Book Description
The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
Customer Reviews:
The most reliable source of solvable nonlinear PDEs.......2007-01-17
It is a very rare occasion when a nonlinear partial differential equation admits an exact solution. Such cases are of the utmost importance as they enable the full and most detailed analysis of the problem concerned. This reference book contains the most extended list of nonlinear PDEs known to be solvable to date and gives not only their exact solutions but also solution methods.
It is a really good book.
Book Description
An Introduction to Partial Differential Equations with MATLAB exposes the basic ideas critical to the study of PDEs-- characteristics, integral transforms, Green's functions, and, most importantly, Fourier series and related topics. The author approaches the subject from a motivational perspective, detailing equations only after a need for them has been established. He uses MATLAB software to solve exercises and to generate tables and figures. Included This volume includes are examples of many important PDEs and their applications. The first chapter introduces PDEs and makes analogies to familiar ODE concepts, then strengthens the connection by exploring the method of separation of variables. Chapter 2 examines the "Big Three" PDEs-- the heat, wave, and Laplace equations, and is followed by chapters explaining how these and other PDEs on finite intervals can be solved using the Fourier series, for arbitrary initial and boundary conditions. Chapter 5 investigates characteristics for both first- and second-order linear PDEs, the latter revealing how the Big Three equations are important far beyond their original application to physical problems. The book extends the Fourier method to functions on unbounded domains, gives a brief introduction to distributions, then applies separation of variables to PDEs in higher dimensions, leading to the special funtions, including the orthogonal polynomials. Other topics include Sturm-Liouville problems, adjoint and self-adjoint problems, the application of Green's functions to solving nonhomogeneous PDEs, and an examination of practical numerical methods used by engineers, including the finite difference, finite element, and spectral methods.
Customer Reviews:
Good and Clear.......2005-08-08
I used this book for the first time this past semester. It is well written, although a bit informal for my taste (although the students seemed to like it). There are numerous exercises, although sometimes too many of the plug-and-chug variety, and I wish there were a few more of the highly challenging problems. The order of topics is exactly the way I like it, except that Chapter 5 is a little out of place. However, in a course like this I think it may be impossible to find a natural place for the method of characteristics. Most texts put it first, which doesn't seem right for a course that emphasizes Fourier methods. For our course, I interchanged Chapters 5 and 6. The MATLAB is not heavily integrated. That is a good thing, for a couple of reasons. It means that the mathematics, and not MATLAB, is the main focus, and it allows the text to be used with or without it. We did use MATLAB and it worked well. Overall, this was a good basic introduction to the subject. It steers a course between mathematical rigor on the one hand, and computation, physical intuition and applications on the other, and it does so quite well. I could envision its being used for a higher level course for scientists and engineers, though not for a course with a more theoretical bent.
Very well written with excellent explanations........2004-11-19
First, I have to say that I'm biased because I'm a former student of Prof. Coleman's (Multivariable Calc and ODE's). But I was happy to see that he had written a PDE book and I bought it so that I could relearn PDE's, since the PDE course I had wasn't so great. I haven't been disappointed. I've read most of the first six chapters so far - the book is easy to read and the explanations are clear. There are tons of homework problems and applications. However, I don't have access to MATLAB so I can't really comment on that aspect of the book.
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Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics (Chapman & Hall/Crc Applied Mathematics and Nonlinear Science)
Victor A. Galaktionov , and
Sergey R. Svirshchevskii
Manufacturer: Chapman & Hall/CRC
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ASIN: 1584886633 |
Book Description
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
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A Stability Technique for Evolution Partial Differential Equations: A Dynamical Systems Approach (Progress in Nonlinear Differential Equations and Their Applications)
Victor A. Galaktionov , and
Juan Luis Vasquez
Manufacturer: Birkhäuser Boston
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ASIN: 0817641467 |
Book Description
This book introduces a new, state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations; much of the text is dedicated to the application of this method to a wide class of nonlinear diffusion equations. The underlying theory hinges on a new stability result, formulated in the abstract setting of infinite-dimensional dynamical systems, which states that under certain hypotheses, the omega-limit set of a perturbed dynamical system is stable under arbitrary asymptotically small perturbations.
The Stability Theorem is examined in detail in the first chapter, followed by a review of basic results and methods---many original to the authors---for the solution of nonlinear diffusion equations. Further chapters provide a self-contained analysis of specific equations, with carefully-constructed theorems, proofs, and references. In addition to the derivation of interesting limiting behaviors, the book features a variety of estimation techniques for solutions of semi- and quasilinear parabolic equations.
Written by established mathematicians at the forefront of the field, this work is a blend of delicate analysis and broad application, appropriate for graduate students and researchers in physics and mathematics who have basic knowledge of PDEs, ordinary differential equations, functional analysis, and some prior acquaintance with evolution equations. It is ideal for a course or seminar in evolution equations and asymptotics, and the book's comprehensive index and bibliography will make it useful as a reference volume as well.
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Methods for Constructing Exact Solutions of Partial Differential Equations: Mathematical and Analytical Techniques with Applications to Engineering
S. V. Meleshko
Manufacturer: Springer
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ASIN: 0387250603 |
Book Description
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
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Nonlinear Partial Differential Equations in Engineering and Applied Science (Lecture Notes in Pure and Applied Mathematics)
Sternberg
Manufacturer: CRC
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ASIN: 0824769961 |
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Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws: and Well-Balanced Schemes for Sources (Frontiers in Mathematics)
François Bouchut
Manufacturer: Birkhäuser Basel
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ASIN: 3764366656 |
Book Description
This book is devoted to finite volume methods for hyperbolic systems of conservation laws. It differs from previous expositions on the subject in that the accent is put on the development of tools and the design of schemes for which one can rigorously prove nonlinear stability properties. Sufficient conditions for a scheme to preserve an invariant domain or to satisfy discrete entropy inequalities are systematically exposed, with analysis of suitable CFL conditions.
The monograph intends to be a useful guide for the engineer or researcher who needs very practical advice on how to get such desired stability properties. The notion of approximate Riemann solver and the relaxation method, which are adapted to this aim, are especially explained. In particular, practical formulas are provided in a new variant of the HLLC solver for the gas dynamics system, taking care of contact discontinuities, entropy conditions, and including vacuum. In the second half of the book, nonconservative schemes handling source terms are analyzed in the same spirit. The recent developments on well-balanced schemes that are able to capture steady states are explained within a general framework that includes analysis of consistency and order of accuracy. Several schemes are compared for the Saint Venant problem concerning positivity and the ability to treat resonant data. In particular, the powerful and recently developed hydrostatic reconstruction method is detailed.
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Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering (Mathematics and Its Applications)
A.W. Leung
Manufacturer: Springer
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ASIN: 0792301382 |
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Variational Methods for Discontinuous Structures: International Workshop in Villa Erba (Cernobbio), Italy, July 2001 (Progress in Nonlinear Differential Equations and Their Applications)
Manufacturer: Birkhäuser Basel
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ASIN: 3764369132 |
Book Description
This volume contains the Proceedings of the International Workshop "Variational Methods For Discontinuous Structures", held at Villa Erba Antica (Cernobbio) on the Lago di Como, July 4-6, 2001. The workshop was jointly organized by the Dipartimento di Matematica Francesco Brioschi of Milano Politecnico and the International School for Advanced Studies (SISSA) of Trieste. In past years the calculus of variations faced mainly the study of continuous structures, particularly problems with smooth solutions. One of the deepest and more delicate problems was the regularity of weak solutions. More recently, new sophisticated tools have been introduced in order to study discontinuities. In many variational problems solutions develop singularities, and sometimes the most interesting part of a solution is the singularity itself. The conference intended to focus on recent developments in this direction. Some of the talks were devoted to differential or variational modelling of image segmentation, occlusion and textures synthesizing in image analysis, variational description of micro-magnetic materials, dimension reduction and structured deformations in elasticity and plasticity, phase transitions, irrigation and drainage, evolution of crystalline shapes. In most cases theoretical and numerical analysis of these models were provided. Other talks were dedicated to specific problems of the calculus of variations: variational theory of weak or lower-dimensional structures, optimal transport problems with free Dirichlet regions, higher order variational problems, symmetrization in the BV framework. This volume contains contributions by 12 of the 16 speakers invited to deliver lectures in the workshop. Most of the contributions present original results in fields which are rapidly evolving at present.
Book Description
Isaac Leybush Peretz (1852-1915) is one of the most influential figures of modern Jewish culture. Born in Poland and dedicated to Yiddish culture, he recognized that Jews needed to adapt to their times while preserving their cultural heritage, and his captivating and beautiful writings explore the complexities inherent in the struggle between tradition and the desire for progress. This book, which presents a memoir, poem, travelogue, and twenty-six stories by Peretz, also provides a detailed essay about Peretz's life by Ruth R. Wisse. This edition of the book includes as well Peretz's great visionary drama A Night in the Old Marketplace, in a rhymed, performable translation by Hillel Halkin.
Books:
- Hockney's Pictures: The Definitive Retrospective
- Implicit Partial Differential Equations (Progress in Nonlinear Differential Equations and Their Applications)
- Intelligent Cities: Innovation, Knowledge Systems and Digital Spaces
- Introduction to Computational Optimization Models for Production Planning in a Supply Chain
- Introduction to Pdes and Waves for the Atmosphere and Ocean (Courant Lecture Notes)
- Introduction to Perturbation Methods
- Introduction to the Theory of Distributions
- Introduction to Vertex Operator Superalgebras and Their Modules (Mathematics and Its Applications)
- $J$-holomorphic Curves and Symplectic Topology (Colloquium Publications (Amer Mathematical Soc))
- Latent Curve Models : A Structural Equation Perspective (Wiley Series in Probability and Statistics)
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Handbook of Exact Solutions for Ordinary Differential Equations, Second Edition
Handbook of Linear Partial Differential Equations for Engineers and Scientists
Handbook of Integral Equations
Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition
Handbook of First-Order Partial Differential Equations (Differential and Integral Equations and Their Applications)
