Book Description

The theory of distributions is an extension of classical analysis, an area of particular importance in the field of linear partial differential equations. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without a knowledge of this. The material in this book, based on graduate lectures given over a number of years requires few prerequisites but the treatment is rigorous throughout. From the outset, the theory is developed in several variables. It is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces. In this second edition, the notion of the wavefront set of a distribution is introduced. It allows many operations on distributions to be extended to larger classes and gives much more precise understanding of the nature of the singularities of a distribution. This is done in an elementary fashion without using any involved theories. This account will be useful to graduate students and research workers who are interested in the applications of analysis in mathematics and mathematical physics. ... Read more

Reviews (1)

An Excellent Introduction
Every physicist and mathematician uses distributions (sometimes called generalized functions), albeit often unknowingly.From its origins in the Dirac delta `function', distribution theory continues to influence many research areas from quantum mechanics to partial differential equations, but has also grown into an important field in its own right.For anyone interested in learning about the field, this is clearly the first port of call.It presents a balanced introduction to the subject on a level suitable for anyone with a basic grounding in analysis (no knowledge of functional analysis is required).

The book begins by defining the two building blocks of the theory---test functions and distributions.It then quickly expands, filling in the important details of differentiation, multiplication, tensor products and convolution.All of this is written with sufficient mathematical rigor, but never too much that it interferes with the basic understanding of the subject, and is supported throughout by useful exercises. The book then builds up the theory of Fourier and Laplace transforms of distributions, which has important applications in the study of linear partial differential equations. The second edition contains an indispensablenew chapter on the calculus of wavefront sets, which, among its uses, allows the propagation of singularities of solutions to partial differential equations to beproperly treated. All in all, while the book is not for the common man, and does require a certain level of mathematical maturity, it does present an excellent introduction to an important, and often poorly understood, area of mathematics. ... Read more

Book Description

This book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material, yet the presentation is simple enough for the book to be used by advanced undergraduate and beginning graduate students. This third edition includes more proofs, more graphs, and more applications. The author has also updated the contents by adding a new chapter on Higher Order Scalar Difference Equations, and also recent results on local and global stability of one-dimensional maps, a new section on the various notions of asymptoticity of solutions, a detailed proof of Levin-May Theorem, and the latest results on the LPA flour-beetle model. ... Read more

Reviews (8)

An Introduction to Difference Equation
El texto An Introduction to Difference Equations del profesor Dr. Saber N. Elaydi ha sido utilizado en reiteradas ocasiones, en el curso Ecuaciones en Diferencias Finitas, dictado por el profesor Dr. Julio López, de la UniversidadLa Frontera de Chile, curso del cual, este semestre soy alumno.

El texto del profesor Elaydi, es un libro que explica de forma amena, clara y precisa, distintos tópicos de Ecuaciones en Diferencias. Comenzando el estudio de los primeros conceptos a tópicos avanzados del tema, destaco dentro de sus muchas cualidades el gran número de ejemplos y aplicaciones expuestas en distintas áreas de las ciencias, además de gran cantidad de ejercicios propuestos, lo que permite al alumno practicar e internalizar las definiciones, proposiciones y teoremas estudiados.Me parece, sin lugar a duda, el texto más claro e interesante que he leído sobre el tema. Cabe destacar que este texto contiene tópicos, que en otros no son tratados. Otra importante cualidad del texto es, que aunque se tiene sólo ediciones en ingles, el profesor Elaydi, ha escrito su libro de tal manera, que no es un impedimento para los hispano parlantes, tenerlo como libro guía en nuestros cursos.

Alex R. Sepúlveda C.
Alumno de Ingeniería Matemática
Universidad de La Frontera
Chile.

One of the Very Best Introductions on Difference Equations.
Among the few introductory texts to difference equations this book is oneof the very best ones. It has many features that the other texts don'thave, e.g., stability theory, the Z-transform method (including a study ofVolterra systems), and asymptotic behavior of solutions of differenceequations (including Levinson's lemma) are studied extensively. It alsocontains very nice examples that primarily arise in applications in avariety of disciplines, including neural networks, feedback control,biology, Markov chains, economics, and heat transfer. Unfortunately, amongdifferential and difference equations, students usually only learn aboutdifferential equations, although many problems they encounter later can besolved using difference equations. Hence it is very useful for students tostudy difference equations (or even, dynamic equations, which canaccomodate differential and difference equations at the same time), and forsuch an undergraduate or beginning graduate course, Saber's book can beused as a textbook. It is particularly useful for such a purpose since itcontains many exercises and also many programs for the calculator TI-85.Although the first edition did contain several misprints, the secondedition has eliminated most of them. Saber's superb writing style makesreading this book very enjoyable.

Exceptional: the defintive book on difference equations
This book is a must read by all those mathematicians, scientists and engineers who like to understand difference equations and discrete dynamics. It contains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations. Ithas an extensive number of applications in a variety of fields from neuralnetwork to host-parasitoid systems. The most enjoyable part of the book isthe new chapter on continued fractions and orthogonal polynomials and thetotally revised chapter on asymptotics. The chapter on stability theory isby far the best exposition on the subject; it updates most of the materialin the popular LaSalle book. I enjoyed very much the lucid and transparentwriting style of Elaydi which many math books lack. I am planning to usethis textbook in my undergraduate course on differnce equations anddynamical systems in the Fall of 2000. There are some minor misprints anderrors that I was able to decipher. The author may need to considerpublishing a solutiion manual since some of the problems in the book arequite challenging. It is also desirable if the author post an errata on hisweb page and/or on amazon.com.

Needs an errata
A very readable text, but I noticed several annoying misprints, mostly involving references to equations, examples, and theorems within the text.

Recommended, but caveat reader.

a wonderful book that fits several levels
This is the best book on modern difference equations. It contains a wide range of material on difference equations and may be very interesting in applications in Physics, Biology, economics and other many subjects. It iseasy and readable for those who want a quick overlook on the subject. Atthe same time it is very deep and goes to high level and leads to manyresearch problems for those who wish that. I am so impressed by this bookthat I am going to translate it into Arabic through the Arabic Organizationfor Education, Culture and Science. Shortly , this is a wonderful book andI strongly recommended it to every scientist who is working and interestedin discrete models ... Read more

Book Description

This book coversboth the classical and representation theoretic views of automorphic forms in a style that is accessible to graduate students entering the field.The treatment is based on complete proofs, which reveal the uniqueness principles underlying the basic constructions.The book features extensive foundational material on the representation theory of GL(1) and GL(2) over local fields, the theory of automorphic representations, L-functions and advanced topics such as the Langlands conjectures, the Weil representation, the Rankin-Selberg method and the triple L-function, and examines this subject matter from many different and complementary viewpoints. Researchers as well as students in algebra and number theory will find this a valuable guide to a notoriously difficult subject. ... Read more

Book Description

The book contains seven survey papers about ordinary differential equations.

The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.

The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications. ... Read more

Book Description

The last two decades have produced tremendous developments in the mathematical theory of wavelets and their great variety of applications in science and engineering. Wavelets allow complex information, such as music, speech, images and patterns to be decomposed into an elementary form called 'building blocks' at different positions and scales. The information is reconstructed with high precision.

In an effort to acquaint researchers in applied mathematics, physics, statistics, computer science, and engineering and to stimulate further research, a regional research convergence was organized at the University of Central Florida in May 1998. Many distinguished applied mathematicians and engineering scientists participated in the conference and presented a digest of recent developments, open questions and unsolved problems in this rapidly growing and important field. As a follow-up project, this book has developed from chapters written by renowned mathematicians and engineering scientists who have important contribution to the subject of wavelets, wavelet transforms, and time-frequency signal analysis.

The carefully selected chapters in this new text will appeal to the reader interested in a broad perspective of wavelet analysis and time-frequency signal analysis. Wavelet Transforms and Time-Frequency Signal Analysis brings together recent developments in theory and applications of wavelet transforms that are likely to determine fruitful directions for future advanced study and research. The book is designed as a new source for modern topics dealing with wavelets, wavelet transforms, time-frequency signal analysis and other applications for future development of this new, important and useful subject for mathematics, science and engineering.

Topics and Features include:

Provides the reader with a thorough mathematical background and a wide variety of applications that are sufficient to do interdisciplinary collaborative research in applied mathematics and engineering scienceA broad coverage of recent material on wavelet analysis and time-frequency signal analysis that are not covered in other recent reference booksPresents information that puts the reader at the forefront of the current research

Wavelet Transforms and Time-Frequency Signal Analysis will serve as a research reference or as a text for an advanced course in wavelet analysis and time-frequency signal analysis. Professionals working on modern applied mathematics, computer science, computer engineering, electrical engineering, physics, and biomedical engineering will also find this book useful. ... Read more

Book Description

The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. The types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. There are also chapters on the viscosity solution formulation and numerical methods. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations. ... Read more

Book Description

Everything covered: from a background in sandwich structures to mathematics AND the means to analyze, design and optimize various structuresUnique information on properties of various honeycomb and solid core materialsOver 800 formulas, tables and figures reinforce conceptsRecommendations from leaders in the field of soil and crop science, agricultural engineering, wastewater and sludge treatment and industry, soil microbiology and other relevant areas The Behavior of Sandwich Structures of Isotropic and Composite Materials provides a unique presentation of mathematics, descriptions and analyzation techniques in the growing field of sandwich structures. Everything is covered, from a background of sandwich structures, to thermoelastic problems of sandwich structures, sandwich shell theory and much more. This text is ideal for the engineer-in-training, as well as the practical engineer who desires a comprehensive understanding of sandwich structures technology. ... Read more

Book Description

This textbook on real analysis is intended for a one- ortwo-semester course at the undergraduate or beginning graduate level. It gives athorough account of real analysis in one or several variables, from theconstruction of the real number system to an introduction to the Lebesgueintegral. Written in a lively and informal style, the text provides proofs ofall the main results, as well as motivations, examples, applications, exercises,and formal chapter summaries. Three chapters on applications (ordinarydifferential equations, Fourier series, and curves and surfaces) are included toshow how the abstract ideas are used in interesting situations. ... Read more

Reviews (14)

The best book out there for UNDERSTANDING the material
There are many fine books on analysis out there. If you're just looking for something for reference, those by Rudin, or Kolmogorov, or others would work just fine. But if you want to LEARN analysis, if you want to actually understand the motivation behind it, then this is, simply put, the best book out there.

I've used this book along with Kolmogorov's for about a term and a half now in my classical analysis class. As an example of the difference between them, consider their coverage of the implicit function theorem, one of the most fundamental theorems of behind the study of surfaces. Strichartz devoted two sections to this theorem, explaining what it was, what it's motivation was, and even how the proof related to the Newton's Method of First-Year Calculus. I came away from the text feeling I actually understood what the theorem meant and how it fit into the rest of Analysis.

Kolmogorov left it as an exercise to the reader.

This is the kind of textbook you can bring with you on a car trip and easily study along the way. It takes an informal writing style and from the beginning is focused on making sure you, as the reader, understand not just the theorems and proofs, but the concepts of real analysis as well. Every new idea is given not only with a What or a How, but with a Why as well, preparing the reader to ask themselves the same questions as they progress further.

This is not to say the book is without rigor though. The theorems and the proofs are still there, just enriched by the other material contained within the book, and anyone mastering this book will be well prepared for future analysis courses, both mathematically and in their way of thinking about the subject.

"The Weigh of Analysis" Would Be a Better Title for This!
"The Way of Analysis" is intended for a heavy-duty one year course in Real Analysis at the undergraduate level, which may also be the first course some students will encounter rigorous proofs in. Strichartz's text, however, becomes hopelessly bogged down in its well intended efforts to be lucid and explanatory. What we end up with in the revised edition is a verbose, muddled, and poorly organized 600 page tome.

The main fault of the text is the verbosity. Strichartz has a talent for taking simple ideas and brief proofs and turning them into long bloated discussions. For a book that claims to help readers learn rigorous proofs, the inclusion of meandering discussions and long comments about the intuition in the middle of a proof is a poor choice. The author is not even consistent in this approach, because some proofs are simply brushed off by appealing to similarity to another theorem, or given a quick informal "proof." In order to be able to effectively study from this text, the reader will need to either make her own comprehensive notes or take very good lecture notes.

The book is typeset in the standard LaTeX style. The flow of the text is set up in a rather crowded manner. Unlike the usual visually pleasing mathematical publication, where all complicated expressions are displayed on their own line to make the text readable, Strichartz chooses to ram all but the most hideous into the normal paragraphs. I suppose a properly spaced version of this text would have had to take up another few hundred pages.

The organization of the book is also harmed by the verbosity and giant paragraphs. Flipping through the chapters to find a particular fact is quickly seen to be futile. In a unique attempt to combat this problem, each chapter ends with a section that states all the definitions and theorems in the chapter. Strangely, this summary is at times the only place to find a precise statement of some of the definitions. Even the summary is not complete because many basic facts are stated and justified only within a paragraph discussion, and others are not even included. For example, nowhere in the text does Stricahrtz mention that the limit of a sum or product of functions is the sum or product of the limits, respectively.

On the positive side, Strichartz does include a significant amount of heavy duty material in the sections marked with an asterisk. Unfortunately, it is just as muddled as the rest of the text. A positive example is his brief discussion of Dedekind Cuts as an alternative to the usual construction of the real numbers via the equivalence classes of rational Cauchy sequences.

Many, but not all, of the exercises are of the routine variety. The selection is not particularly inspired, and doesn't help the reader extend the material or work out some significant applications or extensions herself.

In conclusion, I would not recommend this text for independent study. Certain casual readers may appreciate the verbose introductions to the topics, but far better texts are dedicated to that. For a serious learner, I strongly recommend Serge Lang's "Undergraduate Analysis," published by Springer-Verlag and currently in the 2nd edition. Lang takes a much more concise and clean approach, and it gets the reader to the core of the material much faster.

The best to understand and do Analysis
This is the best Analysis book I ever read, you can learn not only the subject, but how to do Math, the introductive paragraph in each chapter gives the motivation of the topic, for example the introduction to the Lebesgue integral is memorable, many people "learn" the Lebesgue theory passively, some think it is a play to integrate strange functions, instead Prof. Strichartz treats estensively the PRACTICAL weaknesses of the Riemann theory.
For important theorems it is underlined the importance of every hypotheses, often from many points of view, the errors of the past are cited, I think one can learn more from explanations and errors than from a crystallized theory.
The notation is not standard and the printing is not good, however these are light faults.

All mathematics books should be like this.
This book is terrible for reference but EXCELLENT for LEARNING real analysis, certainly the best I have ever seen.

The main issue that divides most readers is one of style, should mathematics books be succinct and clean or should they contain some "entertainment" as well? Should there be some extra explanation or not.

As a student, the answer to this question can be given easily: The more explanation, the better. Just as the title suggests, the author leads you to understand analysis, to understand how things fit together, why certain things need to be proved and why other things are obvious.

If a book just states theorems and proofs, it is unclear to me how that makes you better at mathematics because the question is, could you have thought of these proofs yourself? Given the theorems, can you come up with the proofs? Do you have a feeling for what's going on?

After reading Strichartz you might not remember all the proofs but given any theorem, one should be able to reconstruct the proof from the understanding of the material. One should have a feeling for the concepts and that is something NO OTHER ANALYSIS BOOK seeks to develop.

Also, Strichartz lays things out in a very natural way, not a single topic just comes out of nowhere. There is a flow to the text.

Overall assessment: I love this book, made me get an A+ in the analysis, which I had already given up on, thought I would never get it...

Experimental, heavy, and different
Many people might agree that other books may serve as a text for intro to analysis course better than 'The Way' . However, i find that the writing is very motivated (albeit sometimes he got carried away) and the math is, at least, comprehensible. I sometimes use this as a source of some challenging analysis problems. I am not really sure about using it as a main text, though (I used it as a supplementary text during my freshman year). ... Read more

Book Description

The boundary element method (BEM) is a modern numerical technique which has enjoyed increasing popularity over the last two decades, and is now an established alternative to traditional computational methods of engineering analysis. The main advantage of the BEM is its unique ability to provide a complete solution in terms of boundary values only, with substantial savings in modelling effort.

This two volume book set is designed to provide the readers with a comprehensive and up-to-date account of the boundary element method and its application to solving engineering problems. Each volume is a self-contained book including a substantial amount of material not previously covered by other text books on the subject. Volume 1 covers applications to heat transfer, acoustics, electrochemistry and fluid mechanics problems, while volume 2 concentrates on solids and structures, describing applications to elasticity, plasticity, elastodynamics, fracture mechanics and contact analysis. The early chapters are designed as a teaching text for final year undergraduate courses. Both volumes reflect the experience of the authors over a period of more than twenty years of boundary element research.

This volume, Applications in Thermo-Fluids and Acoustics, provides a comprehensive presentation of the BEM from fundamentals to advanced engineering applications and encompasses:

• Steady and transient heat transfer

• Potential and viscous fluid flows

• Frequency and time-domain acoustics

• Corrosion and other electrochemical problems.

Written by an internationally recognised authority in the field, this is essential reading for postgraduates, researchers and practitioners in civil, mechanical and chemical engineering and applied mathematics. ... Read more

Book Description

A Course in Real Analysis provides a firm foundation in real analysis concepts and principles while presenting a broad range of topics in a clear and concise manner. This student-oriented text balances theory and applications, and contains a wealth of examples and exercises. Throughout the text, the authors adhere to the idea that most students learn more efficiently by progressing from the concrete to the abstract. McDonald and Weiss have also created real application chapters on probability theory, harmonic analysis, and dynamical systems theory. The text offers considerable flexibility in the choice of material to cover.

* Motivation of Key Concepts: The importance of and rationale behind key ideas are made transparent
* Illustrative Examples: Roughly 200 examples are presented to illustrate definitions and results
* Abundant and Varied Exercises: Over 1200 exercises are provided to promote understanding
* Biographies: Each chapter begins with a brief biography of a famous mathematician ... Read more

Reviews (1)

One of the better books on real analysis
I have several books in real analysis including those by rudin, kolmogorov, reisz, etc. Of all the book I have on real analysis, this is by far the most lucid. It is thicker than all of them but only because the authors (McDonald and Weiss) spend time in explaining and motiviating the material. I have learned more in a shorter amount of time from this book than any other advanced math book I own (and I own at least 50 on everything from topology to stochastic processes to algebra). The proofs are clear and the steps are explained in layman's terms (at the level of something like Scientific American's typical readership). The material covers the Lebesgue theory of integration, abstract measure theory, mesure theoretic probability, hilbert spaces, etc. My goal is to learn stochastic calculus beyond the mere manipulation of Ito's lemma and I must say this book, more than any other, is getting me to that level of mathematical maturity quickly. Now I feel pretty confident I can understand that proof in HJM (for you finance buffs out there) involving the stochastic version of Fubini's theorem that always bugged me! ... Read more

Book Description

Responding to the increasing interest in, and demand for, in-depth publications in the field, this stimulating, new resource presents the latest in graph domination by leading researchers from around the world;furnishing known results, open research problems, and proof techniques.Maintaining standardized terminology and notation throughout for greater accessibility, Domination in Graphs covers recent developments indomination in graphs and digraphs dominating functions combinatorial problems on chessboards Vizing's conjecture domination algorithms and complexity varieties of domination domatic numbers changing and unchanging domination numbers and more! ... Read more

Book Description

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. The first part comprises the basic core of a course in complex analysis for junior and senior undergraduates. The second part includes various more specialized topics as the argument principle the Poisson integral, and the Riemann mapping theorem. The third part consists of a selection of topics designed to complete the coverage of all background necessary for passing Ph.D. qualifying exams in complex analysis. ... Read more

Reviews (4)

Average
Not the best but not the worst. The countless errors can be a hassle. Overall, I would suggest waiting for the next edition.

Interesting Book
Gamelin's book covers an interesting and wide range of topics in a somewhat unorthodox manner. Examples: Riemann surfaces are introduced in the first chapter, whereas winding numbers don't make an appearance until halfway into the book. Cauchy's theorem and its kin are instead developed in the context of piecewise-smooth boundaries of domains (in particular, simple closed curves) and only later generalized to arbitrary closed paths, almost as an afterthought.

In general, the author successfully conveys the spirit of the subject, and manages to do so quite efficiently. It's not the most painstakingly rigorous text out there, and the reader is expected to fill in some of the details himself, but the payoff is that a lot of ground is covered without getting bogged down in technicalities. In many books on this subject it can be tough to see the forest for the trees. This one is a pleasant exception.

There are a lot of good complex analysis books out there: Conway, Ahlfors, Remmert, Palka, Narasimhan, the second half of big Rudin, and of course Needham's "Visual Complex Analysis." (And many others that are well-regarded but that I have not looked at, such as Lang and Jones/Singerman, as well as the old classics by Hille, Knopp, Cartan, Saks and Zygmund.) Every one of these has its own perspective, and complex analysis is a big, multifaceted subject that is perhaps best studied from multiple points of view. Anyone wanting to learn this subject well will benefit from having several books at hand.

Gamelin's contribution to the pantheon is not revolutionary, but it does collect between its pages a wide assortment of topics not generally found in a single text. The reader is whisked from the basics to the Riemann mapping theorem in 300 pages with surprising ease. The ensuing "topics" chapters include a dynamical systems-flavored section on Julia sets and fractals; special functions (gamma, zeta, etc.); the prime number theorem; and an introduction to abstract Riemann surfaces.

Overall a fun text. Certainly not the only complex analysis book one should read, but then again the the same can be said of any complex analysis book. My only real complaint is that the selection of exercises is somewhat small in some chapters.

Great read!!
This is a neat textbook on complex analysis. Covers the basic undergraduate curriculum, plus it has some surprisingly refreshing material thrown in towards the end.
The exercises are really helpful and there is a nice variety of problems. The good part is that there are partial hints to problems in the back. With the hints and the answers, one feels that one is heading in the right direction.
I would definitely recommend it.

Here comes Ramblin' Gamelin'
A fantastic book. Quite clear and readable, and really brings out the beauty of the subject. Topics cover standard introductory material, standard not-so-introductory material, and a little bit of the crazy stuff just for fun.

I used this book as a companion to Teddy G's course, and it was grreat. Excellent for PHD-level qualifying exams (especially at UCLA). ... Read more

Book Description

This book is a collection of materials gathered by the author while teaching real analysis over a period of years. It is intended for use as a supplement to a traditional analysis textbook, or to provide material for seminars or independent study in analysis and its historical development. The book includes historical and biographical information, a wide range of problem types, selected readings on a variety of topics, and many references for additional study. Since all these materials are collected into a single book, teachers and students can easily choose items most suitable for their purpose. Teachers may use the book as a supplement to their courses, while students may read much of the book on their own. No other book has been written specifically as a supplement for a real analysis course. ... Read more

Book Description

This book examines abstract convex analysis and presents the results of recent research, specifically on parametrizations of Minkowski type dualities and of conjugations of type Lau. It explains the main concepts through cases and detailed proofs. ... Read more

Reviews (2)

A fundamental book on convexity theory
Singer's book studies abstract convexity, and it will appear to mathematicians with an interest in approximation theory, general topology, lattice theory, or convex analysis---especially those interested in generalizing duality theory from real vector spaces to convexity systems, etc.I'll register one complaint:I cannot find the definition of "complete lattice" in the book!(I hope Birkhoff's definition is intended.)

Singer is a gifted expositor who has previously written books on Bases in Banach Spaces and Approximation Theory, which often exhibit virtuosity in "hard analysis".In contrast, this book is quite abstract, although a nice introduction reviews convex duality and quasi-convex ("surrogate") duality as motivation.

A related book is A. M. Rubinov's Abstract Convexity and Optimization (the title may be slightly wrong), which has been published by Kluwer in its Nonconvex Optimization Series. Rubinov's book would make collateral reading for researchers in global minimization algorithms.

I wrote this review to warn that the previous reviewer must have been writing about another book, apparently in signal processing!

Well written book...
This book talk about a standard wavelet multiresolution analysis can be defined via a sequence of projectors onto a monotone sequence of closed vector subspaces possessing certain properties. It also propose a nonlinearextension of this framework in which the vector subspaces are replaced byconvex subsets. These sets are chosen so as to provide a recursive,monotone approximation scheme that allows for various signal and imagefeatures to be investigated. Several classes of convex multiresolutionanalyses are discussed and numerical applications to signal andimage-processing problems are demonstrated. Therefore I recommended. ... Read more

Reviews (2)

Well presented , well orginized and broad coverage
Dr. Rao's approach to the Wavelet Transform takes a less traditional method to the study of this complex field. His text starts with a firm development of the fundamentals. This provides a secure foundation for the intermediate level topics to follow. He ends the book with some complex developments and new directions taken by the transform. His approach is mathematical but never looses sight of the practicality of the transform. Applications and examples are peppered throughout the text to provide the reader with reinforcing tools. Relevant exercises and projects are also provided along with Matlab routines to perform most of the topics discussed. A great text and a valuable reference. Attention is paid to the development of Filter Banks and the relationship to the Wavelet Transform. A background in Digital Filtering is recommended to any reader. Wavelet Packets are discussed along with topics in Image Compression, Denoising, Edge and Object Detection and general Wavelet Filter Design.

First easy to read book on Wavelets
This book has been written in an easy to read and understand fashion without compromising on the fundamentals. If you wonder what wavelets can do, or what they are, start with this book. Highly recommended for anyone who is starting to learn about wavelets. ... Read more

Book Description

Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers revised coverage of basic theory and standard techniques, with updated discussions of line search methods, Newton and quasi-Newton methods, and conjugate direction methods, as well as a comprehensive treatment of restricted step or trust region methods not commonly found in the literature. Also includes recent developments in hybrid methods for nonlinear least squares; an extended discussion of linear programming, with new methods for stable updating of LU factors; and a completely new section on network programming. Chapters include computer subroutines, worked examples, and study questions. ... Read more

Reviews (2)

Paperback reprint of 2nd Ed. from 1987
This is a good book from an award winning author and researcher in this subject. However, the 2000 publication date shown refers to the release of the paperback version. There is no new content since 1987 when the 2nd ed. was originally published in hardcover.

I prefer Dennis and Schnabel's _Numerical Methods for Unconstrained Optimization and Nonlinear Equations_ for Newton-derived methods in unconstrained optimization, but Fletcher's book has the added material on constrained optimization (Part 2) that makes it more complete if one wants a single reference that covers the gamut of optimization.

Help you know what's under the hood
This is a very well-written book. It achieved both mathematical clearness and simplicity. I especially like the first part, unconstrained optimization. On the one hand, unconstrained optimization is very widely used. On the other hand, there isn't much content in it. Yet, there aren't many books explaining this small area clearly. This book starts with describing the structures of all methods, which gives you a sort of bird's eye view. It then devotes one chapter to each of the 3 major families of optimization methods. Comparing with another popular book, Numerical Recipes, which is orgnized by individual algorithms, this book will cerntainly gives the reader better understanding of the essence of all the algorithms. And as the name says, it's about 'practial' methods. You'll have no problem to implement the algorithms in the book and there are also many working examples to help you see how an algorithm works and help verify the implementation. ... Read more

Book Description

Carefully focused on reading and writing proofs, this introduction to the analysis of functions of a single real variable helps readers in the transition from computationally oriented to abstract mathematics. It features clear expositions and examples, helpful practice problems, many drawings that illustrate key ideas, and hints/answers for selected problems.Logic and Proof. Sets and Functions. The Real Numbers. Sequences. Limits and Continuity. Differentiation. Integration. Infinite Series. Sequences and Series of Functions.For anyone interested in Real Analysis or Advanced Calculus. ... Read more

Reviews (2)

Definitely a good first text
I bought this book because I have been looking for a Introductory analysis text that isn't too advanced, but yet doesn't gloss over the essential stuff, and I found it in Lay's book. For the self-studier, this book is excellent! I have several books on analysis: Shilov, Kolomogorov, Rosenlicht, Ross,etc... For the beginner, this book is superior to all of them. A plethora of examples. Also, a good range of problems:from straight forward problems requiring only the use of a definition to more advanced problems requiring a little thought. If you already have had some Analysis, then this book is probably not for you. But, if you are a student who wants to learn Analysis on your own, then this book would be hard to beat. After this book, one should be able to tackle "Papa Rudin". For according to Rudin, all that is needed to study his "Real and Complex Analysis" tome, is the first seven chapters of his "Principles of Mathematical Analysis". This book covers all that Rudin covers with the exception of Riemann-Stieltjes integration. On the whole, this is a great start! If proof-based math is new to you, then you will appreciate the first chapter on proofs. Would have given five stars, but I would have liked to seen Riemann-Stieltjes integration. That's really only nit picking, though.

This book was surprisingly good
I didn't think this book was going to be very good, but the author has "proved" me wrong ;-) This book starts out so basic that in my class (which was the first analysis course in our math department) we actually skipped the first 1/3 or so of the book. The first 9 or 10 sections consist of stuff like basic set theory, logic, definition of a function, etc. I would think that even the most elementary Analysis books would completely leave this out and expect that the reader is already familiar with this. So if you need it, this book will be a good resource for you.

Then the book goes into a very nice introduction to topology. Basic concepts like open/closed sets, accumulation points, compact sets, etc. Topology can be a little intimidating simply because it's _so_ abstract, but this book makes the basic concepts very easy to understand, and prepares one for a more advanced course in topology. Alot of (good) Elementary Analysis books leave topology out, but I'm glad this book contained it. It is a very interesting subject.

All the material in the book is explained probably about as easily as the concepts CAN be explained. If you still have trouble with it, you might consider a different major. Not to say that this book transforms a very difficult subject into a pathetically easy piece of cake because that's impossible, but the material is presented probably as easily as it can be in order to maintain precision and detail (which is the whole point of Analysis).

The book is definitely not running short in the examples or end-of-section problems department, so that is another plus. The problems at the end of each section range in difficulty from problems that almost exactly match an example worked in detail in the section, to fairly challenging problems. With enough time though the average student could probably do every problem at the end of every section.

I'd recommend this book for self study as well as a supplement to any introductory analysis course. If you have already have exposure to rigorous proof of calculus theorems, then this book will probably be too basic for you.

The reason this book got 4 stars instead of 5 is because of its utterly ridiculous price. Just as good is Elementary Analysis: The Theory of Calculus, ISBN: 038790459X, except that it doesn't include the section on Topology ... ... Read more

Book Description

The Encyclopedia of Neuroscience CD-ROM is designed to make the neurosciences readily accessible to both the specialist and non-specialist reader. This landmark work, with its broad scope and interdisciplinary coverage, has become an essential reference and learning tool for everyone involved in the study of the brain and how it mediates behavior.
This 3rd Edition CD-ROM has been further expanded and significantly updated, in most cases by the original authors. The Encyclopedia represents the culmination of a massive international effort to present the neurosciences in one concise source, and includes contributions from renowned experts in their respective fields from around the world, including several Nobel Prize winners. 18% of the approximately 900 entries are new, 60% are completely revised and updated.

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