The Analysis of Linear Partial Differential Operators I

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Publisher : Springer
ISBN 13 : 9783540523437
Total Pages : 460 pages
Book Rating : 4.5/5 (234 download)

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Book Synopsis The Analysis of Linear Partial Differential Operators I by : Lars Hörmander

Download or read book The Analysis of Linear Partial Differential Operators I written by Lars Hörmander and published by Springer. This book was released on 1990-08-10 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.

Lectures on Linear Partial Differential Equations

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Publisher : American Mathematical Soc.
ISBN 13 : 0821852841
Total Pages : 432 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lectures on Linear Partial Differential Equations by : Grigoriĭ Ilʹich Eskin

Download or read book Lectures on Linear Partial Differential Equations written by Grigoriĭ Ilʹich Eskin and published by American Mathematical Soc.. This book was released on 2011 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory.

Linear Partial Differential Equations with Constant Coefficients

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Publisher : CRC Press
ISBN 13 : 9780677011905
Total Pages : 552 pages
Book Rating : 4.0/5 (119 download)

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Book Synopsis Linear Partial Differential Equations with Constant Coefficients by : Francois Treves

Download or read book Linear Partial Differential Equations with Constant Coefficients written by Francois Treves and published by CRC Press. This book was released on 1966 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Existence and approximation theorems for general differential operators -- General L2 estimates -- Fundamental solutions -- The approximation theorem -- Existence theorems for differential operators with constant coefficients -- Convexity with respect to a differential polynomial -- Interior regularity of solutions -- Partial hypoellipticity -- Existence and approximation theorems in spaces of analytic functions -- Appendix A. Semi-algebraic sets -- Appendix B. On uniqueness in the Cauchy problem -- Appendix C. Some formulas of non-commutative algebra.

Linear Partial Differential Equations with Constant Coefficients

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Publisher :
ISBN 13 :
Total Pages : 534 pages
Book Rating : 4.:/5 (861 download)

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Book Synopsis Linear Partial Differential Equations with Constant Coefficients by : Francois Treves

Download or read book Linear Partial Differential Equations with Constant Coefficients written by Francois Treves and published by . This book was released on 1984 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Partial Differential Equations

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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.

Solutions to Differential Equations

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Publisher : Laxmi Publications
ISBN 13 : 9788170088714
Total Pages : 536 pages
Book Rating : 4.0/5 (887 download)

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Book Synopsis Solutions to Differential Equations by : N. Gupta

Download or read book Solutions to Differential Equations written by N. Gupta and published by Laxmi Publications. This book was released on 2006-08 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Linear Partial Differential Equations

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Publisher : CRC Press
ISBN 13 : 9780677025209
Total Pages : 140 pages
Book Rating : 4.0/5 (252 download)

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Book Synopsis Linear Partial Differential Equations by : Francois Treves

Download or read book Linear Partial Differential Equations written by Francois Treves and published by CRC Press. This book was released on 1970-01-01 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers existence and approximation theorems in functional analysis, L-squared inequalities, necessary and sufficient conditions for existence of solutions (variable coefficients), and L-squared estimates and pseudo-convexity. Includes further reading and bibliographic references.

Partial Differential Equations II

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Publisher : Springer Science & Business Media
ISBN 13 : 3642578764
Total Pages : 269 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Partial Differential Equations II by : Yu.V. Egorov

Download or read book Partial Differential Equations II written by Yu.V. Egorov and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear Partial Differential and Difference Equations and Simultaneous Systems with Constant or Homogeneous Coefficients

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Publisher : CRC Press
ISBN 13 : 1040010172
Total Pages : 243 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Linear Partial Differential and Difference Equations and Simultaneous Systems with Constant or Homogeneous Coefficients by : Luis Manuel Braga da Costa Campos

Download or read book Linear Partial Differential and Difference Equations and Simultaneous Systems with Constant or Homogeneous Coefficients written by Luis Manuel Braga da Costa Campos and published by CRC Press. This book was released on 2024-06-07 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Partial Differential and Difference Equations and Simultaneous Systems: With Constant or Homogeneous Coefficients is part of the series "Mathematics and Physics for Science and Technology," which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass, and electricity; and their interactions. This is the third book of the volume. The book starts with six different methods of solution of linear partial differential equations (p.d.e.) with constant coefficients. One of the methods, namely characteristic polynomial, is then extended to a further five classes, including linear p.d.e. with homogeneous power coefficients and finite difference equations and simultaneous systems of both (simultaneous partial differential equations [s.p.d.e.] and simultaneous finite difference equations [s.f.d.e.]). The applications include detailed solutions of the most important p.d.e. in physics and engineering, including the Laplace, heat, diffusion, telegraph, bar, and beam equations. The free and forced solutions are considered together with boundary, initial, asymptotic, starting, and other conditions. The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical, and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics.

Ordinary and Partial Differential Equations for the Beginner

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Publisher : World Scientific Publishing Company
ISBN 13 : 9814725013
Total Pages : 256 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Ordinary and Partial Differential Equations for the Beginner by : László Székelyhidi

Download or read book Ordinary and Partial Differential Equations for the Beginner written by László Székelyhidi and published by World Scientific Publishing Company. This book was released on 2016-05-24 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended for college, undergraduate and graduate students, emphasizing mainly on ordinary differential equations. However, the theory of characteristics for first order partial differential equations and the classification of second order linear partial differential operators are also included. It contains the basic material starting from elementary solution methods for ordinary differential equations to advanced methods for first order partial differential equations. In addition to the theoretical background, solution methods are strongly emphasized. Each section is completed with problems and exercises, and the solutions are also provided. There are special sections devoted to more applied tools such as implicit equations, Laplace transform, Fourier method, etc. As a novelty, a method for finding exponential polynomial solutions is presented which is based on the author's work in spectral synthesis. The presentation is self-contained, provided the reader has general undergraduate knowledge.

The Analysis of Linear Partial Differential Operators II

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Publisher : Springer
ISBN 13 : 3540269649
Total Pages : 404 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis The Analysis of Linear Partial Differential Operators II by : Lars Hörmander

Download or read book The Analysis of Linear Partial Differential Operators II written by Lars Hörmander and published by Springer. This book was released on 2005-12-12 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author received the 1962 Fields Medal Author received the 1988 Wolf Prize (honoring achievemnets of a lifetime) Author is leading expert in partial differential equations

Solving Linear Partial Differential Equations: Spectra

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Publisher : World Scientific
ISBN 13 : 9811216320
Total Pages : 407 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Solving Linear Partial Differential Equations: Spectra by : Martin Schechter

Download or read book Solving Linear Partial Differential Equations: Spectra written by Martin Schechter and published by World Scientific. This book was released on 2020-06-16 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'This booklet provides a very lucid and versatile introduction to the methods of linear partial differential equations. It covers a wealth of very important material in a concise, nevertheless very instructive manner, and as such it may serve as an excellent guide to further, more advanced and detailed reading in this area of both classical and contemporary mathematics.'zbMATHPartial differential equations arise in many branches of science and they vary in many ways. No one method can be used to solve all of them, and only a small percentage have been solved. This book examines the general linear partial differential equation of arbitrary order m. Even this involves more methods than are known. We ask a simple question: when can an equation be solved and how many solutions does it have?The answer is surprising even for equations with constant coefficients. We begin with these equations, first finding conditions which allow one to solve and obtain a finite number of solutions. It is then shown how to obtain those solutions by analyzing the structure of the equation very carefully. A substantial part of the book is devoted to this. Then we tackle the more difficult problem of considering equations with variable coefficients. A large number of such equations are solved by comparing them to equations with constant coefficients.In numerous applications in the sciences, students and researchers are required to solve such equations in order to get the answers that they need. In many cases, the basic scientific theory requires the resulting partial differential equation to have a solution, and one is required to know how many solutions exist. This book deals with such situations.

Handbook of Linear Partial Differential Equations for Engineers and Scientists

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Publisher : CRC Press
ISBN 13 : 1420035320
Total Pages : 800 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Linear Partial Differential Equations for Engineers and Scientists by : Andrei D. Polyanin

Download or read book Handbook of Linear Partial Differential Equations for Engineers and Scientists written by Andrei D. Polyanin and published by CRC Press. This book was released on 2001-11-28 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering. Parabolic, hyperbolic, and elliptic equations with

Partial Differential Equations and Boundary-Value Problems with Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 0821868896
Total Pages : 545 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Partial Differential Equations and Boundary-Value Problems with Applications by : Mark A. Pinsky

Download or read book Partial Differential Equations and Boundary-Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.

A Friendly Introduction to Differential Equations

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Publisher : CreateSpace Independent Publishing Platform
ISBN 13 : 1506004539
Total Pages : 163 pages
Book Rating : 4.5/5 (6 download)

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Book Synopsis A Friendly Introduction to Differential Equations by : Mohammed K A Kaabar

Download or read book A Friendly Introduction to Differential Equations written by Mohammed K A Kaabar and published by CreateSpace Independent Publishing Platform. This book was released on 2015-01-05 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, there are five chapters: The Laplace Transform, Systems of Homogenous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In addition, there are exercises at the end of each chapter above to let students practice additional sets of problems other than examples, and they can also check their solutions to some of these exercises by looking at "Answers to Odd-Numbered Exercises" section at the end of this book. This book is a very useful for college students who studied Calculus II, and other students who want to review some concepts of differential equations before studying courses such as partial differential equations, applied mathematics, and electric circuits II.

Linear Differential Operators with Constant Coefficients

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Publisher : Springer
ISBN 13 :
Total Pages : 464 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Linear Differential Operators with Constant Coefficients by : Viktor Pavlovich Palamodov

Download or read book Linear Differential Operators with Constant Coefficients written by Viktor Pavlovich Palamodov and published by Springer. This book was released on 1970 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic exposition of the facts relating to partial differential equations with constant coefficients. The study of systems of equations in general form occupies a central place. Together with the classical problems of the existence, the uniqueness, and the regularity of the solutions, we also consider the specific problems that arise in connection with overdetermined and underdetermined systems of equations: the extendabiIity of the solutions into a wider region, the extendability of regularity, M-cohomology and so on. Great attention is paid to the connections and the parallels with the theory of functions of several complex variables. The choice of material was dictated by a number of considerations. Among all the facts relating to general systems of equations, the book contains none that relate to the behavior of differential operators in spaces of slowly growing functions. Missing also are results relating to a single equation in one unknown function: the correctness of the Cauchy problem, certain theorems on p-convexity, and the theory of boundary values, are all set forth in other monographs (Gel'fand and Silov [3], Hormander [10] and Treves [4]). The book consists of two parts. In the first, we set forth the analytic method which forms the basis for the contents of the second part, which itself is dedicated to differential equations. The first part is pre ceded by an introduction in which the content and methods of Part I are described. All the notes and bibliographical references are collected together in a special section.

Lectures on Cauchy's Problem in Linear Partial Differential Equations

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Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.:/5 (1 download)

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Book Synopsis Lectures on Cauchy's Problem in Linear Partial Differential Equations by : Jacques Hadamard

Download or read book Lectures on Cauchy's Problem in Linear Partial Differential Equations written by Jacques Hadamard and published by . This book was released on 1923 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: