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Spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of their 1988 book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since then.

This second new treatment, Evolution to Complex Geometries and Applications to Fluid Dynamics, provides an extensive overview of the essential algorithmic and theoretical aspects of spectral methods for complex geometries, in addition to detailed discussions of spectral algorithms for fluid dynamics in simple and complex geometries. Modern strategies for constructing spectral approximations in complex domains, such as spectral elements, mortar elements, and discontinuous Galerkin methods, as well as patching collocation, are introduced, analyzed, and demonstrated by means of numerous numerical examples. Representative simulations from continuum mechanics are also shown. Efficient domain decomposition preconditioners (of both Schwarz and Schur type) that are amenable to parallel implementation are surveyed. The discussion of spectral algorithms for fluid dynamics in single domains focuses on proven algorithms for the boundary-layer equations, linear and nonlinear stability analyses, incompressible Navier-Stokes problems, and both inviscid and viscous compressible flows. An overview of the modern approach to computing incompressible flows in general geometries using high-order, spectral discretizations is also provided.

The recent companion book Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions. The essential concepts and formulas from this book are included in the current text for the reader’s convenience.

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Simplex geometry is a topic generalizing geometry of the triangle and tetrahedron. The appropriate tool for its study is matrix theory, but applications usually involve solving huge systems of linear equations or eigenvalue problems, and geometry can help in visualizing the behaviour of the problem. In many cases, solving such systems may depend more on the distribution of non-zero coefficients than on their values, so graph theory is also useful. The author has discovered a method that in many (symmetric) cases helps to split huge systems into smaller parts. Many readers will welcome this book, from undergraduates to specialists in mathematics, as well as non-specialists who only use mathematics occasionally, and anyone who enjoys geometric theorems. It acquaints the reader with basic matrix theory, graph theory and elementary Euclidean geometry so that they too can appreciate the underlying connections between these various areas of mathematics and computer science. ... Read more

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This monograph presents the basic theorems of differential geometry in three-dimensional space, including a thorough coverage of surface theory. By means of a series of carefully selected and representative mathematical models this monograph also explains at length how these theorems are used in three-dimensional elasticity and in shell theory. The presentation is essentially selfcontained, with a great emphasis on pedagogy. In particular, no "a priori" knowledge of differential geometry or of elasticity theory is assumed, the only requirements are a reasonable knowledge of basic analysis, functional analysis, and some acquaintance with ordinary and partial differential equations.

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Merrill Geometry Applications and Connections, LESSON PLANS (Includes a detailed one-page lesson plan master for every lesson in Merrill Geometry) ... Read more

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One of the authors' stated goals for this publication isto "modernize" the course through the integration ofMathematica. Besides introducing students to the multivariable uses ofMathematica, and instructing them on how to use it as a tool insimplifying calculations, they also present intoductions to geometry,mathematical physics, and kinematics, topics of particular interest toengineering and physical science students. In using Mathematica as atool, the authors take pains not to use it simply to define things asa whole bunch of new "gadgets" streamlined to the taste of theauthors, but rather they exploit the tremendous resources built intothe program.

They also make it clear that Mathematica is not algorithms. At thesame time, they clearly see the ways in which Mathematica can makethings cleaner, clearer and simpler. The problem sets give students anopportunity to practice their newly learned skills, covering simplecalculations with Mathematica, simple plots, a review of one-variablecalculus using Mathematica for symbolic differentiation, integrationand numberical integration. They also cover the practice ofincorporating text and headings into a Mathematica notebook. ADOS-formatted diskette accompanies the printed work, containing bothMathematica 2.2 and 3.0 version notebooks, as well as sampleexamination problems for students. This supplementary work can be usedwith any standard multivariable calculus textbook. It is assumed thatin most cases students will also have access to an introductory primerfor Mathematica. ... Read more

Customer Reviews (1)

awful book
This is one of the worst technical books I have ever read. It seems like something cobbled together. It teaches very little vector calculus or mathematica. ... Read more

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This book contains more than two thousand exercises in algebra. These exercises are currently used in teaching a fundamental course in algebra in the Department of Mechanics and Mathematics at Moscow State University. The text is divided into three parts, which correspond to three semesters of study. Each section contains not only standard exercises, but also more difficult exercises at the end of some sections, these more challenging exercises being marked with asterisks. At the end of the book results of calculations, a list of notations and basic definitions are given. ... Read more

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The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.

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Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks. Combinatorial Geometry and Its Algorithmic Applications is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography. ... Read more

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Over the past fifteen years, the geometrical and topological methods of the theory of manifolds have assumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics. The three volumes of "Modern Geometry - Methods and Applications" contain a concrete exposition of these methods together with their main applications in mathematics and physics. This third volume, presented in highly accessible languages, concentrates in homology theory. It contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto. Both scientists and students of mathematics as well as theoretical physics will find this book to be a valuable reference and text. ... Read more

Customer Reviews (2)

One of the best treatises on geometry/topology available these days!
I first got acquainted with Dubrovin/Novikov/Fomenko collection when I was still a second year (sophomore in the US system) student in Math-Phys
trying to learn the basics on plane/space differential curves as a
complement for my Calculus courses. And since then I've made countless references to this book and its siblings.

The pace is fast compared to
other well known introductions on differential geometry/topology
but the text has many insightful and non-trivial examples
examples. Challenging problems are present everywhere in the text!
Though there are a few problems per chapter, the problems sometimes really
require some mastery of the material being far from immediate
applications of the theory developed(for the joy or despair of the
reader). Intentionally the authors try, whenever possible, to replace calculations and
difficult deductions with conceptual proofs. Frequent links with
physical theories (e.g. mechanics, electromagnetism, general
relativity, field theory etc.) compound a good deal of the text
which makes its reading still more delightful. As a con, I would
say the text is quite hard for a beginner but stubborness pays-off in this case.
The second volume of this series covers differential topology w/ emphasis on many aspects of modern physics, like GR, solitons and Yang-Mills theory. There's also a nice account on complex manifolds, mainly Riemman surfaces and it's relation to Abel's thm. Among other topics: classification of compact surfaces , hyperbolic geometry etc.
The third volume covers Homology theory and included a readable account of Spectral sequences for those who may need to learn the machinery for qualifications exams and or applications of complex geometry to contemporary physics (e.g. twistor theory). Viktor Prasolov has recently published a treatise on Homology with more problems and more rigorous proofs. A nice complement to Novikov's exposition.
Eclectic, but at the same time superb.

You should read this if you can afford the price.
I feel puzzled nobody so far has reviewd this excellent text by Novikov (and Fomenko).The view-point is somewhat different from Bredon or May or Spanier, but together with Part 2, they forma good introduction to"geometric" topology. ... Read more

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This book begins with a new approach to the geometry ofpseudo-Finsler manifolds. It also discusses the geometry ofpseudo-Finsler manifolds and presents a comparison between the inducedand the intrinsic Finsler connections. The Cartan, Berwald, and Rundconnections are all investigated. Included also is the study oftotally geodesic and other special submanifolds such as curves,surfaces, and hypersurfaces.
Audience: The book will be of interest to researchers working onpseudo-Finsler geometry in general, and on pseudo-Finsler submanifoldsin particular. ... Read more

Customer Reviews (1)

For the first time!
This book is considered the first one in the field which is a very powerful and nicely organized book. Both Professor Aurel Bejancu and Professor Hani farran (Authors of the book) are of the best researchers and teachers in Kuwait University. I wish them all the best.
Hussain ... Read more

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Are you looking for a concise summary of the theory of Schrödinger operators? Here it is. Emphasizing the progress made in the last decade by Lieb, Enss, Witten and others, the three authors don’t just cover general properties, but also detail multiparticle quantum mechanics – including bound states of Coulomb systems and scattering theory. This corrected and extended reprint contains updated references as well as notes on the development in the field over the past twenty years.

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This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers---including two articles by Mandelbrot---provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry.

In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications.

This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications. ... Read more

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Chapter Tests-2 Forms, Quizzes, Performance-Based Assessment ... Read more

Customer Reviews (2)

This is book is completely lacking in everything.
This book is lacking in examples, diagrams and as well as facts and information. The diagrams that are present do not provide the necessary information to actually LEARN form the book. As a result, we have to deviate from the textbook making it completely comfusing. DO NOT BUY THIS BOOK. It is simply not worth it.

I suggest Prentice Hall if you need a book, after using Prentice Hall for several years; I find it completely helpful and easy to learn from.

The book has few examples and it doesn't show HOW to do the problem, rather, it just explains what the problem is and quickly gives the solution. The chapters are organized in a fashionable manner but it is lacking in material, the answers are at the back of the book but what really ticks me off is the 'real life problems'. They give 4-5 of those in a lesson and they take at least half an hour of think and writing [that doesn't involve math' and then on the test, they never show up becuase the problem had nothing to do with the chapter. The book is just lacking in materials. Look at the publiciation date. 1998--this book is just wayyy out dated.

The perfect one!
Now this is type of Geometry book it should be. More examples, answer key, and a glossary. Unlike that complicated Michael Serra Geometry book from hell. ... Read more

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Contains one practice Master for every lesson in geometry. Full-size answers make it easy for teacher or student to check their work. ... Read more

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In recent years noncommutative geometry has been a richtopic of research with discoveries leading to an increasing number ofapplications in mathematics and theoretical physics.Very little hasappeared in book form since Alain Connes' work in the early 90s todeal with this subject."Elements of Noncommutative Geometry" fillsan important gap in the literature.

Key features of the work include: * unified and comprehensive presentation of core topics and key research results drawing from several branches of mathematics
* rigorous, well-written, nearly self-contained exposition of noncommutative geometry and some of its useful applications to quantum theory
* excellent exposition of introductory material; main topics covered repeatedly in the text at gradually more demanding levels of difficulty
* many applications to diverse fields: index theory, foliations, number theory, particle physics, and fundamental quantum theory
* rich in proofs, examples and exercises
* comprehensive bibliography and index

This text is an introduction to the language and techniques ofnoncommutative geometry at a level suitable for graduate students, andalso provides sufficient detail to be useful to physicists andmathematicians wishing to enter this rapidly growing field.It mayalso serve as a reference text on several topics that are relevant tononcommutative geometry. ... Read more

Customer Reviews (2)

right complement
Pepe and Joe have been involved in NCG research
since the first physical calculations. And
the book happened to be published in a very
adequate time range, so it contains up-to-date
information on all the developments, including
the finding of Connes-Kreimer renormalization
algebra (hopf algebras and butcher groups).

It is a compulsory complement to Connes's book.

right complement
Pepe and Joe have been involved in NCG research
since the first physical calculations. And
the book happened to be published in a very
adequate time range, so it contains up-to-date
information on all the developments, including
the finding of Connes-Kreimer renormalization
algebra (hopf algebras and butcher groups).

It is a compulsory complement to Connes's book. ... Read more

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This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a self-contained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role.

The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and mesh generation in finite element methods.

This volume will be very useful to graduate students and researchers in pure and applied mathematics.

Contents: An Introduction to Differential Geometry in 3 (P G Ciarlet); An Introduction to Shell Theory (P G Ciarlet & C Mardare); Some New Results and Current Challenges in the Finite Element Analysis of Shells (D Chapelle); A Differential Geometry Approach to Mesh Generation (P Frey). ... Read more