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Partial Differential Equations

Partial Differential Equations Author Lawrence C. Evans
ISBN-10 9780821849743
Release 2010
Pages 749
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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

Partial Differential Equations Author David Colton
ISBN-10 9780486138435
Release 2012-06-14
Pages 320
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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.



Partial Differential Equations

Partial Differential Equations Author Jürgen Jost
ISBN-10 0387954287
Release 2002-01-01
Pages 325
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This book is intended for readers who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. This book 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.



Partial Differential Equations

Partial Differential Equations Author Phoolan Prasad
ISBN-10 0852267223
Release 1985
Pages 252
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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.



Partial Differential Equations

Partial Differential Equations Author F. John
ISBN-10 9781461599791
Release 2012-12-06
Pages 250
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These Notes grew out of a course given by the author in 1952-53. Though the field of Partial Differential Equations has changed considerably since those days, particularly under the impact of methods taken from Functional Analysis, the author feels that the introductory material offered here still is basic for an understanding of the subject. It supplies the necessary intuitive foundation which motivates and anticipates abstract formulations of the questions and relates them to the description of natual phenomena. Added to this second corrected edition is a collection of problems and solutions, which illustrate and supplement the theories developed in the text. Fritz John New York September, 1974 vii TABLE OF CONTENTS Introd uction 1 CHAPrER I - THE SINGLE FIRST ORDER EQUATION 1. The linear and quasi-linear equations. 6 2. The general first order equation for a function of two variables. • • • • • • • • • 15 The general first order equation for a function 3. of n independent variables. • • • • • 37 CHAPrER II - THE CAUCHY PROBLEM FOR HIGHER ORDER EQUATIONS 1. Analytic functions of several real variables • 48 2. Formulation of the Cauchy problem. The notion of characteristics. • • • 54 3. The Cauchy problem for the general non-linear equation ••• 71 4. The Cauchy-Kowalewsky theorem. 76 CHAPTER III - SECOND ORDER EQUATIONS WITH CONSTANT COEFFICIENTS 1. Equations in two independent variables.



Partial Differential Equations

Partial Differential Equations Author J. Wloka
ISBN-10 0521277590
Release 1987-05-21
Pages 518
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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.



An Elementary Course in Partial Differential Equations

An Elementary Course in Partial Differential Equations Author T. Amaranath
ISBN-10 9781449668396
Release 2011-08-25
Pages 156
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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.



Applied Partial Differential Equations

Applied Partial Differential Equations Author J. David Logan
ISBN-10 0387209352
Release 2004-05-11
Pages 209
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"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.



Applied Partial Differential Equations

Applied Partial Differential Equations Author Paul DuChateau
ISBN-10 0486419762
Release 2002
Pages 620
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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.



Partial Differential Equations

Partial Differential Equations Author Thomas Hillen
ISBN-10 9781118438435
Release 2014-08-21
Pages 696
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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.



Analytic Methods for Partial Differential Equations

Analytic Methods for Partial Differential Equations Author Gwynne Evans
ISBN-10 3540761241
Release 2000
Pages 299
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The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. J ames Clerk Maxwell, for example, put electricity and magnetism into a unified theory by estab lishing Maxwell's equations for electromagnetic theory, which gave solutions for problems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechankal processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier-Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forcasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.



Introduction to Partial Differential Equations

Introduction to Partial Differential Equations Author G. B. Folland
ISBN-10 0691043612
Release 1995
Pages 324
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The aim of this text is to aquaint the student with the fundamental classical results of partial differential equations and to guide them into some of the modern theory, enabling them to read more advanced works on the subject



Partial Differential Equations

Partial Differential Equations Author Emmanuele DiBenedetto
ISBN-10 0817637087
Release 1994-12-22
Pages 416
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This text is meant to be a self-contained, elementary introduction to Partial Differential Equations, assuming only advanced differential calculus and some basic LP theory. Although the basic equations treated in this book, given its scope, are linear, we have made an attempt to approach them from a nonlinear perspective. Chapter I is focused on the Cauchy-Kowaleski theorem. We discuss the notion of characteristic surfaces and use it to classify partial differential equations. The discussion grows out of equations of second order in two variables to equations of second order in N variables to p.d.e.'s of any order in N variables. In Chapters II and III we study the Laplace equation and connected elliptic theory. The existence of solutions for the Dirichlet problem is proven by the Perron method. This method clarifies the structure ofthe sub(super)harmonic functions and is closely related to the modern notion of viscosity solution. The elliptic theory is complemented by the Harnack and Liouville theorems, the simplest version of Schauder's estimates and basic LP -potential estimates. Then, in Chapter III, the Dirichlet and Neumann problems, as well as eigenvalue problems for the Laplacian, are cast in terms of integral equations. This requires some basic facts concerning double layer potentials and the notion of compact subsets of LP, which we present.



Introduction to Partial Differential Equations

Introduction to Partial Differential Equations Author Donald Greenspan
ISBN-10 0486414507
Release 1961
Pages 195
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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.



Partial Differential Equations

Partial Differential Equations Author Edward Thomas Copson
ISBN-10 0521098939
Release 1975-10-02
Pages 280
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In this book, Professor Copson gives a rigorous account of the theory of partial differential equations of the first order and of linear partial differential equations of the second order, using the methods of classical analysis. In spite of the advent of computers and the applications of the methods of functional analysis to the theory of partial differential equations, the classical theory retains its relevance in several important respects. Many branches of classical analysing have their origins in the rigourous discussion of problems in applies mathematics and theoretical physics, and the classical treatment of the theory of partial differential equations still provides the best method of treating many physical problems. A knowledge of the classical theory is essential for pure mathematics who intend to undertake research in this field, whatever approach they ultimately adopt. The numerical analyst needs a knowledge of classical theory in order to decide whether a problem has a unique solution or not.



Partial Differential Equations and Their Applications

Partial Differential Equations and Their Applications Author Peter Charles Greiner
ISBN-10 0821870149
Release 1997-01-01
Pages 315
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Just list for purposes of NBB.



Lectures on Partial Differential Equations

Lectures on Partial Differential Equations Author Vladimir I. Arnold
ISBN-10 3540404481
Release 2003-10-29
Pages 162
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Choice Outstanding Title! (January 2006) This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.