Book Description
Translated by Richard Silverman. Famous Russian work covers basic theory of the more important special functions and their application to specific problems of physics and engineering. Most space devoted to application of cylinder functions and spherical harmonics. Also treated: gamma function, probability integral and related functions, Airy functions, hyper-geometric functions, more.
Customer Reviews:
Excellent book for people who want to actually apply special functions........2006-01-19
As the title indicates, the book is designed with the goal of application front and center. That said, it is also important to note that the theoretical background is developed with full mathematical rigor. You can easily see this from the fact that whenever an infinite series is differentiated, its uniform convergence in the region of interest is always established beforehand. And this is just one example.
Now, given the fact that special functions is a vast subject, and the fact that the book is barely 300 pages long, it is obvious that the theoretical coverage, though rigorous, has to be reined in. By this I refer to the fact that most functions are developed from the point of view of series solutions to differential equations, while solution by contour integrals in the plane is basically absent. But then again, it doesn't matter how you develop the functions, the key is to know their properties and be able to apply them. The book will show you just how to do that. HIGHLY RECOMMENDED.
For a more broad-based theoretical coverage, I recommend Whittaker and Watson (but of course), and the book "Special Functions" by X. Z. Wang. These two books complement each other like lovers.
extremely useful, very concise.......2005-08-10
Well worth buying, extremely handy, tons of information very much organized for you
Excellent discussion of the functions used to solve PDE.......2003-03-14
Yet another excellect translation by Silverman. I've only been in possession of this book for a few days but it's already becoming a favorite mathematics text. Not a pure mathematics text but certainly a very thorough, lucid and most certainly enjoyable discussion of applied mathematics with a particularly engaging discussion of the solution of partial differential equations (Laplacian, Poisson etc.) by means of separation of variables and integral transforms. Along the way it develops the theoretical essentials of gamma functions, exponential integrals, orthogonal polynomials, Bessel functions, spherical harmonics among others. Clearly written with an emphasis on explaining the process of discovering solutions rather than merely presenting particular solutions (though it does have enlightening examples). IMO, well worth the price.
A good book on this subject.......2002-08-28
Of course this book cannot be compared to " A course of modern analysis ", but as a book in special functions, it have served its purpose. I would also like to make a tribute to Richard Silverman for translating ( not just direct traslating, he translate in a style make it readable to English world. )
Excellent Source of Applications for Special Functions.......2000-06-03
This is a book which I cannot say much about except for the unusual thoroughness, accompanied by detail and depth in treatment of the underlying mathematical properties and applications of Special Functions.
Lebedev is the quintessential mathematical expert in applying Special Functions to problems in Physics and Engineering, being that he can illustrate all important concepts clearly and umambiguously with carefully prepared diagrams as well as words. I was able to cite the solution of the a problem involving a propagating electromagnetic wave along a transmission line for an important Engineering course project. For such a problem, Lebedev offers a far more detailed and precise solution with given Special Functions than anything I have ever seen in other books of the same nature with the possible exception of a specialized treatise by an MIT EE faculty member on applied electromagnetism. He also comes across as meticulous in derivations of solutions to problems worked out compared to many other authors whose works I have read. This is because he hardly ever skips an important step in deriving a solution for any given problem by leaving it out for the reader's imagination. Yet we know Lebedev as perhaps a mathematician who may not be realistically expected to come up with such complete and exhaustive solutions to practical or real-world problems, worked out with clarity as well as precision and depth. There are numerous other examples which he worked out for different applications (e.g, Legendre's and Laguerre's functions) invariably after he took pains to delineate the various mathematical properties of the Special Functions utilized to obtain the closed-form solutions. He also covers various mathematical functions which may not be as familiar to many engineering practitioners but nonetheless have an important place in applied mathematical analysis. In a sense, he saves them for occasions when we as readers may need to probe further into unfamiliar territory.
So if you are looking for depth and precision in analysis of physical problems in Engineering and Science, or are trying to cope with reaearch problems in Applied Mathematics, try out this book by Lebedev. It can initially come across as difficult to understand, but Lebedev expects the reader to follow along through diligence. It is almost one of a kind, being that it is very clear and lucid without noticeable loss in depth and mathematical rigor. I highly recommend it because I believe that few other books can even come close in offering good examples in solutions to real-world problems and, at the same time, demonstrate the power of Special Functions in applications. Of course, it is also very inexpensive.
Book Description
This revised and updated Second Edition of Green's Functions and Boundary Value Problems maintains a careful balance between sound mathematics and meaningful applications. Central to the text is a down-to-earth approach that shows the reader how to use differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics.
Ivar Stakgold incorporates developments that have altered the field of applied mathematics in recent decades—particularly in areas of modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods. This modernized text, however, retains the many features that made its predecessor one of the most successful graduate-level texts of its kind, including:
- A unique blend of topics
- A balanced discussion of theory and applications
- 44 illustrations and numerous practical examples that supplement the text
- Chapter introductions and clear explanations of basic concepts
- Plentiful exercises, many of which are new to this edition
Green's Functions and Boundary Value Problems is an ideal text for a modern course in applied mathematics designed for students in the physical sciences, engineering, and mathematics. It is also an excellent reference for practicing professionals in these areas.
Customer Reviews:
Systematic, not a 'cookbook'.......2002-05-10
Actually, I preferred the first (2 volume) edition of this work and used the first volume along with Whittaker and Watson to teach first semester math methods to physics and engineering students. This book provides the most readable, systematic approach to boundary-value problems, based on Weyl's lemma. Not to be compared with the usual cookbooks on math methods because it shows you how to construct nonstandard orthogonal expansions, not merely the usual Fourier, Bessel and Legendre variety. Also very good on Dirac's delta funaction. For second semester, for years I also used Bender and Orszag.
G is called 'the Green function' and not 'the Green's function' (one does not say 'the Bessel's function').
This is one of the best books on applicable PDE's.......1997-02-26
This is a classic text. The authors not only knows much more than is in the book but also has a clear idea about the applied side of math.
A close competitor is Sobolev's book on PDE's.
Average customer rating:
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Theory of Function Spaces III (Monographs in Mathematics)
Hans Triebel
Manufacturer: Birkhäuser Basel
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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 |
Book Description
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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Complex Hyperbolic Geometry (Oxford Mathematical Monographs)
William M. Goldman
Manufacturer: Oxford University Press, USA
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Book Description
Complex hyperbolic geometry is a particularly rich area of study, enhanced by the confluence of several areas of research including Riemannian geometry, complex analysis, symplectic and contact geometry, Lie group theory, and harmonic analysis. The boundary of complex hyperbolic geometry, known as spherical CR or Heisenberg geometry, is equally rich, and although there exist accounts of analysis in such spaces there is currently no account of their geometry. This book redresses the balance and provides an overview of the geometry of both the complex hyperbolic space and its boundary. Motivated by applications of the theory to geometric structures, moduli spaces and discrete groups, it is designed to provide an introduction to this fascinating and important area and invite further research and development.
Book Description
This incisive text, directed to advanced undergraduate and graduate students in mathematics, physics and engineering, deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. 570 exercises.
Customer Reviews:
Rigor and intuition -- a classic.......2000-11-17
I learned Fourier analysis on my own, and mostly from this book. Its intuitive content is excellent, but it is a rigorous math text, approaching the subject form an algrbraic viewpoint. He treats convergence issies in detail and in a well-motivated fashion. "Read Who is Fourier" for an intro, and read this for the math behind the intuition.
FOURIER SERIES, THE SOLUTION TO ALL ENGRG PROBLEMS........2000-05-02
During the course of my studying the book, i discovered that the book goes indepth in making the concept of fourier series analysis simplified. As an engineer i make use of fourier series applications often both in my research work and in the teaching of my students to a great extent i have found this book extremely useful in that it aids the level of understanding. I have also realised that even to a novice that picks up this book will find it very interesting to a large extent.As it is known that fourier series is very usefu in engineering study , especially in the area of solving heat condition problems and for specific applications in engineering design. The book has taken a more comprehensive form which makes reading very easy . I prefer this book because it follows a progressive sequence of explanation.The introduction of fourier integral into the fourier series solution has brought to a great extent the use of partial differential equations in eral life engineering problems . The book has also made the engineering concepts defined practicable, by demonstration of a straight forward attempt aimed at pionting out the extent to which engineerig is usefuk in our everyday lives. This book should be recomended in schools as the true book avalaible in the understanding of the concept of fourier series. Orthogonal function study has also been made in such a way that a first time reader will find it easy in terms of the concept and context.
Average customer rating:
- A wonderful book
- Very thorough, very challenging exercises.
|
Classical Complex Analysis (Jones and Bartlett Books in Mathematics and Computer Science)
Liang-Shin Hahn , and
Bernard Epstein
Manufacturer: Jones & Bartlett Publishers
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ASIN: 086720494X |
Customer Reviews:
A wonderful book.......2007-04-27
For me this text is a joy and a delight. In the preface the authors remark that to acquire a thorough grasp of the subject requires hard work They assert the virtues of this book to be clarity of presentation, selection of topics, and interesting exercises. They express their hope that the book will help the student to become as enthusiastic about the subject as the authors are. In my case they achieve their goals.
Very many years ago I took complex analysis in grad school using the then-recent text by Ahlfors, and with a 100% Teutonic professor; I then found the subject boring. This book, however makes me enthusiastic. It is one of the few math texts I own that I like for bedtime reading, opening it to something of interest, or just to a random section or some exercises, and relaxing while reading as if it were an adventure novel. When I put it down, consequences trickle through my mind as I go to sleep. No, it's not an easy subject, but the authors make it an enthralling one, at least for me.
Very thorough, very challenging exercises........2006-06-16
This is not the easiest book on complex analysis to read, but nevertheless I really like it. If I had to use one word to describe it, it would be thorough. I have not read much beyond the first half of it, so my comments do not apply to the more advanced chapters.
The prose is sometimes clear, but at times you have to think very hard to get through it. Although there are a number of diagrams, I do not find them particularly helpful. The book does not move too fast, it actually moves quite slowly, but it explores a lot--it is very thorough.
This book has a ton of exercises, and some of them are very hard and very deep. I think the exercises are the best part of this book. This book makes me realize that a lot of other complex analysis textbooks do not have enough exercises, especially challenging ones. My favourite part are the exercises that explore counterexamples to converses of theorems. There are also a lot of great exercises involving infinite series.
I think this book would be most appropriate to someone who had already taken an undergraduate course in complex analysis and was taking a more advanced graduate course, or wanted to enrich their understanding on their own. This is a study text, not a reference text; it is ideal for learning and challenging a student. It is not concise, and it is harder to follow than the books by Lang, Newman & Bak, or Gamelin. However, I am convinced that someone reading this book would reach a deeper understanding of the subject than someone reading any of those other books.
Book Description
This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. For the 4th edition, the concept of the book has been completely re-arranged. The new emphasis is on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing.
Customer Reviews:
Excellent reference book.......2007-09-19
I highly recommend the Handbook of Mathematics. It is an excellent resource for every engineering student and professional engineer.
Great, but tough to use.......2007-04-25
This handbook contains more material than I find in any other single source that I happen to have. But I don't use it as frequently as I use the analogous CRC handbook, or MathWorld and Wikipedia on the Web, or the ancient NBS handbook. Why not? Because one uses a handbook, not as a textbook, but as a source for things one should know, but don't (or perhaps once knew but have forgotten). So one wants to find the thing one is looking for, refresh or extend one's memory, and then put the handbook aside and go back to the problem one is trying to solve. I have trouble locating what I'm looking for in Bronshtein and Semendayev, and when I find it, I often find that I have to look up things elsewhere in the volume to get all of whatever it is I was looking for. So I try my other sources first, and if they don't answer my question, I pick up this book, resignedly, and expect to spend hours rather than minutes getting whatever it is I want to know. There is nothing wrong with that; indeed, this book often supplies me with answers to questions I can't find answered elsewhere.
In case the reader of this review attributes my difficulties with this book to a lack of mathematical background, I'll remark that my academic training, very many years ago, was in math, so I find that I can follow the discussion in this book of any particular thing I look up; it's just a slow process for me. I'm not surprised that it's a favorite in Germany (and in Europe more generally); Europeans in their mathematical training are expected to deal with tough subjects by dogged persistence, and probably feel more comfortable with this style than I do, given my US background. So, overall, it's a book I couldn't do without, but hate having to spend time in.
Loaded with Content.......2005-02-25
This book is exactly what the title says it is; a handbook of mathematical techniques and formulas for scientists and engineers. It is more a handbook than a book on mathematics and assumes a prior knowledge on the subjects covered. Readers of this english version of the Bronshtein should take note that it is a "raw" translation of the german version and so some discussion may not do justice to the theory. This in no way takes away from the fact it is an exceptional book and you'd be hard pressed to find any other book with more mathematical content.
There are several Bronshteins.......2004-10-25
Bronstein's "Taschenbuch der Mathematik" is a longtime favorite among german science and engineering students. English language readers should be aware however, that there are numerous different editions of this book. Not only were the german editions constantly enlarged and reworked, but there were also two publishers of the same book, one in East Germany (Teubner Verlag), one in West Germany (Harri Deutsch Verlag). Today both of these publishers sell a "Taschenbuch der Mathematik" based on the original Bronstein, yet they are completely different books. The english edition by Springer Verlag advertised above is based on the current Harri Deutsch edition. An english translation of the Teubner edition is now available as the "Oxford Users' Guide to Mathematics" from Oxford University Press. It is mostly considered to be the better 'Bronstein' (even though Teubner and OUP have dropped his name because the new edition was completely rewritten by E. Zeidler).
Clasic.......2004-03-22
For me it was a remarkable fact, how few of the people in western countries have heard about this handbook. In the east this is probably the most popular mathematical handbook ever. I dont know any eastern european scientist in a field of mathematics, engineering and physics who don't have it. The main reason is it's extensivity and usefulness. In Croatian print it has about 1000 pages in very small format covering all possible parts of applied mathematics up to special functions/markov chains/complex integration/vector algebra. It's "allways in backpack book" and my hot recomandation to any technical scientist.
Book Description
Written by a distinguished physicist and leading researcher, this volume describes the theory and selected applications of one of the most important mathematical tools used in the theoreticial investigation of collective excitations in statistical physics. The text offers an introduction to functional integral techniques in equilibrium statistical physics, and discusses the expression of partition functions and Green functions in terms of functional integrals. Sections of the book deal with the application of functional integrals in superfluid Bose systems, systems with Coulomb interaction, and superfluid Fermi systems. The book also considers the application of the concept of Bose-condensation of auxiliary fields to the theory of crystals, heavy atoms and also to the theory of model Hamiltonians.
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