Product Description
Designed for students having no previous experience with rigorous proofs, this text can be used immediately after standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, as well as for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied, while many abstract ideas, such as metric spaces and ordered systems, are avoided completely. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics, and optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals. ... Read more

Customer Reviews (24)

A good intro book, but
My school's advanced calculus class uses this book, so I bought it from amazon. It is pretty good for beginners who goes into advanced calculus. However, sometimes the proof is hard to follow. I remember getting lost once or twice when I was reading it.

A good purchase
Thank you for speedy shipping. I am working on it and it is hard to analyze. HA!

The perfect transition to life after calculus
I certainly wasn't ready for Rudin after my freshman calculus series, and Ross's book was the perfect stepping stone. Almost nothing is assumed of the reader, the book starts out gently holding your hand through all the proofs, skipping not even trivial calculations. Don't worry the proofs get more concise as the book moves on to more complicated topics, but still maintains a high degree of readability. The examples are very insightful and there are many figures to speak to and help develop the readers intuition. This also makes it a great book for self study. In addition the sketch of the proofs to many of the exercises are provided in the back of the book!

From a pedagogical standpoint many colleges do not require their "mathematics education" majors to take analysis, perhaps because they don't have a course at the level of this book. A high school math teacher doesn't necessarily need to master Real Analysis at the level of Rudin, but they certainly need to know the basic theory of one dimensional calculus (especially if they are going to teach AP calc).

In summary this book is excellent for (1) freshman and sophomores taking calculus who want a bit more theory, (2) an analysis course for math education majors, (3) a transition course to a more advanced class, (4) current high school and community college math teachers who want a light brush up on the theory behind what they teach, (5) a reference for when you get lost in a more advanced text.

Good Intro Text
If you had a rigorous, proof-heavy calculus course, you could probably skip this book and go straight to something more advanced, like Apostol or Rudin. On the other hand, if your calculus class skimped on proofs, preferred a cookbook approach, or if the word "limit" doesn't automatically conjure up images of deltas and epsilons, then this is the analysis book for you.

While Ross assumes a working knowledge of calculus and basic proof-writing skills, he does NOT assume the reader has encountered too many of the results before. Thus, he includes numerous examples and exercises to familiarize the reader the definitions. The theorems aren't proven in the simplest way possible, but rather in a more intuitive way with few gaps. Sure, the proofs would be a lot shorter if he used some basic results from topology, but that would be a bit distracting for someone who wasn't very familiar with the material or with proof-writing in general.

In summary, this is an excellent introductory book for newcomers to analysis. If you learned calculus from Stewart, go here first. If you learned calculus from Apostol or Courant, this is a good companion to Rudin.

Excellent book
I went through a lot of math books that made me wonder if the author was purposely making it hard or if they were just bad at explaining things.
I didn't have that experience with this book. This book is well written and easy to understand (given its subject). Highly recommended for anyone learning Advanced Calculus 1 for the first time.



... Read more

Product Description
This is the first part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. The book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The book's approach begins with the question "what are the most important applications" and proceeds to try to answer this question. The applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. The presentation is self-contained. As for prerequisites, the reader should be familiar with some basic facts of calculus.

The second part of this textbook has been published under the title, Applied Functional Analysis: Main Principles and Their Applications. ... Read more

Customer Reviews (3)

motivated , well written, easy to read , nearly complete
This is a incredible book on applied functional analyses.Every topic is motivated with an applied problem.The definitions are motivated either by the aplication or by the subsequent use.There are remainders showing you the inteconections between the subjects and finally the index and the Symbols index are both complete and very usefull.The book is not complete. However he missing subjects usually are in the other colection by the same author.

Excellent account on modern operator theory
This well-written text covers the fundamentals of modern linear operator theory and points out most of its connections to other branches of mathematics and physics ( differential equations, integral equations,finite elements, elasticity, quantum mechanics, and more). It includes allthe basic theory on Banach spaces, Hilbert spaces, orthogonality, Fourierseries, etc., and a chapter on the PDE's of mathematical physics. Theexcercises are both illustrating and challenging. I find it useful forundergrads, graduate students, and as a reference for workingmathematicians. Must read companion volume 109 also.

Please check myother reviews in my member page (just click on my name above).

Indispensible to any serious student of Mathematics!
Prof. Zeidler has done the world of mathematicians an incredible serviceby writing this book. It is self-contained, very lucid, beautifullyorganised, and actually takes the trouble to relate various topics to eachother. It makes the field of Functional Analysis more accessible tostudents taking their first course in it. It also is a handy reference forpracticing mathematicians. I loved the little schematics in the book whichpoint out connections between seemingly disconnected ideas. All in all- agreat book. If you don't have it, and are interested enough in Math to bereading this review- go buy it!!!! ... Read more

Product Description
( 20 ) OF EXPRESSION AND INTERPRETATION. A Proposition iB a sentence which either affirms or denies, as, All men are mortal, No creature is independent. A Proposition has necessarily two terms, as men, mortal; the former of which, or the one spoken of, h culled the subject; the latter, or tha! which is affirmed or denied of the subject, the predicate. These are connected together by the copula w, or m not, or by some other modification of the substantive verb. The substantive verb is the only verb recognised in Logic; all others are resolvable by means of the verb to be and a participle or adjective, e. g. " The Romans conquered"; the word conquered U both copula and predicate, being equivalent to "were (copula) victorious" (predicate). A Proposition must either be affirmative or negative, and must be also either universal or particular. Thus we reckon in ail, four kinds of pure categorical Propositions. 1st. Universal-affirmative, usually represented by A, Ex. All Xs

About the Publisher

Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the difficult to read text. Read books online for free at www.forgottenbooks.org ... Read more

Customer Reviews (1)

What sould I do?
I'm 16 years old and I'm a boy and I'm from Switzerland, that's it ... Read more

Product Description
From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics. The book presents a balanced view of the methods and their usefulness: integrals on the real line and in the complex plane which arise in different contexts, and solutions of differential equations not expressible as integrals. Murray includes both historical remarks and references to sources or other more complete treatments. More useful as a guide for self-study than as a reference work, it is accessible to any upperclass mathematics undergraduate. Some exercises and a short bibliography included. Even with E.T. Copson's Asymptotic Expansions or N.G. de Bruijn's Asymptotic Methods in Analysis (1958), any academic library would do well to have this excellent introduction." (S. Puckette, University of the South) #Choice Sept. 1984#1 ... Read more

Product Description
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations. ... Read more

Customer Reviews (6)

excellent
This is the best functional analysis book for beginners, in my opinion. It is written for people that are interested in functional analysis as a tool for differential equations. What makes it different from other books on this subject are the numerous examples and applications to differential equations. Highly recommended.

Great transaction
Fast delivery, newer edition than what was advertised but that's perfectly fine with me

The essential spectrum of tools for physical observables.
Books on mathematical methods "for physicists" are often criticized by their superficiality, a sacrifice deemed necessary for achieving completeness. This one is a glaring exception: the first of a set of 4 (!) volumes dealing with the finest tools for dealing with the delicate mathematical questions in quantum theory - namely, functional analysis. Of course, this sounds rather vague, since quantum physics makes use of functional-analytic tools as diverse as distributions, Hilbert, Banach and locally convex spaces, spectral theory, semigroup theory, operator algebras, etc.

However, do not expect ready-brew formulae and cookbook recipes: this book gets his job done at least as well as Rudin, Yosida and Riesz-Sz.Nagy, just to mention the classics. Most theorems are rigorously proved, and although the book becomes more and more biased towards mathematical physics (i.e., methods for proving self-adjointness, analysis of spectra and scattering theory, as stated in the section "Three Mathematical Problems in Quantum Mechanics". These methods occupy most of the three remaining volumes) as it proceeds - this bias becomes the true reason of being for the last two volumes - this particular volume has precisely the most useful stuff: metric, Banach, topological, locally convex, and Hilbert spaces, bounded and unboundedoperators. A supplement extracted from the second volume with the basics of Fourier transforms makes it self-contained as a monograph.

However, the best things, that make this book nearly unbeatable, are the several wisely chosen examples and counterexamples, the notes at the end of each chapter and the wonderful - and useful - exercises. Many working mathematicians I know use this book seriously in their research and their courses in Functional Analysis - a fact that cannot be underestimated and will hardly be equaled by any book on mathematical physics.

If you work on (axiomatic) quantum field theory you may also want to keep an eye on the second volume of the set, "FourierAnalysis, Self-adjointness", which is a bit more specialized butjust as wonderful.

The best available text on this subject.
This superb book may be the best available text on elementary general topology, functional analysis and spectral theory of bounded normal operators on Hilbert spaces. The exercises are excellent as well. Mustreading!

Excellent
We used this book in Math 401 at Princeton. This book is great, well-written, well-problemed. It is curious that the other reviewer complains that there is nothing original in this book, because this subjectis older than the author, who is an expert in Schrodinger operators.Theparts of the next three volumes which I have read have also been great. ... Read more

Product Description
Ideal for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written at a level accessible to advanced undergraduates and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of intriguing topics that are uncommon in a book at this level. The flexibility afforded by the supplementary topics and applications makes the book adaptable either to a short, one-term course or to a comprehensive, full-year course. Detailed solutions of the exercises both serve as models for students and facilitate independent study. Supplementary exercises, not solved in the book, provide an additional teaching tool. This second edition has been painstakingly revised by the author's son, himself an award-winning mathematical expositor. ... Read more

Customer Reviews (3)

Superb book for the mathematically mature
This is a master class in complex analysis. It goes way beyond most comparable books, but you have to be mathematically mature to get this (you should have met real analysis, and dated it). Just to take one example, the presentation of the proof of Cauchy's theorem is superb; trotting alongside the master, you see what is really going on. The author's casual asides, sprinkled throughout the text, are stimulating. The footnotes are a treasurehouse for those with some curiosity about the history of the subject. Of course, this is not an efficient Schaum-series style textbook; that explains the orthogonal ratings given to this book by the two preceding reviewers. If you want to get good grades at some exam, there are plenty of other books on the market that will do the job. But if you have dispensed with such mundane concerns and want to really understand complex analysis, buy this book as I have.

Examples are poor and low readability
The book was used at UCLA recently and I found it not enjoyable to read at all.The examples were very poor and did not seem to relate to the topicscovered.Not a book I would recommend.

An adequate text in complex analysis
This was the text used by our class at the State Universityof New York at Buffalo for complex analysis.Most of usfound the text to be too highly condensed.In other words, we were dissatisfied with the time spent on explanations, especially for some of the subtleties that can arise. A fine selection for a reference text, but, somewhat unpleasant as a text for teaching oneself the subject. Admittedly, complex analysis is a difficult topic.The author (a famous mathematician) does very well, actually, in the space alloted.(text by Ahlfors is superior, though) ... Read more

Product Description

This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.

Product Description
In Who is Fourier? A Mathematical Adventure, the student authors take the reader along on their adventure of discovery of Fourier's wave analysis, creating a work that gradually moves from basics to the more complicated mathematics of trigonometry, exponentiation, differentiation, and integration. This is done in a way that is not only easy to understand, but is actually fun!

Professors and engineers, with high school and college students following closely, comprise the largest percentage of our readers. It is a must-have for anyone interested in music, mathematics, physics, engineering, or complex science.

Dr. Yoichiro Nambu, 2008 Nobel Prize Winner in Physics, served as a senior adviser to the English version of Who is Fourier? A Mathematical Adventure. ... Read more

Customer Reviews (42)

Excellent intro to wave mechanics
I've taken many physics and engineering courses that use wave equations in one form or another.What they all lacked, however, was the overarching principles that tied wave equations in one discipline to wave equations in another.This book explains those connections and how one complicated wave equation can be broken down into its constituent parts.I highly recommend this book to those who love science but struggle with the math behind periodic systems.

Who is fourier?
Excellente book. I don't have doubt to recommend this example for a dummies like me in complex but useful maths. I also suggest for a students of geophysics and engineer in general. They transform the difficult into a easy way to solve the problems.

Very well written summary of Fourier analysis
I have read through most of the book.In general, this is an excellent introduction to the concept of Fourier analysis.It covers the basic concepts quite well.What I found quite interesting is that the authors of this book were able to take a relatively complicated idea and break it down and explain it in plain language, so that the reader developed an intuitive understanding of the concepts.The math in this book is a little heavy, and a familiarity with advanced algebra is necessary, and some background in calculus is helpful but not essntial because the authors do provide some background material in that area.

I used this book as a supplement to an engineering math course, and the explanations here were quite helpful to me in understanding the fundamental ideas.

My only complaint is that some of the cutesy stuff was a little distracting for me.When the authors stuck to straight language in explaining the material the book is at its best.Overall I highly recommend this book.

Fourier made easy
One of the best math books for non PHD audience. I have a math degree myself and I have read a number of books covering Fourier transform. In all honesty this was the only book I really enjoyed. It had an easy to understand language, practical implications of the transform as well as background and meaning of Fourier coefficients. This book allowed me to develop the easiest and cleanest implementation of the Fourier transform.

Who is Fourier ?
It is a Gem for anyone who wants to meet the spirit of fourier transforms. The approach is excellent and takes you off to the basics of fourier transforms smoothly.Books like these would surely get rid of the fears among students. I would suggest such books must be used as text books in high schools or even first year undergraduates to draw the interests of students ... Read more

Product Description
The book uses the appealing theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms.

The presentation is elementary, and the topics are interesting to nonspecialists. The theory is quite beautiful and developing rapidly. Exercises with answers, an annotated bibliography, and research problems are included. The text would be appropriate as supplementary reading for undergraduate research seminars or courses in algorithmic analysis and for graduate courses in combinatorial algorithms, operations research, economics, or analysis of algorithms.

Donald E. Knuth is one of the most prominent figures of modern computer science. His works in The Art of Computer Programming are classic. He is also renowned for his development of TeX and METAFONT. In 1996, Knuth won the prestigious Kyoto Prize, considered to be the nearest equivalent to a Nobel Prize in computer science. ... Read more

Customer Reviews (1)

A very good computer book....
This book is very good for someone who is either new to the field or fairly experienced. Knuth is the king of computer algorithms ! ... Read more

Product Description
If you want top grades and thorough understanding of numerical analysis, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you accompanying related problems with fully worked solutions. You also get additional problems to solve on your own, working at your own speed. (Answers at the back show you how you're doing.) Famous for their clarity, wealth of illustrations and examples--and lack of dreary minutiae--Schaum's Outlines have sold more than 30 million copies worldwide. This guide will show you why! ... Read more

Customer Reviews (6)

The worst of all Schaums guides
there are several problems with using this book as self-study material:
1) it is dated - though published in 1989, and by definition out of date in 2010, the first 11 chapters list many techniques that even in that period are condsidered to be of historical interest in the computer age - interpolation, collocation operators etc
2) there is not a single worked example
3) the solved problems make several leaps of logic - I wouldnt have got anywhere without referencing Wikipedia, Cliffs briefs on differential equations, Schuams advanced calculus etc.
4) sometimes new formulas are actually introduced in worked problems - eg Everet's formula
5) problems are not self contained - referencing other chapters, other problems and sometimes other problems in other chapters.

In short, this book was a struggle, and although it will give you conceptualization of different techniques, it will not give you a modern or holistic perspective on the field.

Predates the computer age but a LOT of fun!
This isn't a good book on how to do numerical analysis on a computer.It's more about the methods that people used to use when they did numerical analysis with pencil and paper.

This book goes into a lot of depth into how interpolation equations are derived,and into the calculus of finite differences.Personally I think that's a beautiful subject and a lot of fun,be it useful or not - that's what math is for math's sake.

I worked all of the problems in this book when I was in high school and I recognized many of the tricks when I took a combinatorics class years later.

A book with an audience
With no previous background in numerical analysis, I bought this book on the recommendation of my boss who loved the first edition.
I had also ordered a whole lot of other books (many from Dover editions). It turns out this is the one I love to pick up from time to time so as to learn a new idea.
It goes straight to the point and gives your mind something to munch on.
I suppose that with time I'll be completing with some of my other books, to look for the rigorous proofs and so on, but for the time being this book is preparing me.

A book with no audience?
Looking for a supplementary text for my Numerical Analysis course, I had my students pick up this text-I have found that other Outlines give a lot of excellent worked examples and provide good summaries- Not this text.If you are a beginning student, go get yourself a real text (I would highly recommend Burden and Faires, or the new text by Tim Sauer).This text offers little to no insight into the algorithms or the analysis, and spends way too much space on one dimensional interpolation problems.If you're simply looking for summaries of algorithms and practical advice on implementation, a much better text is the "Numerical Recipes" books.In summary, I'm not sure who the audience is for this book-There are many, much better, options out there.

Excellent Solutions Book for Fast Answers!
I've had this outline for years. My only complaint about Schaum's is that sometimes their answers are not in enough detail and their indexes are skimpy. Outlines live and die based on their detailed solutions to solved problems and their index. This particular outline is excellent. All the basic numerical methods are presented with the standard format: theory, solved problems, problems with answers. What could be added, either here, or in future text (separate) would be an optimization methods section: differential search, Hooke & Jeeves min./max. search and the Golden Mean search. The later, especially, is easy to program into Excel so it would useful to show the pitfalls in these methods. All in all, this is a text you want in your engineering collection for those problems that require detailed analysis.

If this review was useful, please say so. ... Read more

Product Description

This book is an outline of the core material in the standard graduate-level real analysis course. It is intended as a resource for students in such a course as well as others who wish to learn or review the subject. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form.

Customer Reviews (1)

A book that will generally only be useful to the person needing a quick refresher
For reasons I cannot really explain, when I was reading this book the metaphor of an altered "Whack-A-Mole" game came to mind. The scenario is that it has been decided that a sequence of mathematical objects is to be covered and the author then goes down the list hitting each briefly with a segment of text from a mathematical word processor. With only 99 pages, a few of which are blank due to space at the end of the chapters, the author has the goal of developing a primer on real analysis. Given the depth and breadth of the subject, this is a daunting task, meaning that only the essentials can be covered and none in any real depth.
The chapter titles are:

*) Topology
*) Measure and Integration: Central Theory
*) Measure and Integration: Constructions and Special Examples
*) Rudiments of Functional Analysis
*) Function Spaces
*) Topics in Analysis on Euclidean Space

Key theorems are stated but even the most detailed proofs that appear are mere sketches and in most cases nothing in the way of proof is offered.
With little in the way of explanations, this would be a very hard book to learn from; only the most determined and capable could use it in isolation. Therefore, the best use of this book would be as a quick refresher, for example someone that has the opportunity to teach a course in advanced real analysis but is uncertain if they remember enough of the subject. A quick reading of this book would help them make the decision.
... Read more

Product Description
Multivariate Analysis deals with observations on more than one variable where there is some inherent interdependence between the variables. With several texts already available in this area, one may very well enquire of the authors as to the need for yet another book. Most of the available books fall into two categories, either theoretical or data analytic. The present book not only combines the two approaches but it also has been guided by the need to give suitable matter for the beginner as well as illustrating some deeper aspects of the subject for the research worker. Practical examples are kept to the forefront and, wherever feasible, each technique is motivated by such an example. ... Read more

Customer Reviews (3)

nice coverage by Mardia and company
This book provides an excellent general treatment of multivariate analysis.It uses the geometric approach much more than other texts with the exception of Gnanadesikan's.It is written with elegant style.It does not describe thoroughly the multivariate normal distribution theory that one find in the classic text of Anderson.Anderson takes a much more algebraic approach and concentrates heavily on multivariate normal theory.Matrix algebra is important when studying multivaraite analysis and is particularly important if you want to read and understand Anderson.It is not as critical for this and some of the other.As with many other books on multivariate analysis, factor analysis and structural equation modelling are given little or no coverage even though they are important in applied problems.Specialized books like Harman and Bollen give a detailed treatment of factor analysis and structural equation models respectively.Also this book and many others do not cover the bootstrap methods.The bootstrap plays an important role in multivariate analysis and it is nice to see that at least Anderson gives it some coverage in the second edition of his book.This may in part be due to the fact that he is a Stanford Professor who has seen the efforts of Efron, Tibshirani and Romano on the Stanford campus.

Excellent if you know some linear algebra
A very good book for someone who knows linear algebra. In fact, it is probably a good introduction to advanced statistics for someone with a numerical background.

The reason I did not give if 5 is that it has started to show its age and insists that data is best arranged in rows. Those with a numerical background invariably use columns (unless they are doing funky stuff).

The description of Principal Component Analysis (PCA) is based on eigendecompositions rather than a singular value decomposition. Apart from being a numerical no-no, it is also a nice description of the data.

Every 10-20 years a statistician reinvents a minor variant of PCA (often without obvious knowledge of the previous ones). It would be nice if this was made more explicit. The connection with factor analysis is mentioned (and it has a good chapter of its own), but it would be nice to mention at least the Harkunen-Loeve and Hotelling-transform.

best book on multivariate analysis
This book gives the clearest and most elegant presentation of the theory of multivariate analysis I have seen.The reader should have a good background in linear algebra before starting this one, but with this background the authors give a very concise treatment of a large area of statistics.Many topics that are not covered in most multivariate analysis texts are covered here.The exercises are also outstanding.Many of them are very difficult and lead to more profound results.I highly recommend this text! ... Read more

Product Description
Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component—modeling—to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters. Partial Differential Equations: Modeling, Analysis, Computation enables readers to deepen their understanding of a topic ubiquitous in mathematics and science and to tackle practical problems. The advent of fast computers and the development of numerical methods have enabled the modern engineer to use a large variety of packages to find numerical approximations to solutions of PDEs. Problems are usually standard and a thorough knowledge of a well-chosen subset of analytical and numerical tools and methodologies is necessary when dealing with real-life problems. When one is dealing with PDEs in practice, it becomes clear that both numerical and analytical treatments of the problem are needed.This comprehensive book is intended for graduate students in applied mathematics, engineering, and physics and may be of interest to advanced undergraduate students.Mathematicians, scientists, and engineers also will find the book useful.ContentsList of Figures; List of Tables; Notation; Preface; Chapter 1: Differential and difference equations; Chapter 2: Characterization and classification; Chapter 3: Fourier theory; Chapter 4: Distributions and fundamental solutions; Chapter 5: Approximation by finite differences; Chapter 6: The Equations of continuum mechanics and electromagnetics; Chapter 7: The art of modeling; Chapter 8: The analysis of elliptic equations; Chapter 9: Numerical methods for elliptic equations; Chapter 10: Analysis of parabolic equations; Chapter 11: Numerical methods for parabolic equations; Chapter 12: Analysis of hyperbolic equations; Chapter 13: Numerical methods for scalar hyperbolic equations; Chapter 14: Numerical methods for hyperbolic systems; Chapter 15: Perturbation methods; Chapter 16: Modeling, analyzing, and simulating problems from practice; Appendices: Useful definitions and properties; Bibliography; Index. ... Read more

Customer Reviews (1)

Good reference, bad instructional material
The book by Mattheij outlines the general forms of PDEs rather well, but falls short as an instructional resource.When completing the homework problems at the end of each set, I found myself requiring additional resources online and in other textbooks, since only the basic idea is given and developed in each section, without elaboration.
As the book wore on into Numerical Methods, the nomenclature became far more confusing to deal with and far harder to follow.
The one saving grace of this book was its application problems in the back.These were exceptionally well written and very well representative of the final projects that our class was to use.The explanations helped clear up any issues that I had with those specific scenarios. ... Read more

Product Description
This book is a survey of asymptotic methods set in the current applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. Asymptotic expansions developed in the text are justified rigorously, and students are shown how to obtain solid error estimates for asymptotic formulae. The book relates examples and exercises to subjects of current research interest, such as the problem of locating the zeros of Taylor polynomials of entire nonvanishing functions and the problem of counting integer lattice points in subsets of the plane with various geometrical properties of the boundary. The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects. ... Read more

Product Description
Basic text for graduate and advanced undergraduate deals with search for roots of algebraic equations encountered in vibration and flutter problems and in those of static and dynamic stability. Other topics devoted to matrices and eigenvalue problems, large-scale linear systems, harmonic analysis and data analysis, more.
... Read more

Customer Reviews (6)

An interesting if some what dated book
Applied Analysis, by Cornelius Lanczos is, in the author's words in the Preface, that branch of analysis devoted to the analysis of finite algorithms, or "workable mathematics". Today it would be called numerical analysis.

Written in 1956,foloowing assignments with then North american Aviation and the Boeing Airplane Company, the book is a compendium of compuational techniques for the solution of cubic, quartic and higher order algebraic equations, matrices and eigenvalue problems, large scale linear systems, harmonic analyis.An entire chapter of 65 pages is devoted to data analysis, the problems associates with processing large amounts of data, and some of the hidden dangers of straightforward(equidistant) interpolation. A chapter is devoted to quadrature methods, and the book concludes with a chapter on power expansions.

Most of the computational methods are devoted to hand calculation, or electro mechanical calculation. Today, algorithms developed specifically for high speed digital processors make most of these methods obsolete.

I bought the book because of an interest in Legendre polynomials, and their use in fitting to data. However, fascinating tidbits (at least to me) pop up unexpectedly. One tidbit that caught my eye was in the chapter on Data Analysis(Chapter V) in which the Sturm-Liouville equation suddenly appears, is solved by an application of Green's identity, and hence the result is a proof of the orthoganility of a class of equations (Legendre's being just one of several) in just two steps. Perhaps I missed something when I studied Series and Special Functions, but I've not seen this anywhere else.

A very pleasant characteristic of the book is the almost seamless movement back and forth between theory and computationl application. On the other hand, be prepared to spend time with a pencil and paper following not only the derivations and proofs, but the computational algorithms. For someone doing, or planning to do, a massive amount of number crunching of large collections of physical date, this is probably a good book to have.

Master of Exposition
It's an excellent book.The best parts for
we were the chapters on Matrices and on
Harmonic Analysis. An outstanding aspect
of the latter chapter is Lanczos's exposition
of the motivation behind the Fourier integral
(transform) and its basic theory.The quality
of the writing is superb, very classical
and lucid.

It cannot, of course, serve as a textbook.
But if you're taking a Fourier theory
course using Stein and Shakarchi's book, say,
as I am currently, then it's a very handy
book that can complement abstract theory
with physical intuition.

very fine but could be more advanced
Lanczos' work is a fine, thorough text that covers most areas of advanced analysis in a readable style. His derivations are clear, his tangential explorations are absorbing, and he cites practical examples. The one area in which I find the book weak is harmonic functions, potential theory, and the applications of these to the calculus of resides. Consequently, the book is not "one-shop stopping" for all the mathematical techniques that an electrical engineer or physicist might require in his bag of tricks....

If you don't want just recipes...
Then this is the best book. Well, Hamming's is also so good! For Fourier analysis, and the taming of the Gibbs phenomenon, go straight to Lanczos. He knew it all, and was one of the inventorsof the fast Fourier transform. This book is in the class of Sommerfeld's "Partial Differential Equations of Physics" and Lighthill's "Fourier Analysis and Generalizaed Functions". This is a very high compliment. Did you know hewas also a first rate physicist, and a pioneer of quantum mechanics?

Simply the best book on numerical analysis
My dissertation advisor introduced me to this book over thirty years ago.I have since read it in its entirety twice and it is still the first book I consult when confronted with a new mathematical problem.

Lanczos'sunderstanding of applied mathematics is very deep and he has a rare way ofexplaining things clearly yet concisely.I find his description of linearsystems in terms of multidimensional coordinate systems, both orthogonaland skewed, to be the best anywhere.Also, his understanding andexplanation of harmonic analysis (he invented the FFT after all) is worththe price of the book by itself.

Buy it, read it (at least once) then seeif really need any other book on applied mathematics. ... Read more

Product Description

This text prepares readers for fluency with analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. This book is designed to challenge advanced readers while encouraging and helping readers with weaker skills. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, showing readers the motivation behind the mathematics and enabling them to construct their own proofs.

Customer Reviews (17)

Worst "Analysis" Text book ever
This book is an insult to all the great Analysis text books out there. I am pretty sure Walter Rudin would turn in his grave when he sees this one. No rigor, poor exposition, poor organization, and worst of all, computational and routine exercises. In an Analysis text bookthese are surely a recipe for disaster. Go buy Rudin's PMA if you really want to start learning Mathematical Analysis. This book will do you no good.Run!. This book should be called Advanced computational Calculus. An introduction to Analysis my a**. And like one of the other reviewers said, if you can't handle the rigor and abstraction in RudinPrinciples of Mathematical Analysis, Third Edition (or the like), then you are not cut out to do Math at graduate level.

The following Text books are also very good (for a beginner Real Analysis course) .
Real Mathematical Analysis
The Way of Analysis, Revised Edition (Jones and Bartlett Books in Mathematics)
Basic Real Analysis and Advanced Real Analysis Set (Cornerstones)

Terrible Book
First of all the binding of the 3rd edition is horrible, and I barely used it. My class used this book for analysis 2, basically just using the second half of the book. The notation is horrible, there is almost no expository writing between the proofs and theorems. Often proofs are longer than they need to be, but others are extremely terse and skip key pieces of logic. For analysis 1 I loved Ross's Book "Elementary analysis: the theory of calculus", and I think analysis 2 would have been better off transitioning to Rudin as opposed to this book.

Everything Fine
The book arrived in a timely manner.I was pleased with the appearance and wear of the book.The description was right on, and I got what I expected.Thank you

Messy Layout, Messy Ideas
I used this for an undergraduate Analysis text for multivariate integration.

On the theory aspect, it was not entirely rigorous. Many fundamental ideas had to be found in asides randomly located in the text as "it can be shown" without justification. While this is true, when encountering the subject for the first time, the student might wish to at least have these facts readily available for reference, or explicitly included in the proofs. But worse, in the sections on vector calculus, the approach was explicitly non-rigorous, and any point requiring a rigorous explanation was relegated to "see Spivak's Calculus on Manifolds," a reference repeated several times throughout the later sections.

In terms of applications, there are plenty of computational examples and exercises. Unfortunately, the examples tend to be relatively easy compared with the exercises, and often rely on some trick which avoids the general principle to arrive at a quick solution. For instance, for parametrized curves, the examples involve things like connected line segments, while the exercises are much, much more complicated.

This attempt to balance rigor and applications unfortunately leaves the student confused and frustrated, not knowing the theoretical foundation or how to apply the results beyond toy problems. Just because a book has less rigor doesn't mean it's easier! It leaves the reader confused as to what rigorous proof even means, which is one of the key elements of introductory analysis classes.

That said, I haven't read the earlier chapters, and there may be something worthwhile inside them.

Terrible Book: Only buy it if your class forces you to
I am really sorry if your instructor has forced you to buy this book.Buy Mary Hart's Guide to Analysis in order to understand the material Guide to Analysis (Macmillan Mathematical Guides).It will get you through the first half of Wade, but sadly ends before the second half of Wade.Only use wade so that you have the assignment questions.

The author skips major sections of proofs necessary to understanding the material with a snide arrogance that is downright insulting to the student.It is astounding what tenured professors and coddled publishers can get away with these days. ... Read more