Plane Waves And Spherical Means Applied To Partial Differential Equations

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Plane Waves and Spherical Means

Author : F. John
Publisher : Springer Science & Business Media
ISBN 13 : 1461394538
Total Pages : 174 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Plane Waves and Spherical Means by : F. John

Download or read book Plane Waves and Spherical Means written by F. John and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author would like to acknowledge his obligation to all his (;Olleagues and friends at the Institute of Mathematical Sciences of New York University for their stimulation and criticism which have contributed to the writing of this tract. The author also wishes to thank Aughtum S. Howard for permission to include results from her unpublished dissertation, Larkin Joyner for drawing the figures, Interscience Publishers for their cooperation and support, and particularly Lipman Bers, who suggested the publication in its present form. New Rochelle FRITZ JOHN September, 1955 [v] CONTENTS Introduction. . . . . . . 1 CHAPTER I Decomposition of an Arbitrary Function into Plane Waves Explanation of notation . . . . . . . . . . . . . . . 7 The spherical mean of a function of a single coordinate. 7 9 Representation of a function by its plane integrals . CHAPTER II Tbe Initial Value Problem for Hyperbolic Homogeneous Equations with Constant Coefficients Hyperbolic equations. . . . . . . . . . . . . . . . . . . . . . 15 Geometry of the normal surface for a strictly hyperbolic equation. 16 Solution of the Cauchy problem for a strictly hyperbolic equation . 20 Expression of the kernel by an integral over the normal surface. 23 The domain of dependence . . . . . . . . . . . . . . . . . . . 29 The wave equation . . . . . . . . . . . . . . . . . . . . . . 32 The initial value problem for hyperbolic equations with a normal surface having multiple points . . . . . . . . . . . . . . . . . . . . 36 CHAPTER III The Fundamental Solution of a Linear Elliptic Differential Equation witL Analytic Coefficients Definition of a fundamental solution . . . . . . . . . . . . . . 43 The Cauchy problem . . . . . . . . . . . . . . . . . . . . . 45 Solution of the inhomogeneous equation with a plane wave function as right hand side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 The fundamental solution. . . . . . . . . . . . . . . . . . . . . .

Plane Waves and Spherical Means

Author : F. John
Publisher : Springer
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Plane Waves and Spherical Means by : F. John

Download or read book Plane Waves and Spherical Means written by F. John and published by Springer. This book was released on 1955 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of results on partial differential equations employs certain elementary identities for plane and spherical integrals of an arbitrary function, showing how a variety of results on fairly general differential equations follow from those identities. Explores the decomposition of arbitrary functions into functions of the type of plane waves; Radon transformation; more.

Plane Waves and Spherical Means Applied to Partial Differential Equations

Author : Fritz John
Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.3/5 ( download)

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Book Synopsis Plane Waves and Spherical Means Applied to Partial Differential Equations by : Fritz John

Download or read book Plane Waves and Spherical Means Applied to Partial Differential Equations written by Fritz John and published by . This book was released on 1955 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Plane Waves and Spherical Means Applied to Partial Differential Equations

Author : Fritz John
Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.3/5 (243 download)

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Book Synopsis Plane Waves and Spherical Means Applied to Partial Differential Equations by : Fritz John

Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture

Author : Birgit Bergmann
Publisher : Springer Science & Business Media
ISBN 13 : 3642224636
Total Pages : 297 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture by : Birgit Bergmann

Download or read book Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture written by Birgit Bergmann and published by Springer Science & Business Media. This book was released on 2011-10-24 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: A companion publication to the international exhibition "Transcending Tradition: Jewish Mathematicians in German-Speaking Academic Culture", the catalogue explores the working lives and activities of Jewish mathematicians in German-speaking countries during the period between the legal and political emancipation of the Jews in the 19th century and their persecution in Nazi Germany. It highlights the important role Jewish mathematicians played in all areas of mathematical culture during the Wilhelmine Empire and the Weimar Republic, and recalls their emigration, flight or death after 1933.

Partial Differential Equations

Author : Lawrence C. Evans
Publisher : American Mathematical Society
ISBN 13 : 1470469421
Total Pages : 662 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Partial Differential Equations by : Lawrence C. Evans

Download or read book Partial Differential Equations written by Lawrence C. Evans and published by American Mathematical Society. This book was released on 2022-03-22 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 usePartial Differential Equationsto 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 in Mechanics 1

Author : A.P.S. Selvadurai
Publisher : Springer Science & Business Media
ISBN 13 : 3662040069
Total Pages : 610 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Partial Differential Equations in Mechanics 1 by : A.P.S. Selvadurai

Download or read book Partial Differential Equations in Mechanics 1 written by A.P.S. Selvadurai and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.

Partial Differential Equations in Mechanics 2

Author : A.P.S. Selvadurai
Publisher : Springer Science & Business Media
ISBN 13 : 3662092050
Total Pages : 713 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Partial Differential Equations in Mechanics 2 by : A.P.S. Selvadurai

Download or read book Partial Differential Equations in Mechanics 2 written by A.P.S. Selvadurai and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.

Partial Differential Equations

Author : Emmanuele DiBenedetto
Publisher : Springer Science & Business Media
ISBN 13 : 0817645527
Total Pages : 404 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Partial Differential Equations by : Emmanuele DiBenedetto

Download or read book Partial Differential Equations written by Emmanuele DiBenedetto and published by Springer Science & Business Media. This book was released on 2009-10-17 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Partial Differential Equations with MATLAB

Author : Jeffery M. Cooper
Publisher : Springer Science & Business Media
ISBN 13 : 1461217547
Total Pages : 549 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Partial Differential Equations with MATLAB by : Jeffery M. Cooper

Download or read book Introduction to Partial Differential Equations with MATLAB written by Jeffery M. Cooper and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with constant coeffi cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter.

Partial Differential Equations

Author : David Colton
Publisher : Courier Corporation
ISBN 13 : 0486138437
Total Pages : 322 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Partial Differential Equations by : David Colton

Download or read book Partial Differential Equations written by David Colton and published by Courier Corporation. This book was released on 2012-06-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Journey Into Partial Differential Equations

Author : William O. Bray
Publisher : Jones & Bartlett Publishers
ISBN 13 : 0763772569
Total Pages : 334 pages
Book Rating : 4.7/5 (637 download)

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Book Synopsis A Journey Into Partial Differential Equations by : William O. Bray

Download or read book A Journey Into Partial Differential Equations written by William O. Bray and published by Jones & Bartlett Publishers. This book was released on 2012 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the International Series in Mathematics Ideal for the 1-term course, A Journey into Partial Differential Equations provides a solid introduction to PDEs for the undergraduate math, engineering, or physics student. Discussing underlying physics, concepts and methodologies, the text focuses on the classical trinity of equations: the wave equation, heat/diffusion equation, and Laplace's equation. Bray provides careful treatment of the separation of variables and the Fourier method, motivated by the geometrical notion of symmetries and places emphasis on both the qualitative and quantitative methods, as well as geometrical perspectives. With hundred of exercises and a wealth of figures, A Journey into Partial Differential Equations proves to be the model book for the PDE course.

Partial Differential Equations

Author : Lipman Bers
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896983
Total Pages : 372 pages
Book Rating : 4.8/5 (969 download)

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Book Synopsis Partial Differential Equations by : Lipman Bers

Download or read book Partial Differential Equations written by Lipman Bers and published by American Mathematical Soc.. This book was released on 1964-12-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Partial Differential Equations and Hilbert Space Methods

Author : Karl E. Gustafson
Publisher : Courier Corporation
ISBN 13 : 0486140873
Total Pages : 500 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to Partial Differential Equations and Hilbert Space Methods by : Karl E. Gustafson

Download or read book Introduction to Partial Differential Equations and Hilbert Space Methods written by Karl E. Gustafson and published by Courier Corporation. This book was released on 2012-04-26 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.

Partial Differential Equations

Author : Emmanuele DiBenedetto
Publisher : Springer Nature
ISBN 13 : 3031466187
Total Pages : 768 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Partial Differential Equations by : Emmanuele DiBenedetto

Download or read book Partial Differential Equations written by Emmanuele DiBenedetto and published by Springer Nature. This book was released on 2023 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes, Navier-Stokes equations, and more. The “Problems and Complements” sections have also been updated to feature new exercises, examples, and hints toward solutions, making this a timely resource for students. Partial Differential Equations: Third Edition is ideal for graduate students interested in exploring the theory of PDEs and how they connect to contemporary research. It can also serve as a useful tool for more experienced readers who are looking for a comprehensive reference.

Partial Differential Equations and Related Topics

Author : J.A. Goldstein
Publisher : Springer
ISBN 13 : 354037440X
Total Pages : 398 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Partial Differential Equations and Related Topics by : J.A. Goldstein

Download or read book Partial Differential Equations and Related Topics written by J.A. Goldstein and published by Springer. This book was released on 2006-11-15 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Distributions, Partial Differential Equations, and Harmonic Analysis

Author : Dorina Mitrea
Publisher : Springer
ISBN 13 : 3030032965
Total Pages : 615 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Distributions, Partial Differential Equations, and Harmonic Analysis by : Dorina Mitrea

Download or read book Distributions, Partial Differential Equations, and Harmonic Analysis written by Dorina Mitrea and published by Springer. This book was released on 2018-12-29 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a format suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to cover all intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have been carefully chosen to amplify the effect, and substantiate the power and scope, of the theory of distributions. Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. Throughout, a special effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance to see the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed tools (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonic analysis, at the earliest opportunity. The main additions to the current, second edition, pertain to fundamental solutions (through the inclusion of the Helmholtz operator, the perturbed Dirac operator, and their iterations) and the theory of Sobolev spaces (built systematically from the ground up, exploiting natural connections with the Fourier Analysis developed earlier in the monograph).