Partielle Differentialgleichungen

Eine Einführung

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Author: Walter A. Strauss

Publisher: Springer-Verlag

ISBN: 366312486X

Category: Mathematics

Page: 458

View: 7582

Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.

Partial Differential Equations: An Introduction, 2nd Edition

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Author: Walter A. Strauss

Publisher: Wiley Global Education

ISBN: 111831316X

Category: Mathematics

Page: 464

View: 6413

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.

Student Solutions Manual to Accompany Partial Differential Equations: An Introduction, 2e

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Author: Julie L. Levandosky,Walter A. Strauss,Steven P. Levandosky

Publisher: John Wiley & Sons

ISBN: 0470260718

Category: Mathematics

Page: 215

View: 8536

Practice partial differential equations with this student solutions manual Corresponding chapter-by-chapter with Walter Strauss's Partial Differential Equations, this student solutions manual consists of the answer key to each of the practice problems in the instructional text. Students will follow along through each of the chapters, providing practice for areas of study including waves and diffusions, reflections and sources, boundary problems, Fourier series, harmonic functions, and more. Coupled with Strauss's text, this solutions manual provides a complete resource for learning and practicing partial differential equations.

Applied Partial Differential Equations: An Introduction

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Author: Alan Jeffrey

Publisher: Academic Press

ISBN: 9780123822529

Category: Mathematics

Page: 394

View: 6324

This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations. It is a more modern, comprehensive treatment intended for students who need more than the purely numerical solutions provided by programs like the MATLAB PDE Toolbox, and those obtained by the method of separation of variables, which is usually the only theoretical approach found in the majority of elementary textbooks. This will fill a need in the market for a more modern text for future working engineers, and one that students can read and understand much more easily than those currently on the market. * Includes new and important materials necessary to meet current demands made by diverse applications * Very detailed solutions to odd numbered problems to help students * Instructor's Manual Available

An Introduction to Second Order Partial Differential Equations

Classical and Variational Solutions

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Author: Doina Cioranescu,Patrizia Donato,Marian P Roque

Publisher: World Scientific Publishing Company

ISBN: 9813229195

Category: Mathematics

Page: 300

View: 2731

The book extensively introduces classical and variational partial differential equations (PDEs) to graduate and post-graduate students in Mathematics. The topics, even the most delicate, are presented in a detailed way. The book consists of two parts which focus on second order linear PDEs. Part I gives an overview of classical PDEs, that is, equations which admit strong solutions, verifying the equations pointwise. Classical solutions of the Laplace, heat, and wave equations are provided. Part II deals with variational PDEs, where weak (variational) solutions are considered. They are defined by variational formulations of the equations, based on Sobolev spaces. A comprehensive and detailed presentation of these spaces is given. Examples of variational elliptic, parabolic, and hyperbolic problems with different boundary conditions are discussed.

Linear and Semilinear Partial Differential Equations

An Introduction

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Author: Radu Precup

Publisher: Walter de Gruyter

ISBN: 3110269058

Category: Mathematics

Page: 296

View: 497

This textbook provides a brief and lucid introduction to the theory of linear partial differential equations. It clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions. The solution operators associated to non-homogeneous equations are used to make transition to the theory of nonlinear PDEs. Organized on three parts, this material is suitable for three one-semester courses, a beginning one in the frame of classical analysis, a more advanced course in modern theory and a master course in semi-linear equations.

Partielle Differentialgleichungen und numerische Methoden

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Author: Stig Larsson,Vidar Thomee

Publisher: Springer-Verlag

ISBN: 3540274227

Category: Mathematics

Page: 272

View: 1300

Das Buch ist für Studenten der angewandten Mathematik und der Ingenieurwissenschaften auf Vordiplomniveau geeignet. Der Schwerpunkt liegt auf der Verbindung der Theorie linearer partieller Differentialgleichungen mit der Theorie finiter Differenzenverfahren und der Theorie der Methoden finiter Elemente. Für jede Klasse partieller Differentialgleichungen, d.h. elliptische, parabolische und hyperbolische, enthält der Text jeweils ein Kapitel zur mathematischen Theorie der Differentialgleichung gefolgt von einem Kapitel zu finiten Differenzenverfahren sowie einem zu Methoden der finiten Elemente. Den Kapiteln zu elliptischen Gleichungen geht ein Kapitel zum Zweipunkt-Randwertproblem für gewöhnliche Differentialgleichungen voran. Ebenso ist den Kapiteln zu zeitabhängigen Problemen ein Kapitel zum Anfangswertproblem für gewöhnliche Differentialgleichungen vorangestellt. Zudem gibt es ein Kapitel zum elliptischen Eigenwertproblem und zur Entwicklung nach Eigenfunktionen. Die Darstellung setzt keine tiefer gehenden Kenntnisse in Analysis und Funktionalanalysis voraus. Das erforderliche Grundwissen über lineare Funktionalanalysis und Sobolev-Räume wird im Anhang im Überblick besprochen.

Bifurcation Theory

An Introduction with Applications to Partial Differential Equations

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Author: Hansjörg Kielhöfer

Publisher: Springer Science & Business Media

ISBN: 1461405025

Category: Mathematics

Page: 400

View: 3966

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations. The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.

Partial Differential Equations

An Introduction

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Author: Walter A. Strauss

Publisher: John Wiley & Sons Incorporated

ISBN: 9780470385531

Category: Mathematics

Page: 454

View: 4241

This book covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them.

An Elementary Course in Partial Differential Equations

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Author: T. Amaranath

Publisher: Jones & Bartlett Publishers

ISBN: 1449657540

Category: Mathematics

Page: 156

View: 7548

An Elementary Course in Partial Differential Equations is a concise, 1-term introduction to partial differential equations for the upper-level undergraduate/graduate course in Mathematics, Engineering and Science. Divided into two accessible parts, the first half of the text presents first-order differential equations while the later half is devoted to the study of second-order partial differential equations. Numerous applications and exercises throughout allow students to test themselves on key material discussed.

An Introduction to Partial Differential Equations

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Author: Michael Renardy,Robert C. Rogers

Publisher: Springer Science & Business Media

ISBN: 0387216871

Category: Mathematics

Page: 434

View: 3687

Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.

Introduction to Partial Differential Equations for Scientists and Engineers Using Mathematica

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Author: Kuzman Adzievski,Abul Hasan Siddiqi

Publisher: CRC Press

ISBN: 1466510579

Category: Mathematics

Page: 648

View: 943

With a special emphasis on engineering and science applications, this textbook provides a mathematical introduction to PDEs at the undergraduate level. It takes a new approach to PDEs by presenting computation as an integral part of the study of differential equations. The authors use Mathematica® along with graphics to improve understanding and interpretation of concepts. They also present exercises in each chapter and solutions to selected examples. Topics discussed include Laplace and Fourier transforms as well as Sturm-Liouville boundary value problems.

Partial Differential Equations

An Introduction

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Author: Günter Hellwig

Publisher: Springer-Verlag

ISBN: 3663110028

Category: Technology & Engineering

Page: 259

View: 6192

Partial Differential Equations II

Qualitative Studies of Linear Equations

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Author: Michael E. Taylor

Publisher: Springer Science & Business Media

ISBN: 9781441970527

Category: Mathematics

Page: 614

View: 1070

This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.

Partial Differential Equations I

Basic Theory

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Author: Michael Eugene Taylor,Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 9780387946535

Category: Mathematics

Page: 563

View: 1221

This book is intended to be a comprehensive introduction to the subject of partial differential equations. It should be useful to graduate students at all levels beyond that of a basic course in measure theory. It should also be of interest to professional mathematicians in analysis, mathematical physics, and differential geometry. This work will be divided into three volumes, the first of which focuses on the theory of ordinary differential equations and a survey of basic linear PDEs.

Partial Differential Equations

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Author: Jürgen Jost

Publisher: Springer Science & Business Media

ISBN: 9780387493183

Category: Mathematics

Page: 356

View: 550

This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. It also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. It also explores connections between elliptic, parabolic, and hyperbolic equations as well as the connection with Brownian motion and semigroups. This second edition features a new chapter on reaction-diffusion equations and systems.

Partial Differential Equations

An Introduction to a General Theory of Linear Boundary Value Problems

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Author: Aleksei A. Dezin

Publisher: Springer Science & Business Media

ISBN: 3642713343

Category: Mathematics

Page: 165

View: 4413

Let me begin by explaining the meaning of the title of this book. In essence, the book studies boundary value problems for linear partial differ ential equations in a finite domain in n-dimensional Euclidean space. The problem that is investigated is the question of the dependence of the nature of the solvability of a given equation on the way in which the boundary conditions are chosen, i.e. on the supplementary requirements which the solution is to satisfy on specified parts of the boundary. The branch of mathematical analysis dealing with the study of boundary value problems for partial differential equations is often called mathematical physics. Classical courses in this subject usually consider quite restricted classes of equations, for which the problems have an immediate physical context, or generalizations of such problems. With the expanding domain of application of mathematical methods at the present time, there often arise problems connected with the study of partial differential equations that do not belong to any of the classical types. The elucidation of the correct formulation of these problems and the study of the specific properties of the solutions of similar equations are closely related to the study of questions of a general nature.

Partial Differential Equations II

Elements of the Modern Theory. Equations with Constant Coefficients

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Author: Yu.V. Egorov,A.I. Komech,M.A. Shubin

Publisher: Springer Science & Business Media

ISBN: 3642578764

Category: Mathematics

Page: 266

View: 1880

This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.