Search Results: partial-differential-equations

Partial Differential Equations

Author: Lawrence C. Evans

Publisher: American Mathematical Soc.

ISBN: 0821849743

Category: Mathematics

Page: 749

View: 2740

This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography. About the First Edition: I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail. ... Evans' book is evidence of his mastering of the field and the clarity of presentation. --Luis Caffarelli, University of Texas It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations ... Every graduate student in analysis should read it. --David Jerison, MIT I use Partial Differential Equations to prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's ... I am very happy with the preparation it provides my students. --Carlos Kenig, University of Chicago Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge ... An outstanding reference for many aspects of the field. --Rafe Mazzeo, Stanford University

Partial Differential Equations

Author: Jürgen Jost

Publisher: Springer Science & Business Media

ISBN: 1461448093

Category: Mathematics

Page: 410

View: 3630

This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions.

Partial Differential Equations

Author: Fritz John

Publisher: Springer Science & Business Media

ISBN: 9780387906096

Category: Mathematics

Page: 252

View: 4037

This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy’s example of a linear equation without solutions.

Introduction to Partial Differential Equations

Author: Donald Greenspan

Publisher: Courier Corporation

ISBN: 9780486414508

Category: Mathematics

Page: 195

View: 5763

Rigorous presentation, designed for use in a 1-semester course, explores basics; Fourier series; 2nd-order partial differential equations; wave, potential, and heat equations; approximate solution of partial differential equations, more. Exercises. 1961 edition.

Elements of Partial Differential Equations

Author: Ian N. Sneddon

Publisher: Courier Corporation

ISBN: 0486162990

Category: Mathematics

Page: 352

View: 8287

This text features numerous worked examples in its presentation of elements from the theory of partial differential equations, emphasizing forms suitable for solving equations. Solutions to odd-numbered problems appear at the end. 1957 edition.

Applied Partial Differential Equations

Author: J. David Logan

Publisher: Springer Science & Business Media

ISBN: 9780387209357

Category: Mathematics

Page: 209

View: 7005

"This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation, epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of the exercises will have a sound knowledge base for upper division mathematics, science, and engineering courses where detailed models and applications are introduced."--BOOK JACKET.

Partial Differential Equations

An Introduction

Author: David Colton

Publisher: Courier Corporation

ISBN: 0486138437

Category: Mathematics

Page: 320

View: 9974

This text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Features coverage of integral equations and basic scattering theory. Includes exercises, many with answers. 1988 edition.

Beginning Partial Differential Equations

Author: Peter V. O'Neil

Publisher: John Wiley & Sons

ISBN: 9780471238874

Category: Mathematics

Page: 500

View: 6167

An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Partial Differential Equations

Methods and Applications

Author: N.A

Publisher: 清华大学出版社有限公司

ISBN: 9787302099802

Category: Differential equations, Partial

Page: 420

View: 731

Partial Differential Equations

Author: Abdul-Majid Wazwaz

Publisher: CRC Press

ISBN: 9789058093691

Category: Mathematics

Page: 476

View: 5686

This text gathers, revises and explains the newly developed Adomian decomposition method along with its modification and some traditional techniques.

Applied Partial Differential Equations

Author: Paul DuChateau,David W. Zachmann

Publisher: Courier Corporation

ISBN: 9780486419763

Category: Mathematics

Page: 620

View: 1264

Superb introduction devotes almost half its pages to numerical methods for solving partial differential equations, while the heart of the book focuses 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, with solutions for many at end of book. For students with little background in linear algebra, a useful appendix covers that subject briefly.

Basic Partial Differential Equations

Author: David. Bleecker,George. Csordas

Publisher: CRC Press

ISBN: 9780412067617

Category: Mathematics

Page: 768

View: 9893

Topics not usually found in books at this level include but examined in this text: the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.

Partial Differential Equations

Author: Phoolan Prasad,Renuka Ravindran

Publisher: New Age International

ISBN: 9780852267226

Category: Differential equations, Partial

Page: 252

View: 7287

This book provides a basic introductory course in partial differential equations, in which theory and applications are interrelated and developed side by side. Emphasis is on proofs, which are not only mathematically rigorous, but also constructive, where the structure and properties of the solution are investigated in detail. The authors feel that it is no longer necessary to follow the tradition of introducing the subject by deriving various partial differential equations of continuum mechanics and theoretical physics. Therefore, the subject has been introduced by mathematical analysis of the simplest, yet one of the most useful (from the point of view of applications), class of partial differential equations, namely the equations of first order, for which existence, uniqueness and stability of the solution of the relevant problem (Cauchy problem) is easy to discuss. Throughout the book, attempt has been made to introduce the important ideas from relatively simple cases, some times by referring to physical processes, and then extending them to more general systems.

Analytical and Numerical Aspects of Partial Differential Equations

Notes of a Lecture Series

Author: Etienne Emmrich

Publisher: Walter de Gruyter

ISBN: 3110204479

Category: Mathematics

Page: 290

View: 5171

This text contains a series of self-contained reviews on the state of the art in different areas of partial differential equations, presented by French mathematicians. Topics include qualitative properties of reaction-diffusion equations, multiscale methods coupling atomistic and continuum mechanics, adaptive semi-Lagrangian schemes for the Vlasov-Poisson equation, and coupling of scalar conservation laws.

Partial Differential Equations

Second Edition

Author: Emmanuele DiBenedetto

Publisher: Springer Science & Business Media

ISBN: 0817645527

Category: Mathematics

Page: 389

View: 4711

This book offers a self-contained introduction to partial differential equations (PDEs), primarily focusing on linear equations, and also providing perspective on nonlinear equations. The treatment is mathematically rigorous with a generally theoretical layout, with indications to some of the physical origins of PDEs. The Second Edition is rewritten to incorporate years of classroom feedback, to correct errors and to improve clarity. The exposition offers many examples, problems and solutions to enhance understanding. Requiring only advanced differential calculus and some basic Lp theory, the book will appeal to advanced undergraduates and graduate students, and to applied mathematicians and mathematical physicists.

Numerical Solution of Partial Differential Equations

Finite Difference Methods

Author: Gordon D. Smith

Publisher: Oxford University Press

ISBN: 9780198596509

Category: Mathematics

Page: 337

View: 3310

Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.

Partial Differential Equations

Author: J. Wloka

Publisher: Cambridge University Press

ISBN: 9780521277594

Category: Mathematics

Page: 518

View: 4282

A rigorous introduction to the abstract theory of partial differential equations progresses from the theory of distribution and Sobolev spaces to Fredholm operations, the Schauder fixed point theorem and Bochner integrals.

Partial differential equations and Mathematica

Author: Prem K. Kythe,Pratap Puri,Michael R. Schäferkotter


ISBN: 9780849378539

Category: Computers

Page: 378

View: 8196

This book provides an accessible treatment of this demanding subject. The authors integrate the use of Mathematica throughout the book rather than just providing a few sample problems at the end of chapters. Although rich in the theory for developing underlying mathematical analysis, the text emphasizes the development of methods. Partial Differential Equations and Mathematica provides basic concepts and methods for beginners as well as provides training and encouragement for those continuing their studies in the subject or in applied areas.

Partial Differential Equations

Author: Lipman Bers,Fritz John,Martin Schechter

Publisher: American Mathematical Soc.

ISBN: 9780821896983

Category: Differential equations

Page: 343

View: 2644

This book consists of two main parts. The first part, "Hyperbolic and Parabolic Equations", written by F. John, contains a well-chosen assortment of material intended to give an understanding of some problems and techniques involving hyperbolic and parabolic equations. The emphasis is on illustrating the subject without attempting to survey it. The point of view is classical, and this serves well in furnishing insight into the subject; it also makes it possible for the lectures to be read by someone familiar with only the fundamentals of real and complex analysis. The second part, "Elliptic Equations", written by L. Bers and M. Schechter, contains a very readable account of the results and methods of the theory of linear elliptic equations, including the maximum principle, Hilbert-space methods, and potential-theoretic methods. It also contains a brief discussion of some quasi-linear elliptic equations. The book is suitable for graduate students and researchers interested in partial differential equations.

Lectures on Linear Partial Differential Equations

Author: Grigoriĭ Ilʹich Eskin

Publisher: American Mathematical Soc.

ISBN: 0821852841

Category: Mathematics

Page: 410

View: 992

This book is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces with many examples and applications to equations with constant coefficients. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory. The book also covers microlocal analysis, including the theory of pseudodifferential and Fourier integral operators, and the propagation of singularities for operators of real principal type. Among the more advanced topics are the global theory of Fourier integral operators and the geometric optics construction in the large, the Atiyah-Singer index theorem in $\mathbb R^n$, and the oblique derivative problem.

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