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Ordinary Differential Equations

Ordinary Differential Equations
A Book

by Edward L. Ince

  • Publisher : Courier Corporation
  • Release : 1956-01-01
  • Pages : 558
  • ISBN : 0486603490
  • Language : En, Es, Fr & De
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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.

Differential Equations:

Differential Equations:
A Book

by Rukmangadachari

  • Publisher : Pearson Education India
  • Release : 2000
  • Pages : 472
  • ISBN : 9332511640
  • Language : En, Es, Fr & De
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Differential Equations presents the basics of differential equations. With equal emphasis on theoretical and practical concepts, the book provides a balanced coverage of all topics essential to master the subject at the undergraduate level.

Ordinary Differential Equations

Ordinary Differential Equations
An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences

by Morris Tenenbaum,Harry Pollard

  • Publisher : Courier Corporation
  • Release : 1963
  • Pages : 808
  • ISBN : 0486649407
  • Language : En, Es, Fr & De
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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.

The Theory of Differential Equations

The Theory of Differential Equations
Classical and Qualitative

by Walter G. Kelley,Allan C. Peterson

  • Publisher : Springer Science & Business Media
  • Release : 2010-04-22
  • Pages : 423
  • ISBN : 1441957820
  • Language : En, Es, Fr & De
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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.

An Introduction to Ordinary Differential Equations

An Introduction to Ordinary Differential Equations
A Book

by Earl A. Coddington

  • Publisher : Dover
  • Release : 1961
  • Pages : 292
  • ISBN : 9780486659428
  • Language : En, Es, Fr & De
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A thorough and systematic first course in elementary differential equations for undergraduates in mathematics and science, with many exercises and problems (with answers).

An Introduction to Differential Equations and Their Applications

An Introduction to Differential Equations and Their Applications
A Book

by Stanley J. Farlow

  • Publisher : Courier Corporation
  • Release : 2006-03-11
  • Pages : 609
  • ISBN : 048644595X
  • Language : En, Es, Fr & De
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This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

Ordinary and Partial Differential Equations

Ordinary and Partial Differential Equations
A Book

by Victor Henner,Tatyana Belozerova,Mikhail Khenner

  • Publisher : CRC Press
  • Release : 2013-01-29
  • Pages : 644
  • ISBN : 1466515007
  • Language : En, Es, Fr & De
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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.

Partial Differential Equations for Scientists and Engineers

Partial Differential Equations for Scientists and Engineers
A Book

by Stanley J. Farlow

  • Publisher : Courier Corporation
  • Release : 1993
  • Pages : 414
  • ISBN : 048667620X
  • Language : En, Es, Fr & De
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This highly useful text shows the reader how to formulate a partial differential equation from the physical problem and how to solve the equation.

Volterra Integral and Differential Equations

Volterra Integral and Differential Equations
SECOND EDITION

by Ted A. Burton

  • Publisher : Elsevier
  • Release : 2005-04-01
  • Pages : 368
  • ISBN : 0080459552
  • Language : En, Es, Fr & De
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Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems. Thus, the presentation starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory. Liapunov's direct method is gently introduced and applied to many particular examples in ordinary differential equations, Volterra integro-differential equations, and functional differential equations. By Chapter 7 the momentum has built until we are looking at problems on the frontier. Chapter 7 is entirely new, dealing with fundamental problems of the resolvent, Floquet theory, and total stability. Chapter 8 presents a solid foundation for the theory of functional differential equations. Many recent results on stability and periodic solutions of functional differential equations are given and unsolved problems are stated. Key Features: - Smooth transition from ordinary differential equations to integral and functional differential equations. - Unification of the theories, methods, and applications of ordinary and functional differential equations. - Large collection of examples of Liapunov functions. - Description of the history of stability theory leading up to unsolved problems. - Applications of the resolvent to stability and periodic problems. 1. Smooth transition from ordinary differential equations to integral and functional differential equations. 2. Unification of the theories, methods, and applications of ordinary and functional differential equations. 3. Large collection of examples of Liapunov functions. 4. Description of the history of stability theory leading up to unsolved problems. 5. Applications of the resolvent to stability and periodic problems.

Differential Equations with Symbolic Computation

Differential Equations with Symbolic Computation
A Book

by Dongming Wang

  • Publisher : Springer Science & Business Media
  • Release : 2005-08-15
  • Pages : 374
  • ISBN : 9783764373689
  • Language : En, Es, Fr & De
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This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.

Analytic Methods for Partial Differential Equations

Analytic Methods for Partial Differential Equations
A Book

by G. Evans,J. Blackledge,P. Yardley

  • Publisher : Springer Science & Business Media
  • Release : 1999-11-01
  • Pages : 316
  • ISBN : 3540761241
  • Language : En, Es, Fr & De
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This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.

Partial Differential Equations

Partial Differential Equations
A Book

by Avner Friedman

  • Publisher : Courier Corporation
  • Release : 2008
  • Pages : 262
  • ISBN : 0486469190
  • Language : En, Es, Fr & De
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This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists. Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of weak derivatives, proves various inequalities and imbedding problems, and derives smoothness theorems. Part Two concerns evolution equations in Banach space and develops the theory of semigroups. It solves the initial-boundary value problem for parabolic equations and covers backward uniqueness, asymptotic behavior, and lower bounds at infinity. The final section includes independent topics directly related to the methods and results of the previous material, including the analyticity of solutions of elliptic and parabolic equations, asymptotic behavior of solutions of elliptic equations near infinity, and problems in the theory of control in Banach space.

Partial Differential Equations of Applied Mathematics

Partial Differential Equations of Applied Mathematics
A Book

by Erich Zauderer

  • Publisher : John Wiley & Sons
  • Release : 2011-10-24
  • Pages : 968
  • ISBN : 1118031407
  • Language : En, Es, Fr & De
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This new edition features the latest tools for modeling, characterizing, and solving partial differential equations The Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples. Among the new and revised material, the book features: * A new section at the end of each original chapter, exhibiting the use of specially constructed Maple procedures that solve PDEs via many of the methods presented in the chapters. The results can be evaluated numerically or displayed graphically. * Two new chapters that present finite difference and finite element methods for the solution of PDEs. Newly constructed Maple procedures are provided and used to carry out each of these methods. All the numerical results can be displayed graphically. * A related FTP site that includes all the Maple code used in the text. * New exercises in each chapter, and answers to many of the exercises are provided via the FTP site. A supplementary Instructor's Solutions Manual is available. The book begins with a demonstration of how the three basic types of equations-parabolic, hyperbolic, and elliptic-can be derived from random walk models. It then covers an exceptionally broad range of topics, including questions of stability, analysis of singularities, transform methods, Green's functions, and perturbation and asymptotic treatments. Approximation methods for simplifying complicated problems and solutions are described, and linear and nonlinear problems not easily solved by standard methods are examined in depth. Examples from the fields of engineering and physical sciences are used liberally throughout the text to help illustrate how theory and techniques are applied to actual problems. With its extensive use of examples and exercises, this text is recommended for advanced undergraduates and graduate students in engineering, science, and applied mathematics, as well as professionals in any of these fields. It is possible to use the text, as in the past, without use of the new Maple material.

A Text Book of Differential Equations

A Text Book of Differential Equations
A Book

by N. M. Kapoor

  • Publisher : Pitambar Publishing
  • Release : 1997
  • Pages : 628
  • ISBN : 9788120900127
  • Language : En, Es, Fr & De
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An Integral Part Of College Mathematics, Finds Application In Diverse Areas Of Science And Enginnering. This Book Covers The Subject Of Ordinary And Partial Differential Equations In Detail. There Are Ninteeen Chapters And Eight Appendices Covering Diverse Topics Including Numerical Solution Of First Order Equations, Existence Theorem, Solution In Series, Detailed Study Of Partial Differential Equations Of Second Order Etc. This Book Fully Covers The Latest Requirement Of Graduage And Postgraduate Courses.

Ordinary Differential Equations

Ordinary Differential Equations
A Book

by W. Cox

  • Publisher : Butterworth-Heinemann
  • Release : 1996
  • Pages : 222
  • ISBN : 0340632038
  • Language : En, Es, Fr & De
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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 AND PARTIAL DIFFERENTIAL EQUATIONS

ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
THEORY AND APPLICATIONS

by NITA H. SHAH

  • Publisher : PHI Learning Pvt. Ltd.
  • Release : 2015-01-17
  • Pages : 528
  • ISBN : 8120350871
  • Language : En, Es, Fr & De
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This revised and updated text, now in its second edition, continues to present the theoretical concepts of methods of solutions of ordinary and partial differential equations. It equips students with the various tools and techniques to model different physical problems using such equations. The book discusses the basic concepts of ordinary and partial differential equations. It contains different methods of solving ordinary differential equations of first order and higher degree. It gives the solution methodology for linear differential equations with constant and variable coefficients and linear differential equations of second order. The text elaborates simultaneous linear differential equations, total differential equations, and partial differential equations along with the series solution of second order linear differential equations. It also covers Bessel’s and Legendre’s equations and functions, and the Laplace transform. Finally, the book revisits partial differential equations to solve the Laplace equation, wave equation and diffusion equation, and discusses the methods to solve partial differential equations using the Fourier transform. A large number of solved examples as well as exercises at the end of chapters help the students comprehend and strengthen the underlying concepts. The book is intended for undergraduate and postgraduate students of Mathematics (B.A./B.Sc., M.A./M.Sc.), and undergraduate students of all branches of engineering (B.E./B.Tech.), as part of their course in Engineering Mathematics. New to the SECOND Edition • Includes new sections and subsections such as applications of differential equations, special substitution (Lagrange and Riccati), solutions of non-linear equations which are exact, method of variation of parameters for linear equations of order higher than two, and method of undetermined coefficients • Incorporates several worked-out examples and exercises with their answers • Contains a new Chapter 19 on ‘Z-Transforms and its Applications’.

Numerical Solution of Partial Differential Equations by the Finite Element Method

Numerical Solution of Partial Differential Equations by the Finite Element Method
A Book

by Claes Johnson

  • Publisher : Courier Corporation
  • Release : 2009-01-15
  • Pages : 278
  • ISBN : 048646900X
  • Language : En, Es, Fr & De
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This accessible introduction offers the keys to an important technique in computational mathematics. It outlines clear connections with applications and considers numerous examples from a variety of specialties. 1987 edition.

An Introduction to Stochastic Differential Equations

An Introduction to Stochastic Differential Equations
A Book

by Lawrence C. Evans

  • Publisher : American Mathematical Soc.
  • Release : 2012-12-11
  • Pages : 151
  • ISBN : 1470410540
  • Language : En, Es, Fr & De
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These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. --Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. --George Papanicolaou, Stanford University This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically. --Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive ``white noise'' and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

Introduction to Partial Differential Equations

Introduction to Partial Differential Equations
A Book

by G. B. Folland

  • Publisher : Princeton University Press
  • Release : 1995-11-04
  • Pages : 324
  • ISBN : 9780691043616
  • Language : En, Es, Fr & De
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The aim of this text is to aquaint the student with the fundamental classical results of partial differential equations and to guide them into some of the modern theory, enabling them to read more advanced works on the subject.

Applied Partial Differential Equations

Applied Partial Differential Equations
A Book

by Paul DuChateau,David Zachmann

  • Publisher : Courier Corporation
  • Release : 2012-10-30
  • Pages : 640
  • ISBN : 048614187X
  • Language : En, Es, Fr & De
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DIVBook focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included. /div