : Morris Tenenbaum,Harry Pollard |

Publsiher | : Courier Corporation |

Total Pages | : 852 |

Release | : 1985-10-01 |

ISBN | : 0486649407 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations 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.

## Ordinary Differential Equations

Author | : Radu Precup |

Publsiher | : Walter de Gruyter GmbH & Co KG |

Total Pages | : 234 |

Release | : 2018-01-22 |

ISBN | : 3110447509 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

This introductory text combines models from physics and biology with rigorous reasoning in describing the theory of ordinary differential equations along with applications and computer simulations with Maple. Offering a concise course in the theory of ordinary differential equations, it also enables the reader to enter the field of computer simulations. Thus, it is a valuable read for students in mathematics as well as in physics and engineering. It is also addressed to all those interested in mathematical modeling with ordinary differential equations and systems. Contents Part I: Theory Chapter 1 First-Order Differential Equations Chapter 2 Linear Differential Systems Chapter 3 Second-Order Differential Equations Chapter 4 Nonlinear Differential Equations Chapter 5 Stability of Solutions Chapter 6 Differential Systems with Control Parameters Part II: Exercises Seminar 1 Classes of First-Order Differential Equations Seminar 2 Mathematical Modeling with Differential Equations Seminar 3 Linear Differential Systems Seminar 4 Second-Order Differential Equations Seminar 5 Gronwall’s Inequality Seminar 6 Method of Successive Approximations Seminar 7 Stability of Solutions Part III: Maple Code Lab 1 Introduction to Maple Lab 2 Differential Equations with Maple Lab 3 Linear Differential Systems Lab 4 Second-Order Differential Equations Lab 5 Nonlinear Differential Systems Lab 6 Numerical Computation of Solutions Lab 7 Writing Custom Maple Programs Lab 8 Differential Systems with Control Parameters

## Ordinary Differential Equations

Author | : Luis Barreira,Claudia Valls |

Publsiher | : American Mathematical Soc. |

Total Pages | : 248 |

Release | : 2012-06-06 |

ISBN | : 0821887491 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations 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.