Ordinary Differential Equations

1985-10-01
Ordinary Differential Equations

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  • Author: Morris Tenenbaum
  • Publisher: Courier Corporation
  • ISBN: 0486649407
  • Category : Mathematics
  • Languages : en
  • Pages : 852

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

2012-07-01
Ordinary Differential Equations

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  • Author: William A. Adkins
  • Publisher: Springer Science & Business Media
  • ISBN: 1461436184
  • Category : Mathematics
  • Languages : en
  • Pages : 799

Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are immediate and simplified, and solution methods for constant coefficient systems are streamlined. By introducing the Laplace transform early in the text, students become proficient in its use while at the same time learning the standard topics in differential equations. The text also includes proofs of several important theorems that are not usually given in introductory texts. These include a proof of the injectivity of the Laplace transform and a proof of the existence and uniqueness theorem for linear constant coefficient differential equations. Along with its unique traits, this text contains all the topics needed for a standard three- or four-hour, sophomore-level differential equations course for students majoring in science or engineering. These topics include: first order differential equations, general linear differential equations with constant coefficients, second order linear differential equations with variable coefficients, power series methods, and linear systems of differential equations. It is assumed that the reader has had the equivalent of a one-year course in college calculus.

Ordinary Differential Equations: Basics and Beyond

2016-11-10
Ordinary Differential Equations: Basics and Beyond

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  • Author: David G. Schaeffer
  • Publisher: Springer
  • ISBN: 1493963899
  • Category : Mathematics
  • Languages : en
  • Pages : 542

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).

Linear Ordinary Differential Equations

1997-01-01
Linear Ordinary Differential Equations

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  • Author: Earl A. Coddington
  • Publisher: SIAM
  • ISBN: 9781611971439
  • Category : Mathematics
  • Languages : en
  • Pages : 353

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

2019-12-06
Ordinary Differential Equations

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  • Author: Kenneth B. Howell
  • Publisher: CRC Press
  • ISBN: 1000702413
  • Category : Mathematics
  • Languages : en
  • Pages : 928

The Second Edition of Ordinary Differential Equations: An Introduction to the Fundamentals builds on the successful First Edition. It is unique in its approach to motivation, precision, explanation and method. Its layered approach offers the instructor opportunity for greater flexibility in coverage and depth. Students will appreciate the author’s approach and engaging style. Reasoning behind concepts and computations motivates readers. New topics are introduced in an easily accessible manner before being further developed later. The author emphasizes a basic understanding of the principles as well as modeling, computation procedures and the use of technology. The students will further appreciate the guides for carrying out the lengthier computational procedures with illustrative examples integrated into the discussion. Features of the Second Edition: Emphasizes motivation, a basic understanding of the mathematics, modeling and use of technology A layered approach that allows for a flexible presentation based on instructor's preferences and students’ abilities An instructor’s guide suggesting how the text can be applied to different courses New chapters on more advanced numerical methods and systems (including the Runge-Kutta method and the numerical solution of second- and higher-order equations) Many additional exercises, including two "chapters" of review exercises for first- and higher-order differential equations An extensive on-line solution manual About the author: Kenneth B. Howell earned bachelor’s degrees in both mathematics and physics from Rose-Hulman Institute of Technology, and master’s and doctoral degrees in mathematics from Indiana University. For more than thirty years, he was a professor in the Department of Mathematical Sciences of the University of Alabama in Huntsville. Dr. Howell published numerous research articles in applied and theoretical mathematics in prestigious journals, served as a consulting research scientist for various companies and federal agencies in the space and defense industries, and received awards from the College and University for outstanding teaching. He is also the author of Principles of Fourier Analysis, Second Edition (Chapman & Hall/CRC, 2016).

Ordinary Differential Equations

2009-01-01
Ordinary Differential Equations

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  • Author: Jack K. Hale
  • Publisher: Courier Corporation
  • ISBN: 0486472116
  • Category : Mathematics
  • Languages : en
  • Pages : 386

This rigorous treatment prepares readers for the study of differential equations and shows them how to research current literature. It emphasizes nonlinear problems and specific analytical methods. 1969 edition.

Ordinary Differential Equations in the Complex Domain

1997-01-01
Ordinary Differential Equations in the Complex Domain

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  • Author: Einar Hille
  • Publisher: Courier Corporation
  • ISBN: 9780486696201
  • Category : Mathematics
  • Languages : en
  • Pages : 514

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.

Ordinary Differential Equations and Their Solutions

2011-01-01
Ordinary Differential Equations and Their Solutions

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  • Author: George Moseley Murphy
  • Publisher: Courier Corporation
  • ISBN: 0486485919
  • Category : Mathematics
  • Languages : en
  • Pages : 466

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.

Handbook of Ordinary Differential Equations

2017-11-15
Handbook of Ordinary Differential Equations

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  • Author: Andrei D. Polyanin
  • Publisher: CRC Press
  • ISBN: 1466569409
  • Category : Mathematics
  • Languages : en
  • Pages : 1496

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

2023-05-17
Ordinary Differential Equations

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  • Author: Luis Barreira
  • Publisher: American Mathematical Society
  • ISBN: 1470473860
  • Category : Mathematics
  • Languages : en
  • Pages : 264

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.