Differential Equations مراجع

ISBN: 0471612987
Title: Partial Differential Equations of Applied Mathematics (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
Author: Erich Zauderer
Publisher: John Wiley & Sons
Publication Date: 1989-06
Number Of Pages: 891

The only comprehensive guide to modeling, characterizing, and solving partial differential equations This classic text by Erich Zauderer provides a comprehensive account of partial differential equations and their applications. Dr. Zauderer develops mathematical models that give rise to partial differential equations and describes classical and modern solution techniques. With an emphasis on practical applications, he makes liberal use of real-world examples, explores both linear and ........


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ISBN: 0444506160
Title: Numerical Analysis 2000, Volume 7, Partial Differential Equations
Author: Keith Jones, D. Sloan (Editor) , E Suli, S. Vandewaite
Publisher: North Holland
Publication Date: 2001-07-01
Number Of Pages: 480

Editorial Description
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price !Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering


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ISBN: 0127843973
Title: Handbook of Differential Equations (CD-ROM Version 1 only), Third Edition
Author: Daniel Zwillinger
Publisher: Academic Press
Publication Date: 1997-10-27
Number Of Pages: 824

This book and CD-ROM compile the most widely applicable methods for solving and approximating differential equations. The CD-ROM provides convenient access to these methods through electronic search capabilities, andtogether the book and CD-ROM contain numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.

Key Features
* For nearly every technique, the book and CD-ROM provide:
* The types of equations to which the method is applicable
* The idea behind the method
* The procedure for carrying out the method
* At least one simple example of the method
* Any cautions that should be exercised
* Notes for more advanced users
* References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs

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Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations
Springer | ISBN: 0387986901 | 1999 | 299 pages | PDF | 1.3 MB

Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series

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ISBN: 0471588849
Title: An Introduction to the Fractional Calculus and Fractional Differential Equations
Author: Kenneth S. Miller Bertram Ross
Publisher: John Wiley & Sons
Publication Date: 1993-05-19
Number Of Pages: 384

Commences with the historical development of fractional calculus, its mathematical theory—particularly the Riemann-Liouville version. Numerous examples and theoretical applications of the theory are presented. Features topics associated with fractional differential equations. Discusses Weyl fractional calculus and some of its uses. Includes selected physical problems which lead to fractional differential or integral equations

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ISBN: 3764370092
Title: Adaptive Finite Element Methods for Differential Equations (Lectures in Mathematics. ETH Zürich)
Author: Wolfgang Bangerth Rolf Rannacher
Publisher: Birkhäuser Basel
Publication Date: 2003-04-28
Number Of Pages: 207

The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag

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Preface 1 Introduction 12 An ODE Model Case 153 A PDE Model Case 254 Practical Aspects 415 The Limits of Theoretical Analysis 616 An Abstract Approach for Nonlinear Problems 717 Eigenvalue Problems 818 Optimixation Problems 1019 Time-Dependent Problems 11310 Applications in Structural Mechanics 12911 Applications in Fluid Mechanics 14312 Miscellaneous and Open Problems 161A Solutions of exercises 167Bibliography 191Index 203
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ISBN: 0127843973
Title: Handbook of Differential Equations (CD-ROM Version 1 only), Third Edition
Author: Daniel Zwillinger
Publisher: Academic Press
Publication Date: 1997-10-27
Number Of Pages: 824

This book and CD-ROM compile the most widely applicable methods for solving and approximating differential equations. The CD-ROM provides convenient access to these methods through electronic search capabilities, andtogether the book and CD-ROM contain numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.Key Features* For nearly every tec

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ISBN: 0521205832
Title: Partial Differential Equations
Author: Copson
Publisher: Cambridge University Press
Publication Date: 1975-10-31
Number Of Pages: 287

This book has been written in memory of my father-in-law the late Professor Sir Edmund Whittaker, F.R.S., in gratitude for all the
help and encouragement he gave me for over thirty years. Today is the hundredth anniversary of his birth. When I went to Edinburgh as a young lecturer in 1922,1 was surprised to find how different the curriculum was from that in Oxford. It included such topics as Lebesgue integration, matrix theory, numerical analysis, Riemannian geometry, of which I knew nothing. I was particularly impressed by Whittaker's lectures on partial differential equations to undergraduate and postgraduate students, far different from the standard English textbooks of the time. This book is not based on Whittaker's lectures; yet without his inspiration it would never have been written. I have frequently given courses of lectures on partial differential equations and have always regretted that there was no book to which I could refer my students. Friends told me that the remedy was to write one myself; and here it is, a presentation of some of the theory by the methods of classical analysis. There are few references to original sources. After lecturing on the subject for so many years, I could not now say whence the material came. On page 277 will be found a list of the books which
I have read with profit, many of them more advanced than this.

Table of *******s


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Preface page vii 1 Partial differential equations of the first order 1 2 Characteristics of equations of the second order 24 3 Boundary value and initial value problems 44 4 Equations of hyperbolic type 54 5 Riemann's method 77 6 The equation of wave motions 90 7 Marcel Riesz's method 107 8 Potential theory in the plane 131 9 Subharmonic functions and the problem of Dirichlet 175 10 Equations of elliptic type in the plane 186 11 Equations of elliptic type in space 207 12 The equation of heat 238 Appendix 271 Books for further reading 277 Index 279
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ISBN: 3764373687
Title: Differential Equations with Symbolic Computation (Trends in Mathematics)
Author: Dongming Wang Zhiming Zheng
Publisher: Birkhauser
Publication Date: 2005-09-27
Number Of Pages: 374

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. The 20 chapters are written by leading experts and are structured into three parts. The book is worth reading for researchers and students working on this interdisciplinary subject but may also serve as a valuable reference for everyone interested in differential equations, symbolic computation, and their interaction

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ISBN: 0471399647
Title: Ordinary Differential Equations in the Complex Domain (Pure & Applied Mathematics)
Author: Einar Hille
Publisher: John Wiley & Sons Inc
Publication Date: 1976-06
Number Of Pages: 496

Graduate-level text offers full and extensive treatments of existence theorems, representation of solutions by series, representation by integrals, theory of majorants, dominants and minorants, questions of growth, much more. Relevant review material on complex analysis supplied. 675 exercises at chapter ends. Bibliography

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ISBN: 0521355311
Title: Differential Equations: Their Solution Using Symmetries
Author: Hans Stephani
Publisher: Cambridge University Press
Publication Date: 1990-01-26
Number Of Pages: 272

In many branches of physics, mathematics, and engineering, solving a problem means solving a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The emphasis in this text is on how to find and use the symmetries; this is supported by many examples and more than 100 exercises. This book will form an introduction accessible to beginning graduate students in physics, applied mathematics, and engineering. Advanced graduate students and researchers in these disciplines will find the book a valuable reference

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ISBN: 3764376007
Title: Partial Differential Equations and Functional Analysis: The Philippe Clément Festschrift (Operator Theory: Advances and Applications)
Author: Erik Koelink, Jan van Neerven, Ben de Pagter, and Guido Sweers
Publisher: Birkhauser
Publication Date: 2006-06
Number Of Pages: 294


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ISBN: 3764372931
Title: Nonlinear Partial Differential Equations with Applications (International Series of Numerical Mathematics)
Author: Tomás Roubicek
Publisher: Birkhauser
Publication Date: 2005-10-26
Number Of Pages: 405

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads general theory as fast as possible towards the analysis of concrete equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering

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Handbook of Exact Solutions for Ordinary Differential Equations
By Andrei D. Polyanin, V. F. Zaitsev
Publisher: CRC-Press
Number Of Pages: 707
Publication Date: 1995-07-09
ISBN / ASIN: 0849394384

Exact solutions have always played and still play an important role in properly understanding the qualitative features of many phenomena. The Handbook of Exact Solutions for Ordinary Differential Equations contains a collection of more than 5,000 ordinary differential equations and their solutions. Coverage focuses on two types of equations: those that are of interest to researchers but are difficult to integrate (Abel equations, Emden-Fowler equations, Painlev equations, etc.), and equations relevant to applications in heat and mass transfer, nonlinear mechanics, hydrodynamics, nonlinear oscillations, combustion, chemical engineering, and other related fields. The authors also pay special attention to equations containing arbitrary functions, and devote other sections to equations contain one or more arbitrary parameters that the reader can fix at will

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Handbook of Differential Equations, Third Edition
By Daniel Zwillinger
Publisher: Academic Press
Number Of Pages: 801
Publication Date: 1998-01-15
ISBN / ASIN: 0127843965

This book and CD-ROM compile the most widely applicable methods for solving and approximating differential equations. The CD-ROM provides convenient access to these methods through electronic search capabilities, andtogether the book and CD-ROM contain numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.


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* For nearly every technique, the book and CD-ROM provide:* The types of equations to which the method is applicable* The idea behind the method* The procedure for carrying out the method* At least one simple example of the method* Any cautions that should be exercised* Notes for more advanced users* References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs
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Ordinary differential equations: with an introduction to Lie's theory of the group of one parameter.
By James Morris Page
* Publisher: Cornell University Library
* Number Of Pages: 244
* Publication Date: 2007-01-09
* ISBN / ASIN: 1429703822
This volume is produced from digital images from the Cornell University Library Historical Mathematics Monographs collection.


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A Concise Course on Stochastic Partial Differential Equations (Lecture Notes in Mathematics)
By Claudia Prévôt,&nbspMichael Röckner,
* Publisher: Springer
* Number Of Pages: 148
* Publication Date: 2007-07
* ISBN / ASIN: 3540707808

Book Description:
These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale.

There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach” and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach”. A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.

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Applied Partial Differential Equations:: A Visual Approach
By Peter A. Markowich
* Publisher: Springer
* Number Of Pages: 206
* Publication Date: 2006-12-28
* ISBN / ASIN: 3540346457

Book Description:
This book presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables such as mass, velocity, and energy to their spatial and temporal variations. Typically, these equations are highly nonlinear; in many cases they are systems, and they represent challenges even for the most modern and sophisticated mathematical and numerical-analytic techniques. The selected topics reflect the longtime scientific interests of the author. They include flows of fluids and gases, granular-material flows, biological processes such as pattern formation on animal skins, kinetics of rarified gases, free boundaries, semiconductor devices, and socioeconomic processes. Each topic is briefly introduced in its scientific or engineering context, followed by a presentation of the mathematical models in the form of partial differential equations with a discussion of their basic mathematical properties. The author illustrates each chapter by a series of his own high-quality photographs, which demonstrate that partial differential equations are powerful tools for modeling a large variety of phenomena influencing our daily lives

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Advanced Ordinary Differential Equations

Advanced Ordinary Differential Equations (Mathematics and Its Applications)
By K. Friedrichs
* Publisher: Routledge
* Number Of Pages: 216
* Publication Date: 1965-01-01
* ISBN / ASIN: 0677009607
$241.00

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Power Geometry in Algebraic and Differential Equations (North-Holland Mathematical Library)
* Publisher: Elsevier Science
* Number Of Pages: 394
* Publication Date: 2000-06-01
* ISBN / ASIN: 0444502971
$133.00

Book Description:
The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed.

The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems.

The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis

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Partial Differential Equations: An Introduction
By Walter A. Strauss
* Publisher: Wiley
* Number Of Pages: 440
* Publication Date: 1992-03-17
* ISBN / ASIN: 0471548685
Buy New $100.65

Covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them. Uses a broad approach to illustrate the rich diversity of phenomena such as vibrations of solids, fluid flow, molecular structure, photon and electron interactions, radiation of electromagnetic waves encompassed by this subject as well as the role PDEs play in modern mathematics, especially geometry and analysis

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Handbook of Differential Equations:Stationary Partial Differential Equations, Volume 2 (Handbook of Differential Equations)
By
* Publisher: North Holland
* Number Of Pages: 624
* Publication Date: 2005-09-13
* ISBN / ASIN: 0444520457
Buy New $190.00
A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.
Partial differential equations represent one of the most rapidly developing topics in mathematics. This is due to their numerous applications in science and engineering on the one hand and to the challenge and beauty of associated mathematical problems on the other.
Key features:

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Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field
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Handbook of Differential Equations: Ordinary Differential Equations, Volume 2 (Handbook of Differential Equations)
By
* Publisher: North Holland
* Number Of Pages: 584
* Publication Date: 2005-10-20
* ISBN / ASIN: 0444520279
Buy New $190.00

This handbook is the second volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, written
by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields, in order to make the chapters of the volume accessible to a wide audience.

. Six chapters covering a variety of problems in ordinary differential equations.
. Both, pure mathematical research and real word applications are reflected
. Written by leading researchers in the area.

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Linear Partial Differential Equations for Scientists and Engineers
By Tyn Myint-U,&nbspLokenath Debnath,
* Publisher: Birkhäuser Boston
* Number Of Pages: 778
* Publication Date: 2006-12-15
* ISBN / ASIN: 0817643931
Buy New $79.60

One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics.

This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.

Key features include:

* Applications to a wide variety of physical problems in numerous interdisciplinary areas

* Over 900 worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry

* Historical comments on partial differential equations

* Solutions and hints to selected exercises

* A comprehensive bibliographycomprised of many standard texts and reference books, as well as a set of selected classic and recent papersfor readers interested in learning more about the modern treatment of the subject

Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarily serve as a textbook for the first two courses in PDEs, or in a course on advanced engineering mathematics. The book may also be used as a reference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering. Readers will gain a solid mathematical background in PDEs, sufficient to start interdisciplinary collaborative research in a variety of fields.

Also by L. Debnath: Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition, ISBN 0-8176-4323-0.

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Control of Coupled Partial Differential Equations
(International Series of Numerical Mathematics)
By
* Publisher: Birkhäuser Basel
* Number Of Pages: 382
* Publication Date: 2007-05-21
* ISBN / ASIN: 3764377208
Buy New $129.00

This volume contains selected contributions originating from the Conference on Optimal Control of Coupled Systems of Partial Differential Equations, held at the Mathematisches Forschungsinstitut Oberwolfach in April 2005.

With their articles, leading scientists cover a broad range of topics such as controllability, feedback-control, optimality systems, model-reduction techniques, analysis and optimal control of flow problems, and fluid-structure interactions, as well as problems of shape and topology optimization. Applications affected by these findings are distributed over all time and length scales starting with optimization and control of quantum mechanical systems, the design of piezoelectric acoustic micro-mechanical devices, or optimal control of crystal growth to the control of bodies immersed into a fluid, airfoil design, and much more.

The book addresses advanced students and researchers in optimization and control of infinite dimensional systems, typically represented by partial differential equations. Readers interested either in theory or in numerical simulation of such systems will find this book equally appealing

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Partial Differential Equations and Boundary Value Problems with Fourier Series (2nd Edition)
By Nakhle H. Asmar
* Publisher: Prentice Hall
* Number Of Pages: 816
* Publication Date: 2004-05-24
* ISBN-10 / ASIN: 0131480960
* ISBN-13 / EAN: 9780131480964

Book Description:
This example-rich reference fosters a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material accessible even to readers with limited exposure to topics beyond calculus. Encourages computer for illustrating results and applications, but is also suitable for use without computer access. Contains more engineering and physics applications, and more mathematical proofs and theory of partial differential equations, than the first edition. Offers a large number of exercises per section. Provides marginal comments and remarks throughout with insightful remarks, keys to following the material, and formulas recalled for the reader's convenience. Offers Mathematica files available for download from the author's website. A useful reference for engineers or anyone who needs to brush up on partial differential equations

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A Treatise on Differential Equations
By George Boole
* Publisher: Adamant Media Corporation
* Number Of Pages: 573
* Publication Date: 2000-12-21
* ISBN-10 / ASIN: 140218364X
* ISBN-13 / EAN: 9781402183645

Product Description:
This Elibron Classics book is a facsimile reprint of a 1877 edition by Macmillan and Co., London

This is a Masterpiece on the theory of differential equations, This book was forgotton by many people who read newer books on differential equations, but hold on --- this book contains the finest of the expositions of differential equations and can be regarded as an encyclopedia of Theory, Problems and applications of differential equations

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Introduction to Linear Algebra and Differential Equations
By John W. Dettman
* Publisher: Dover Publications
* Number Of Pages: 416
* Publication Date: 1986-12-01
* ISBN-10 / ASIN: 0486651916
* ISBN-13 / EAN: 9780486651910
Book Description:
Excellent introductory text for students with 1 year of calculus. Topics include complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions and boundary-value problems. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

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Paul Blanchard, Robert L. Devaney, Glen R. Hall “Differential Equations, 3rd Edition"
Brooks Cole | 2005-09-19 | ISBN: 0495012653 | 848 pages | Djvu | 12 MB

Incorporating a modeling approach throughout, this exciting text emphasizes concepts and shows that the study of differential equations is a beautiful application of the ideas and techniques of calculus to everyday life. By taking advantage of readily available technology, the authors eliminate most of the specialized techniques for deriving formulas for solutions found in traditional texts and replace them with topics that focus on the formulation of differential equations and the interpretations of their solutions. Students will generally attack a given equation from three different points of view to obtain an understanding of the solutions: qualitative, numeric, and analytic. Since many of the most important differential equations are nonlinear, students learn that numerical and qualitative techniques are more effective than analytic techniques in this setting. Overall, students discover how to identify and work effectively with the mathematics in everyday life, and they learn how to express the fundamental principles that govern many phenomena in the language of differential equations.

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Meshfree Methods for Partial Differential Equations IV (Lecture Notes in Computational Science and Engineering)
By Michael Griebel, Marc Alexander Schweitzer

• Publisher: Springer
• Number Of Pages: 412
• Publication Date: 2008-11-01
• ISBN-10 / ASIN: 3540799931
• ISBN-13 / EAN: 9783540799931

Product Description:
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the proceedings papers of the Fourth International Workshop on Meshfree Methods held in September 2007 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this very active and exciting area of interdisciplinary research and to present recent advances and results in this field

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