The Theory Of Differential Equations
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Theory And Examples Of Ordinary Differential Equations
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Author : Chin-yuan Lin
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-01-03
Theory And Examples Of Ordinary Differential Equations written by Chin-yuan Lin and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-03 with Mathematics categories.
This book presents a complete theory of ordinary differential equations, with many illustrative examples and interesting exercises. A rigorous treatment is offered with clear proofs for the theoretical results and with detailed solutions for the examples and problems.This book is intended for undergraduate students who major in mathematics and have acquired a prerequisite knowledge of calculus and partly the knowledge of a complex variable, and are now reading advanced calculus and linear algebra. Additionally, the comprehensive coverage of the theory with a wide array of examples and detailed solutions, would appeal to mathematics graduate students and researchers as well as graduate students in majors of other disciplines.As a handy reference, advanced knowledge is provided as well with details developed beyond the basics; optional sections, where main results are extended, offer an understanding of further applications of ordinary differential equations.
The Theory Of Differential Equations
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Author : Walter G. Kelley
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-15
The Theory Of Differential Equations written by Walter G. Kelley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-15 with Mathematics categories.
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.
Differential Equations Theory And Applications
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Author : David Betounes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Differential Equations Theory And Applications written by David Betounes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book was written as a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as time-honored and important applications of this theory. His torically, these were the applications that spurred the development of the mathematical theory and in hindsight they are still the best applications for illustrating the concepts, ideas, and impact of the theory. While the book is intended for traditional graduate students in mathe matics, the material is organized so that the book can also be used in a wider setting within today's modern university and society (see "Ways to Use the Book" below). In particular, it is hoped that interdisciplinary programs with courses that combine students in mathematics, physics, engineering, and other sciences can benefit from using this text. Working professionals in any of these fields should be able to profit too by study of this text. An important, but optional component of the book (based on the in structor's or reader's preferences) is its computer material. The book is one of the few graduate differential equations texts that use the computer to enhance the concepts and theory normally taught to first- and second-year graduate students in mathematics. I have made every attempt to blend to gether the traditional theoretical material on differential equations and the new, exciting techniques afforded by computer algebra systems (CAS), like Maple, Mathematica, or Matlab.
The Theory Of Differential Equations
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Author : Abby Enger
language : en
Publisher:
Release Date : 2016-10-01
The Theory Of Differential Equations written by Abby Enger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-01 with categories.
Differential equations have a remarkable ability to predict the world around us. They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. They can describe exponential growth and decay, the population growth of species or the change in investment return over time. A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. Differential equations can be divided into several types. Apart from describing the properties of the equation itself, these classes of differential equations can help inform the choice of approach to a solution. Commonly used distinctions include whether the equation is: Ordinary/Partial, Linear/Non-linear, and Homogeneous/Inhomogeneous. The theory of differential equations is closely related to the theory of difference equations, in which the coordinates assume only discrete values, and the relationship involves values of the unknown function or functions and values at nearby coordinates. Many methods to compute numerical solutions of differential equations or study the properties of differential equations involve approximation of the solution of a differential equation by the solution of a corresponding difference equation.
Theory Of Ordinary Differential Equations
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Author : Earl A. Coddington
language : en
Publisher: Tata McGraw-Hill Education
Release Date : 1955
Theory Of Ordinary Differential Equations written by Earl A. Coddington and has been published by Tata McGraw-Hill Education this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955 with Boundary value problems categories.
This book has developed from courses given by the authors and probably contains more material than will ordinarily be covered in a one-year course. It is hoped that the book will be a useful text in the application of differential equations as well as for the pure mathematician. Prerequisite for this book is a knowledge of matrices and the essentials of functions in a complex variable. The book thoroughly addresses linear equations, and touches on the use of the Riemann-Stieltjes integral, and the Lebesgue integral, and the theorems required from integration theory. The problems, in some cases, give additional material not considered in the text.
Introduction To The Theory And Application Of Differential Equations With Deviating Arguments
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Author : L.E. El'sgol'ts
language : en
Publisher: Academic Press
Release Date : 1973-11-02
Introduction To The Theory And Application Of Differential Equations With Deviating Arguments written by L.E. El'sgol'ts and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-11-02 with Computers categories.
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.
Introduction To The Theory Of Linear Differential Equations
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Author : E. G. C. Poole
language : en
Publisher:
Release Date : 1956
Introduction To The Theory Of Linear Differential Equations written by E. G. C. Poole and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with categories.
Ordinary Differential Equations
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Author : Morris Tenenbaum
language : en
Publisher: Dover Publications
Release Date : 1985-10-01
Ordinary Differential Equations written by Morris Tenenbaum and has been published by Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-10-01 with Mathematics categories.
This unusually well-written, skillfully organized introductory text provides an exhaustive survey of ordinary differential equations — equations which express the relationship between variables and their derivatives. In a disarmingly simple, step-by-step style that never sacrifices mathematical rigor, the authors — Morris Tenenbaum of Cornell University, and Harry Pollard of Purdue University — introduce and explain complex, critically-important concepts to undergraduate students of mathematics, engineering and the sciences. The book begins with a section that examines the origin of differential equations, defines basic terms and outlines the general solution of a differential equation-the solution that actually contains every solution of such an equation. Subsequent sections deal with such subjects as: integrating factors; dilution and accretion problems; the algebra of complex numbers; the linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas; and Picard's Method of Successive Approximations. The book contains two exceptional chapters: one on series methods of solving differential equations, the second on numerical methods of solving differential equations. The first includes a discussion of the Legendre Differential Equation, Legendre Functions, Legendre Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation. Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application. An abundance of solved problems and practice exercises enhances the value of Ordinary Differential Equations as a classroom text for undergraduate students and teaching professionals. The book concludes with an in-depth examination of existence and uniqueness theorems about a variety of differential equations, as well as an introduction to the theory of determinants and theorems about Wronskians.
The Theory Of Partial Differential Equations
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Author : Sigeru Mizohata
language : en
Publisher: CUP Archive
Release Date : 1973-08-02
The Theory Of Partial Differential Equations written by Sigeru Mizohata and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-08-02 with Mathematics categories.
Fourier series and fourier transforms; Distributions; Elliptic equations (fundamental theory); Initial value problems (cauchy problems); Evolution equations; Hyperbolic equations; Semi-linear hyperbolic equations; Green's functions and spectra.
Ordinary Differential Equations
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Author : Edward L. Ince
language : en
Publisher: Courier Corporation
Release Date : 1956-01-01
Ordinary Differential Equations written by Edward L. Ince and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956-01-01 with Mathematics categories.
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.