Analytic Methods for Partial Differential Equations PDF Download
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Author: G. Evans
Publisher: Springer Science & Business Media
ISBN: 1447103793
Category : Mathematics
Languages : en
Pages : 308
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Book Description
This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.
Author: G. Evans
Publisher: Springer Science & Business Media
ISBN: 1447103793
Category : Mathematics
Languages : en
Pages : 308
Get Book Here
Book Description
This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.
Author: Haim Brezis
Publisher: Springer Science & Business Media
ISBN: 0387709142
Category : Mathematics
Languages : en
Pages : 600
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Book Description
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Author: Hiroki Tanabe
Publisher: CRC Press
ISBN: 9780824797744
Category : Mathematics
Languages : en
Pages : 436
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Book Description
Combining both classical and current methods of analysis, this text present discussions on the application of functional analytic methods in partial differential equations. It furnishes a simplified, self-contained proof of Agmon-Douglis-Niremberg's Lp-estimates for boundary value problems, using the theory of singular integrals and the Hilbert transform.
Author: Milan Miklavčič
Publisher: Allied Publishers
ISBN: 9788177648515
Category :
Languages : en
Pages : 316
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Book Description
Author: Mark S. Gockenbach
Publisher: SIAM
ISBN: 0898719356
Category : Mathematics
Languages : en
Pages : 665
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Book Description
A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.
Author: Friedrich Sauvigny
Publisher: Springer Science & Business Media
ISBN: 3540344624
Category : Mathematics
Languages : en
Pages : 401
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Book Description
This encyclopedic work covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Emphasis is placed on the connection of PDEs and complex variable methods. This second volume addresses Solvability of operator equations in Banach spaces; Linear operators in Hilbert spaces and spectral theory; Schauder's theory of linear elliptic differential equations; Weak solutions of differential equations; Nonlinear partial differential equations and characteristics; Nonlinear elliptic systems with differential-geometric applications. While partial differential equations are solved via integral representations in the preceding volume, this volume uses functional analytic solution methods.
Author: Michael Renardy
Publisher: Springer Science & Business Media
ISBN: 0387216871
Category : Mathematics
Languages : en
Pages : 447
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Book Description
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.
Author: Nakhlé H. Asmar
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 904
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Book Description
This reader-friendly book presents traditional material using a modern approach that invites the use of technology. Abundant exercises, examples, and graphics make it a comprehensive and visually appealing resource. Chapter topics include complex numbers and functions, analytic functions, complex integration, complex series, residues: applications and theory, conformal mapping, partial differential equations: methods and applications, transform methods, and partial differential equations in polar and spherical coordinates. For engineers and physicists in need of a quick reference tool.
Author: S. H, Lui
Publisher: John Wiley & Sons
ISBN: 1118111117
Category : Mathematics
Languages : en
Pages : 506
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Book Description
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.
Author: Walter A. Strauss
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
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Book Description
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.
