Theory And Applications Of Partial Differential Equations

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Theory and Applications of Partial Differential Equations

Author : Piero Bassanini
Publisher : Springer Science & Business Media
ISBN 13 : 1489918752
Total Pages : 446 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Theory and Applications of Partial Differential Equations by : Piero Bassanini

Download or read book Theory and Applications of Partial Differential Equations written by Piero Bassanini and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a product of the experience of the authors in teaching partial differential equations to students of mathematics, physics, and engineering over a period of 20 years. Our goal in writing it has been to introduce the subject with precise and rigorous analysis on the one hand, and interesting and significant applications on the other. The starting level of the book is at the first-year graduate level in a U.S. university. Previous experience with partial differential equations is not required, but the use of classical analysis to find solutions of specific problems is not emphasized. From that perspective our treatment is decidedly theoretical. We have avoided abstraction and full generality in many situations, however. Our plan has been to introduce fundamental ideas in relatively simple situations and to show their impact on relevant applications. The student is then, we feel, well prepared to fight through more specialized treatises. There are parts of the exposition that require Lebesgue integration, distributions and Fourier transforms, and Sobolev spaces. We have included a long appendix, Chapter 8, giving precise statements of all results used. This may be thought of as an introduction to these topics. The reader who is not familiar with these subjects may refer to parts of Chapter 8 as needed or become somewhat familiar with them as prerequisite and treat Chapter 8 as Chapter O.

Partial Differential Equations

Author : Michael Shearer
Publisher : Princeton University Press
ISBN 13 : 0691161291
Total Pages : 286 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Partial Differential Equations by : Michael Shearer

Download or read book Partial Differential Equations written by Michael Shearer and published by Princeton University Press. This book was released on 2015-03-01 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors

Theory and Applications of Partial Functional Differential Equations

Author : Jianhong Wu
Publisher : Springer Science & Business Media
ISBN 13 : 1461240506
Total Pages : 441 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Theory and Applications of Partial Functional Differential Equations by : Jianhong Wu

Download or read book Theory and Applications of Partial Functional Differential Equations written by Jianhong Wu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.

Partial Differential Equations

Author : András Vasy
Publisher : American Mathematical Soc.
ISBN 13 : 1470418819
Total Pages : 295 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Partial Differential Equations by : András Vasy

Download or read book Partial Differential Equations written by András Vasy and published by American Mathematical Soc.. This book was released on 2015-12-21 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on partial differential equations is intended for readers who want to understand the theoretical underpinnings of modern PDEs in settings that are important for the applications without using extensive analytic tools required by most advanced texts. The assumed mathematical background is at the level of multivariable calculus and basic metric space material, but the latter is recalled as relevant as the text progresses. The key goal of this book is to be mathematically complete without overwhelming the reader, and to develop PDE theory in a manner that reflects how researchers would think about the material. A concrete example is that distribution theory and the concept of weak solutions are introduced early because while these ideas take some time for the students to get used to, they are fundamentally easy and, on the other hand, play a central role in the field. Then, Hilbert spaces that are quite important in the later development are introduced via completions which give essentially all the features one wants without the overhead of measure theory. There is additional material provided for readers who would like to learn more than the core material, and there are numerous exercises to help solidify one's understanding. The text should be suitable for advanced undergraduates or for beginning graduate students including those in engineering or the sciences.

Introduction to Partial Differential Equations with Applications

Author : E. C. Zachmanoglou
Publisher : Courier Corporation
ISBN 13 : 048613217X
Total Pages : 434 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to Partial Differential Equations with Applications by : E. C. Zachmanoglou

Download or read book Introduction to Partial Differential Equations with Applications written by E. C. Zachmanoglou and published by Courier Corporation. This book was released on 2012-04-20 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Partial Differential Equations

Author : Walter A. Strauss
Publisher : John Wiley & Sons
ISBN 13 : 0470054565
Total Pages : 467 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Partial Differential Equations by : Walter A. Strauss

Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Partial Differential Equations

Author : T. Hillen
Publisher : FriesenPress
ISBN 13 : 152555025X
Total Pages : 683 pages
Book Rating : 4.5/5 (255 download)

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Book Synopsis Partial Differential Equations by : T. Hillen

Download or read book Partial Differential Equations written by T. Hillen and published by FriesenPress. This book was released on 2019-05-15 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides more than 150 fully solved problems for linear partial differential equations and boundary value problems. Partial Differential Equations: Theory and Completely Solved Problems offers a modern introduction into the theory and applications of linear partial differential equations (PDEs). It is the material for a typical third year university course in PDEs. The material of this textbook has been extensively class tested over a period of 20 years in about 60 separate classes. The book is divided into two parts. Part I contains the Theory part and covers topics such as a classification of second order PDEs, physical and biological derivations of the heat, wave and Laplace equations, separation of variables, Fourier series, D’Alembert’s principle, Sturm-Liouville theory, special functions, Fourier transforms and the method of characteristics. Part II contains more than 150 fully solved problems, which are ranked according to their difficulty. The last two chapters include sample Midterm and Final exams for this course with full solutions.

Applications of Lie's Theory of Ordinary and Partial Differential Equations

Author : L Dresner
Publisher : CRC Press
ISBN 13 : 9781420050783
Total Pages : 242 pages
Book Rating : 4.0/5 (57 download)

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Book Synopsis Applications of Lie's Theory of Ordinary and Partial Differential Equations by : L Dresner

Download or read book Applications of Lie's Theory of Ordinary and Partial Differential Equations written by L Dresner and published by CRC Press. This book was released on 1998-01-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

Partial Differential Equations

Author : Thomas Hillen
Publisher : John Wiley & Sons
ISBN 13 : 1118438434
Total Pages : 610 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Partial Differential Equations by : Thomas Hillen

Download or read book Partial Differential Equations written by Thomas Hillen and published by John Wiley & Sons. This book was released on 2014-08-21 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including: • Classification of second-order linear PDEs • Derivation of heat, wave, and Laplace’s equations • Fourier series • Separation of variables • Sturm-Liouville theory • Fourier transforms Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources. Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.

Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems

Author : Irena Lasiecka
Publisher : Cambridge University Press
ISBN 13 : 9780521434089
Total Pages : 678 pages
Book Rating : 4.4/5 (34 download)

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Book Synopsis Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems by : Irena Lasiecka

Download or read book Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems written by Irena Lasiecka and published by Cambridge University Press. This book was released on 2000-02-13 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: First of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations, originally published in 2000.

Partial Differential Equations and Group Theory

Author : J.F. Pommaret
Publisher : Springer Science & Business Media
ISBN 13 : 940172539X
Total Pages : 481 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Partial Differential Equations and Group Theory by : J.F. Pommaret

Download or read book Partial Differential Equations and Group Theory written by J.F. Pommaret and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential control thPory (the classical theory) studies input/output re lations defined by systems of ordinary differential equations (ODE). The various con cepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been re cently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding con cepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differ ential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control the ory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry.

Semigroups of Linear Operators and Applications to Partial Differential Equations

Author : Amnon Pazy
Publisher : Springer Science & Business Media
ISBN 13 : 1461255619
Total Pages : 289 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Semigroups of Linear Operators and Applications to Partial Differential Equations by : Amnon Pazy

Download or read book Semigroups of Linear Operators and Applications to Partial Differential Equations written by Amnon Pazy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Partial Differential Equations

Author : George F. Carrier
Publisher : Academic Press
ISBN 13 : 1483259161
Total Pages : 333 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Partial Differential Equations by : George F. Carrier

Download or read book Partial Differential Equations written by George F. Carrier and published by Academic Press. This book was released on 2014-05-10 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial Differential Equations: Theory and Technique provides formal definitions, notational conventions, and a systematic discussion of partial differential equations. The text emphasizes the acquisition of practical technique in the use of partial differential equations. The book contains discussions on classical second-order equations of diffusion, wave motion, first-order linear and quasi-linear equations, and potential theory. Certain chapters elaborate Green's functions, eigenvalue problems, practical approximation techniques, perturbations (regular and singular), difference equations, and numerical methods. Students of mathematics will find the book very useful.

Theory and Applications of Fractional Differential Equations

Author : A.A. Kilbas
Publisher : Elsevier
ISBN 13 : 9780444518323
Total Pages : 550 pages
Book Rating : 4.5/5 (183 download)

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Book Synopsis Theory and Applications of Fractional Differential Equations by : A.A. Kilbas

Download or read book Theory and Applications of Fractional Differential Equations written by A.A. Kilbas and published by Elsevier. This book was released on 2006-02-16 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.

Introduction to the Theory of Linear Partial Differential Equations

Author : J. Chazarain
Publisher : Elsevier
ISBN 13 : 0080875351
Total Pages : 575 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Introduction to the Theory of Linear Partial Differential Equations by : J. Chazarain

Download or read book Introduction to the Theory of Linear Partial Differential Equations written by J. Chazarain and published by Elsevier. This book was released on 2011-08-18 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to the Theory of Linear Partial Differential Equations

Engineering Differential Equations

Author : Bill Goodwine
Publisher : Springer Science & Business Media
ISBN 13 : 1441979190
Total Pages : 762 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Engineering Differential Equations by : Bill Goodwine

Download or read book Engineering Differential Equations written by Bill Goodwine and published by Springer Science & Business Media. This book was released on 2010-11-11 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.

Nonlinear Partial Differential Equations with Applications

Author : Tomás Roubicek
Publisher : Springer Science & Business Media
ISBN 13 : 3764373970
Total Pages : 415 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Nonlinear Partial Differential Equations with Applications by : Tomás Roubicek

Download or read book Nonlinear Partial Differential Equations with Applications written by Tomás Roubicek and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.