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Symplectic Geometry and Quantum Mechanics (Operator Theory: Advances and Applications / Advances in Partial Differential Equations)
Maurice de Gosson
Manufacturer: Birkhäuser Basel
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ASIN: 3764375744 |
Book Description
This book is devoted to a rather complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.
Book Description
Designed to prepare readers to better understand the current literature in research journals, this book explains the basics of classical PDEs and a wide variety of more modern methods—especially the use of functional analysis—which has characterized much of the recent development of PDEs. It gives equal treatment to elliptic, hyperbolic, and parabolic theory, and features an abundance of applications to equations that are important in physics and engineering—both on the basic and more advanced level. Provides worked, figures and illustrations, and extensive references to other literature. First-Order Equations. Principles for Higher-Order Equations. The Wave Equation. The Laplace Equation. The Heat Equation. Linear Functional Analysis. Differential Calculus Methods. Linear Elliptic Theory. Two Additional Methods. Systems of Conservation Laws. Linear and Nonlinear Diffusion. Linear and Nonlinear Waves. Nonlinear Elliptic Equations. Appendix on Physics. For anyone using PDEs in physics and engineering applications.
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Design Theory (Encyclopedia of Mathematics and its Applications)
Thomas Beth ,
D. Jungnickel , and
H. Lenz
Manufacturer: Cambridge University Press
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ASIN: 0521772311 |
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This volume concludes the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to reflect this. In particular, the growing importance of discrete mathematics to many parts of engineering and science have made designs a useful tool for applications, a fact that has been acknowledged here with the inclusion of an additional chapter on applications. The volume is suitable for advanced courses and for reference use, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. Features include exercises and an extensive, updated bibliography of well over 1800 citations.
Book Description
This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web. This book presents the key ideas along with many figures, examples, and short, elegant MATLAB programs for readers to adapt to their own needs. It covers ODE and PDE boundary value problems, eigenvalues and pseudospectra, linear and nonlinear waves, and numerical quadrature.
Customer Reviews:
setting a precedent in numerical methods books.......2006-05-31
i would have given it a 4-stars, but i feel that i need to counter the negative comment by a reader below who complains that the book is loaded with errors.
first i should say i am not a mathematician although i used mathematics and numerical methods frequently. so there are certainly many details that i overlook or ignore.
in my opinion, most of the errors in the book (inc those not listed on trefethen's website but which i have noticed) are insignificant and inconsequential. they are things like writing 'n' instead of 'N'; the confusions and errors in the indices (this is due to matlab must start from '1', while frequently we are used to start from '0' when writing the mathematics); calling something obvious an inappropriate name, etc. to me, these are trivial errors. (if you are a numerical analysis theorist, i accept that you don't agree with me). only a handful of errors are actually serious in terms of the mathematics, and i believe the number of them are acceptable. every book has errors.
at the level i am reading this book, i just need an introduction to the theory, and then start computing. as far as i am concerned, if the mathematics is seriously wrong, you will notice when you do the computing.
what i like about the book is that it starts you computing right from the first chapter. although mathematical softwares such as matlab have been around for one to two decades, until recently not many books on numerical methods give you an opportunity to do the computations yourself. if the matlab scripts were not provided, i doubt that many would know how to code them (in any language you are familiar with); or even if you do, you may be doing it in an inelegant or inefficient way.
i used to wonder what is the use of a book on advanced numerical methods. for example, i would not know how to write a fluid dynamics code using spectral method to do direct numerical simulation of turbulent flows after reading and even mastering, say, Canuto et al's Spectral Dynamics in Fluid Dynamics. on the other hand, if i am familiar with spectral methods programming, it is also likely that i am familiar with the theory. so what these books are for is just as a store of knowledge and convenient references. you may know that the kind of fluid dynamics code i mentioned above can require a team effort over many years. so most numerical methods books which claim to cover applications are in fact useless, except you are already a practitioner, when come to developing codes for modern advanced simulations.
however, i think introductory books should have examples of how the computer codes to some numerical methods actually look like. before these past few years, i didn't see any such book. only recently, there are at least a dozen books on numerical methods or differential equations with C/C++, Matlab, etc. and i think trefethen's book is setting an example on how to do this without much fuss and long discourse. who knows, you may also learn the basic skills require to work on a much more complicated piece of computational code.
also, trefethen never claims that you can learn matlab with this book. he suggested, for example, higham & higham's matlab guide.
lastly, i should say one should not judge a book by the personality of the author. he may (or may not) be arrogant, but that does not necessarily make his book bad. (it appears to me that the reader below is the arrogant one. just because trefethen probably didn't give him responsive and 'grateful' replies, he wrote this review here).
Loaded with errors, author defensive and arrogant.......2004-06-21
I found glaring errors starting on page 1. I emailed the author for clarification who agreed that his nomenclature was unclear and misleading (come on Professor, we call them mistakes, errata, etc.). The first chapter is available in his web site, go see for yourself. You'll also find a page of errata, which unfortunately is far from complete. My colleagues and I desperately tried to get Professor Trefethen to clarify his nomenclature, which he quite arrogantly dismissed. His matlab code seems to execute fine, but you'll likely spend a good deal of time dissecting it. Any programmer who must use someone elses code despises poorly commented and optimized code. This book just isn't a good place to start for spectral methods or matlab.
A useful introduction to spectral methods.......2001-03-21
The author achieves the hard task of explaining the subject in a very simple and, at the same time, intelligent way. The MATLAB m-files are short, educative and full of useful tricks. The book is well motivated, focused in the essentials and easy to read. I am very fond of most of Prof. Trefethen writings and this book is no disappoitment. It contrasts starkly with the lack of mathematical insight in most of the engineering collocation literature, but at the same time has a hands-on approach to the problems. This book should be useful to anybody interested in solving PDE in regular geometries.
Book Description
From the reviews: "Since E. Hille and K. Yoshida established the characterization of generators of C0 semigroups in the 1940s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory. Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications in a clear and interesting manner. The choice and order of the material, the clarity of the proofs, and the overall presentation make this an excellent place for both researchers and students to learn about C0 semigroups." #Bulletin Applied Mathematical Sciences 4/85#1 "In spite of the other monographs on the subject, the reviewer can recommend that of Pazy as being particularly written, with a bias noticeably different from that of the other volumes. Pazy's decision to give a connected account of the applications to partial differential equations in the last two chapters was a particularly happy one, since it enables one to see what the theory can achieve much better than would the insertion of occasional examples. The chapters achieve a very nice balance between being so easy as to appear disappointing, and so sophisticated that they are incomprehensible except to the expert." #Bulletin of the London Mathematical Society#2
Customer Reviews:
The content is optimal, the printing is poor.......2007-03-21
Although the book is a compilation of class notes, it is very well written, and suitable for the level of a second or third year graduate student. The only needed background is strong foundation on functional analysis. The author explain very well how semigroups become the state of the art for applied mathematicians.
On the other side, the printing of the book is very poor, the letters actually tend to disapear in several pages and I'm not the only that went thru this.
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Lie Pseudogroups and Mechanics (Mathematics and Its Applications)
J. F. Pommaret
Manufacturer: Routledge
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Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (Ergebnisse der Mathematik und ihrer Grenzgebiete. ... / A Series of Modern Surveys in Mathematics)
Michael Struwe
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Calculus of Variations (Cambridge Studies in Advanced Mathematics)
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Functional Analysis (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
ASIN: 3540664793 |
Book Description
Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radó. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The third edition gives a survey on new developments in the field. References have been updated and a small number of mistakes have been rectified.
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Multi-Grid Methods and Applications (Springer Series in Computational Mathematics)
W. Hackbusch
Manufacturer: Springer
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ASIN: 0387127615 |
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The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow. The material is organized into four groups of two chapters each, covering the Poisson equation (chapters 1 & 2); the convection-diffucion equation
(chapters 3 & 4); the Stokes equations (chapters 5 & 6); and the Navier-Stokes equations (chapters 7 & 8). These equations represent important models within the domain of computational fluid dynamics, but they also arise in many other settings. For each PDE model, there is a chapter concerned with
finite element discretization. For each problem and associated solvers there is a description of how to compute along with theoretical analysis which guides the choice of approaches. Illustrative numerical results occur throughout the book, which have been computed with the freely downloadable
IFISS software. All numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the 'computational laboratory' provided by the software. This book provides an excellent introduction to finite elements, iterative linear solvers
and scientific computing aimed at graduates in engineering, numerical analysis, applied mathematics and interdisciplinary scientific computing. Including theoretical problems and practical exercises closely tied with freely downloadable MATLAB software, this book is an ideal teaching and learning
resource.
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Vortices in the Magnetic Ginzburg-Landau Model (Progress in Nonlinear Differential Equations and Their Applications)
Etienne Sandier , and
Sylvia Serfaty
Manufacturer: Birkhäuser Boston
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ASIN: 0817643168 |
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With the discovery of type-II superconductivity by Abrikosov, the prediction of vortex lattices, and their experimental observation, quantized vortices have become a central object of study in superconductivity, superfluidity, and Bose--Einstein condensation. This book presents the mathematics of superconducting vortices in the framework of the acclaimed two-dimensional Ginzburg-Landau model, with or without magnetic field, and in the limit of a large Ginzburg-Landau parameter, kappa.
This text presents complete and mathematically rigorous versions of both results either already known by physicists or applied mathematicians, or entirely new. It begins by introducing mathematical tools such as the vortex balls construction and Jacobian estimates. Among the applications presented are: the determination of the vortex densities and vortex locations for energy minimizers in a wide range of regimes of applied fields, the precise expansion of the so-called first critical field in a bounded domain, the existence of branches of solutions with given numbers of vortices, and the derivation of a criticality condition for vortex densities of non-minimizing solutions. Thus, this book retraces in an almost entirely self-contained way many results that are scattered in series of articles, while containing a number of previously unpublished results as well.
The book also provides a list of open problems and a guide to the increasingly diverse mathematical literature on Ginzburg--Landau related topics. It will benefit both pure and applied mathematicians, physicists, and graduate students having either an introductory or an advanced knowledge of the subject.
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