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Asymptotic Analysis of Differential Equations

Asymptotic Analysis of Differential Equations Author R. B. White
ISBN-10 9781848166073
Release 2010
Pages 405
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"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.



Complex Analysis and Differential Equations

Complex Analysis and Differential Equations Author Luis Barreira
ISBN-10 9781447140085
Release 2012-04-23
Pages 415
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This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty. Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study.



Group Analysis of Differential Equations

Group Analysis of Differential Equations Author L. V. Ovsiannikov
ISBN-10 9781483219066
Release 2014-05-10
Pages 432
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Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.



Analysis and Differential Equations

Analysis and Differential Equations Author Odile Pons
ISBN-10 9789814635981
Release 2015-01-19
Pages 256
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This book presents advanced methods of integral calculus and the classical theory of the ordinary and partial differential equations. It provides explicit solutions of linear and nonlinear differential equations and implicit solutions with discrete approximations. Differential equations that could not be explicitly solved are discussed with special functions such as Bessel functions. New functions are defined from differential equations. Laguerre, Hermite and Legendre orthonormal polynomials as well as several extensions are also considered. It is illustrated by examples and graphs of functions, with each chapter containing exercises solved in the last chapter.



Symmetry Analysis of Differential Equations

Symmetry Analysis of Differential Equations Author Daniel J. Arrigo
ISBN-10 9781118721407
Release 2015-01-20
Pages 192
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A SELF-CONTAINED INTRODUCTION TO THE METHODS AND TECHNIQUES OF SYMMETRY ANALYSIS USED TO SOLVE ODEs AND PDEs "Symmetry Analysis of Differential Equations: An Introduction" presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems. Thoroughly class-tested, the author presents classical methods in a systematic, logical, and well-balanced manner. As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility. "Symmetry Analysis of Differential Equations: An Introduction" also features: Detailed, step-by-step examples to guide readers through the methods of symmetry analysis End-of-chapter exercises, varying from elementary to advanced, with select solutions to aid in the calculation of the presented algorithmic methods " Symmetry Analysis of Differential Equations: An Introduction" is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics. The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential equations. DANIEL J. ARRIGO, PhD, is Professor in the Department of Mathematics at the University of Central Arkansas. The author of over 30 journal articles, his research interests include the construction of exact solutions of PDEs; symmetry analysis of nonlinear PDEs; and solutions to physically important equations, such as nonlinear heat equations and governing equations modeling of granular materials and nonlinear elasticity. In 2008, Dr. Arrigo received the Oklahoma-Arkansas Section of the Mathematical Association of America's Award for Distinguished Teaching of College or University Mathematics.



A First Course in the Numerical Analysis of Differential Equations

A First Course in the Numerical Analysis of Differential Equations Author A. Iserles
ISBN-10 9780521734905
Release 2009
Pages 459
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lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.



A First Course in the Numerical Analysis of Differential Equations

A First Course in the Numerical Analysis of Differential Equations Author Arieh Iserles
ISBN-10 0521556554
Release 1996-01-18
Pages 378
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Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance between theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics. Dr Iserles concentrates on fundamentals: deriving methods from first principles, analysing them with a variety of mathematical techniques and occasionally discussing questions of implementation and applications. By doing so, he is able to lead the reader to theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations.



Techniques of Functional Analysis for Differential and Integral Equations

Techniques of Functional Analysis for Differential and Integral Equations Author Paul Sacks
ISBN-10 9780128114575
Release 2017-05-16
Pages 320
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Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations, and especially partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and as PhD research preparation in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs are limited, and their sources precisely identifie d, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. Provides an introduction to the mathematical techniques widely used in applied mathematics and needed for advanced research Establishes the advanced background needed for sophisticated literature review and research in both differential and integral equations Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics



Applied Functional Analysis and Partial Differential Equations

Applied Functional Analysis and Partial Differential Equations Author Milan Miklav?i?
ISBN-10 9810235356
Release 1998
Pages 294
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This book is an introduction to partial differential equations (PDEs) and the relevant functional analysis tools which they require. It is based on a course which has been taught at Michigan State University for a number of years. The purpose of the course, and of the book, is to give students a rapid and solid research-oriented foundation in areas of PDEs, such as semilinear parabolic equations, that include studies of the stability of fluid flows and, more generally, of the dynamics generated by dissipative systems, numerical PDEs, elliptic and hyperbolic PDEs, and quantum mechanics.



Methods of Nonlinear Analysis

Methods of Nonlinear Analysis Author Pavel Drabek
ISBN-10 9783034803878
Release 2013-01-18
Pages 649
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In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. A large number of methods are applied to boundary value problems for both ordinary and partial differential equations. In this edition we have made minor revisions, added new material and organized the content slightly differently. In particular, we included evolutionary equations and differential equations on manifolds. The applications to partial differential equations follow every abstract framework of the method in question. The text is structured in two levels: a self-contained basic level and an advanced level - organized in appendices - for the more experienced reader. The last chapter contains more involved material and can be skipped by those new to the field. This book serves as both a textbook for graduate-level courses and a reference book for mathematicians, engineers and applied scientists



Nonlinear Functional Analysis and Differential Equations

Nonlinear Functional Analysis and Differential Equations Author Lamberto Cesari
ISBN-10 0824764528
Release 1976-10-01
Pages 368
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Nonlinear Functional Analysis and Differential Equations has been writing in one form or another for most of life. You can find so many inspiration from Nonlinear Functional Analysis and Differential Equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Nonlinear Functional Analysis and Differential Equations book for free.



Partial Differential Equations and Complex Analysis

Partial Differential Equations and Complex Analysis Author Steven G. Krantz
ISBN-10 9781351425803
Release 2018-05-04
Pages 320
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Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.



Harmonic Analysis and Partial Differential Equations

Harmonic Analysis and Partial Differential Equations Author Michael Christ
ISBN-10 0226104559
Release 2001-06-01
Pages 360
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Alberto P. Calderón (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about everything from harmonic analysis to partial differential equations and from signal processing to tomography. In addition, he helped define the "Chicago school" of analysis, which remains influential to this day. In 1996, more than 300 mathematicians from around the world gathered in Chicago for a conference on harmonic analysis and partial differential equations held in Calderón's honor. This volume originated in papers given there and presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest scholars working in these areas. An important addition to the literature, this book is essential reading for researchers in these and other related fields.



Functional Analysis Sobolev Spaces and Partial Differential Equations

Functional Analysis  Sobolev Spaces and Partial Differential Equations Author Haim Brezis
ISBN-10 9780387709147
Release 2010-11-02
Pages 600
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This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.



Ordinary Differential Equations

Ordinary Differential Equations Author Hartmut Logemann
ISBN-10 9781447163985
Release 2014-07-08
Pages 333
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The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature. The following topics are particularly emphasised: • existence, uniqueness and continuation of solutions, • continuous dependence on initial data, • flows, • qualitative behaviour of solutions, • limit sets, • stability theory, • invariance principles, • introductory control theory, • feedback and stabilization. The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability. Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.



Symmetry Analysis of Differential Equations with Mathematica

Symmetry Analysis of Differential Equations with Mathematica  Author Gerd Baumann
ISBN-10 9781461221104
Release 2013-11-21
Pages 521
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The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact with the code presented within the book. In addition, the author's proprietary "MathLie" software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations.



Fourier Analysis and Partial Differential Equations

Fourier Analysis and Partial Differential Equations Author Rafael José Iorio, Jr
ISBN-10 052162116X
Release 2001-03-15
Pages 411
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A 2001 introduction to Fourier analysis and partial differential equations; aimed at beginning graduate students.