The Theory Of Differential Equations PDF Download
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| Author | : Walter G. Kelley |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2010-04-15 |
| Genre | : Mathematics |
| ISBN | : 1441957839 |
Download The Theory of Differential Equations Book in PDF, ePub and Kindle
For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with ordinary differential equations. Unlike most textbooks on the subject, this text includes nonstandard topics such as perturbation methods and differential equations and Mathematica. In addition to the nonstandard topics, this text also contains contemporary material in the area as well as its classical topics. This second edition is updated to be compatible with Mathematica, version 7.0. It also provides 81 additional exercises, a new section in Chapter 1 on the generalized logistic equation, an additional theorem in Chapter 2 concerning fundamental matrices, and many more other enhancements to the first edition. This book can be used either for a second course in ordinary differential equations or as an introductory course for well-prepared students. The prerequisites for this book are three semesters of calculus and a course in linear algebra, although the needed concepts from linear algebra are introduced along with examples in the book. An undergraduate course in analysis is needed for the more theoretical subjects covered in the final two chapters.
| Author | : Barbara D. MacCluer |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 874 |
| Release | : 2019-10-02 |
| Genre | : Differential equations |
| ISBN | : 1470447975 |
Download Differential Equations: Techniques, Theory, and Applications Book in PDF, ePub and Kindle
Differential Equations: Techniques, Theory, and Applications is designed for a modern first course in differential equations either one or two semesters in length. The organization of the book interweaves the three components in the subtitle, with each building on and supporting the others. Techniques include not just computational methods for producing solutions to differential equations, but also qualitative methods for extracting conceptual information about differential equations and the systems modeled by them. Theory is developed as a means of organizing, understanding, and codifying general principles. Applications show the usefulness of the subject as a whole and heighten interest in both solution techniques and theory. Formal proofs are included in cases where they enhance core understanding; otherwise, they are replaced by informal justifications containing key ideas of a proof in a more conversational format. Applications are drawn from a wide variety of fields: those in physical science and engineering are prominent, of course, but models from biology, medicine, ecology, economics, and sports are also featured. The 1,400+ exercises are especially compelling. They range from routine calculations to large-scale projects. The more difficult problems, both theoretical and applied, are typically presented in manageable steps. The hundreds of meticulously detailed modeling problems were deliberately designed along pedagogical principles found especially effective in the MAA study Characteristics of Successful Calculus Programs, namely, that asking students to work problems that require them to grapple with concepts (or even proofs) and do modeling activities is key to successful student experiences and retention in STEM programs. The exposition itself is exceptionally readable, rigorous yet conversational. Students will find it inviting and approachable. The text supports many different styles of pedagogy from traditional lecture to a flipped classroom model. The availability of a computer algebra system is not assumed, but there are many opportunities to incorporate the use of one.
| Author | : Richard Bellman |
| Publisher | : Courier Corporation |
| Total Pages | : 178 |
| Release | : 2013-02-20 |
| Genre | : Mathematics |
| ISBN | : 0486150135 |
Download Stability Theory of Differential Equations Book in PDF, ePub and Kindle
Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies. The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.
| Author | : L.E. El'sgol'ts |
| Publisher | : Academic Press |
| Total Pages | : 356 |
| Release | : 1973-11-02 |
| Genre | : Computers |
| ISBN | : 0080956149 |
Download Introduction to the Theory and Application of Differential Equations with Deviating Arguments Book in PDF, ePub and Kindle
Introduction to the Theory and Application of Differential Equations with Deviating Arguments 2nd edition is a revised and substantially expanded edition of the well-known book of L. E. El’sgol’ts published under this same title by Nauka in 1964. Extensions of the theory of differential equations with deviating argument as well as the stimuli of developments within various fields of science and technology contribute to the need for a new edition. This theory in recent years has attracted the attention of vast numbers of researchers, interested both in the theory and its applications. The development of the foundations of the theory of differential equations with a deviating argument is still far from complete. This situation, of course, leaves its mark on our suggestions to the reader of the book and prevents as orderly and systematic a presentation as is usual for mathematical literature. However, it is hoped that in spite of these deficiencies the book will prove useful as a first acquaintanceship with the theory of differential equations with a deviating argument.
| Author | : Marius van der Put |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 446 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642557503 |
Download Galois Theory of Linear Differential Equations Book in PDF, ePub and Kindle
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
| Author | : Viktor Vladimirovich Nemytskii |
| Publisher | : Princeton University Press |
| Total Pages | : 532 |
| Release | : 2015-12-08 |
| Genre | : Mathematics |
| ISBN | : 1400875951 |
Download Qualitative Theory of Differential Equations Book in PDF, ePub and Kindle
Book 22 in the Princeton Mathematical Series. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
| Author | : Luis Barreira |
| Publisher | : American Mathematical Society |
| Total Pages | : 264 |
| Release | : 2023-05-17 |
| Genre | : Mathematics |
| ISBN | : 1470473860 |
Download Ordinary Differential Equations Book in PDF, ePub and Kindle
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.
| Author | : David A. Sanchez |
| Publisher | : Courier Dover Publications |
| Total Pages | : 179 |
| Release | : 2019-09-18 |
| Genre | : Mathematics |
| ISBN | : 0486837599 |
Download Ordinary Differential Equations and Stability Theory: Book in PDF, ePub and Kindle
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.
| Author | : Jack K. Hale |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 374 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 146129892X |
Download Theory of Functional Differential Equations Book in PDF, ePub and Kindle
Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more compre hensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research. The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory. There is also an appendix on the location of the zeros of characteristic polynomials. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit.
| Author | : Po-Fang Hsieh |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 480 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461215064 |
Download Basic Theory of Ordinary Differential Equations Book in PDF, ePub and Kindle
Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.
