Book Description

Students and research workers in mathematics, physics, engineering and other sciences will find this compilation of more than 2000 mathematical formulas and tables invaluable. They will see quickly why half a million copies were sold of the first edition! All the information included is practical -- rarely used results are excluded. Topics range from elementary to advanced-from algebra, trigonometry and calculus to vector analysis, Bessel functions, Legendre polynomials and elliptic integrals. Great care has been taken to present all results concisely and clearly. Excellent to keep as a handy reference! ... Read more

Reviews (8)

Indispensible for the physicist
A fantastic summation of neccesary mathematics for any engineer or physicist...the only reason for 4 stars is that it's integral table is a little short.

Not as much help as it should be
I bought this book as an aid to EM theory and Quantum Mechanics. I found little really useful stuff. The series expansion didn't have (1+u)^-3/2 for example, or the curl operator in cylindrical and spherical coordinates. The integral table is limited. The authors should look at books like Dwight, for example, and make sure their coverage is more complete. I am disapointed in it. For the money, it should be much better.

Inexpensive reference!
As an undergraduate physics major, it is necessary to have some sort of mathematical handbook containing tables of integrals, trig identities, differentiation rules, vector identities, etc. As such, I cannot give this book higher praise! While does not contain as many features as the CRC Handbook of Tables and Formulae, or many of the other big famous hardcovers, it makes up for this in many ways. It is compact, lightweight and fits in most bookbags. It contains the tables and rules which will be most used in undergraduate homework problems. Most importantly, it is affordable on a student budget! I carry this with me to study groups and tutoring sessions.

You are crazy if you don't have this book!
Great reference for formulas and identities that you have forgotten. Integral table is awsome. This book is week on more advanced stuff like bessel functions etc...This is some of the best money I have ever spent. Used it all the time in my physics classes and ALWAYS carry it with me. How did I ever get on without it?

Best money i've ever spent
This handbook was pretty much all I ever needed from college through my Ph.D. in physics. An extremely valuable resources. If the formula you need isn't in here, chances are you did the problem wrong ... Read more

Book Description

Published by McGraw-Hill since its first edition in 1941, this classic text is an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics.It will primarily be used by students with a background in ordinary differential equations and advanced calculus.There are two main objectives of this text.The first is to introduce the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets.The second is a clear presentation of the classical method of separation of variables used in solving boundary value problems with the aid of those representations. ... Read more

Reviews (4)

Excellent
This book is quite thorough, but remains easy to follow (considering the material). It starts out with partial differential equations (no previous PDE experience needed) and shows where Fourier series comes from, which I found motivating since the purpose of Fourier Analysis was evident from the beginning. It then goes into making solutions of arbitrary functions out of sine and cosine functions as well as touching on other orthogonal sets.

The book's main focus is on starting with PDEs and ending with a solution of a Fourier series.

The first chapter was the hardest since the approaches to problems were much different than in calculus, but after adjusting to the material and the approaches to the problems, it gets easier!

Great text for an intro to pde's course!
My first encounter with partial differential equations was out of this book. Since then, I've had another course on pde's, and used this book as a reference quite often. Fourier Series adn Boundary Value Problems is very much like Complex Variables and Applicatoins, also by Churchill and Brown. It's accessible to a large audience. Though it would help to have had an advanced calculus course, it isn't necessary to understand the mechanics of solving pde's (namely the variables seperable cases, which is mostly what's in this book). If you're an undergraduate math, engineering or physics student, you'll probably be using this book.

Try Another Text
I found Dr. Brown, in conjunction with Dr. Churchill, to have written a very dry and non-useful text. It fails to provide the undergraduate student with the resources and background information that more highly touted books offer. There are a few examples that are somewhat helpful, but overall I found myself having to use reference texts to supplement this one. I am not a math major, but am continually searching for good math texts to help me grasp the fundamentals of more difficult topics. I did not find that help here. Too much 'math prose' and not enough to-the-point definitions and examples, which is the cry of every non-math major. Their treatment of the Laplacian is not even worth the bother of placing it in the book. The physical size of the book is small, (9 1/2 by 6") with 335 pages. Not nearly enough for the treatment of its titled subject.

An excellent book on Fourier Series
This is a great book that gives precise examples which are easy to comprehend. Dr. Brown proves to be an excellent author once again. ... Read more

Book Description

This book outlines an elementary, one-semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. ... Read more

Reviews (8)

beware, no solutions
Good book, but no solutions to any exercises. Usually Springer books do have some solutions, so it was a bit disappointing.

the missing star
Stephen Abbott is with no doubt a very talented writer in mathematics. The book is a fun to read because
of its style : each chapter starts describing a basic mathematical question that challenged the human mind
in history. This always makes you curious to read further to discover the great constructs made by the creative thinkers who solved these problems. Also, each chapter ends with adescription of related topics and some historical notes . I really like this style ....

However I did not give this book a five star rating for the following reasons :

-Some proofs contain gaps that are left as an exercise to the reader. Not all of these exercises are
staightforward however. It sometimes took me several hours to find a solution for these exercises ...
This is OK for real exercises, though it is no fun to have to spend this time filling up some basic proofs..
Sometimes I also had the impression that the hints were misleading. For example, I completed the proof on the double summation bit did not at all understood why we needed the hint prooved in exercise 2.8.4. Also when I tried to complete the
proof of the sequential criterium for nonuniform continuity (theorem 4.4.6), I did not see why we would need the hint
to take values 1/n for epsilon...
-Some explanations are missing, (maybe this will be solved in second edition). For instance :
a)please give a clear definition of what an interval is before using the name interval throughout the book.
b)In baires theorem, the author claims that every open set is either a finite or countable union of open intervals .... Please explain why ...
-Especially the 'more advanced' topics like baire 's theorem, fourier analysis, metric spaces, ... are rather presented as one big exercise. If you want to learn these topics, there are better books, providing you with much more information....
-This book only covers a limited range of topics. All the analysis is done for real variables in one dimension.

I think we need a broader scope, even for an introductionary course. My opinion is that modern analysis should start from the beginnig with n-dimensional metric spaces, conveying your mind to the beautifull theories of normed linear spaces and banach spaces.
-Since the book is targeted to the beginning student of abstract math, it would be good idea to include some pages
(appendix) on logic reasoning like second order predicate calculus, and some basic set theory ....

So, no five stars for this edition (maybe for a next edition ??)...
Giving this beautifull book less then four stars however would be unfair, since it definitely has it strengths : the things that are explained are explained very clear and the narrative style of the author always keeps the reader interested!!! Nobody could have done that better !!

A Joy to Read
This is my first analysis book. So, I have no basis for camparing it as an analysis book. But, as a math book, it is honestly the most readable and enjoyable I have ever read.

excellent introduction to mathematics and analysis
Understanding Analysis is an excellent textbook for anyone wanting to learn more about mathematics beyond the high school and calculus levels. It shows how mathematics is more than simply multiplying numbers or solving integrals. Elementary analysis rigorously builds the foundations of calculus starting from first principles. If you ever had trouble understanding limits, sequences, series, derivatives, or integrals and want to really learn them, I strongly recommend this book.

The book provides a lucid introduction to proof writing and non-computational mathematics best suited to students who have just completed calculus. In the author's own words, "The proofs in Understanding Analysis are written with the introductory student firmly in mind. Brevity and other stylistic concerns are postponed in favor of including a significant level of detail." When contrasted with many other mathematics books that are terse presentations of theorems, the textbook is remarkably readable, focusing on teaching material and developing students.

Very Readable
As an engineering student trying to specialize in sigal processing, I found my mathematics background filled with holes. I embarked upon a journey to try to fill these holes and discovered what disservice my engineering education had done to me in terms of dealing with abstract notions like probability theory, etc. This book has been indispensible in re-engaging not only my anlytical skills but also continue on my path to a better understanding of the mathematics required to succeed professionally. Thank you, Prof. Abbott! ... Read more

Amazon.com

At the very beginning of his book on i, the square root of minus one, Paul Nahin warns his readers: "An Imaginary Tale has a very strong historical component to it, but that does not mean it is a mathematical lightweight. But don't read too much into that either. It is *not* a scholarly tome meant to be read only by some mythical, elite group.... Large chunks of this book can, in fact, be read and understood by a high school senior who has paid attention to his or her teachers in the standard fare of pre-college courses. Still, it will be most accessible to the million or so who each year complete a college course in freshman calculus.... But when I need to do an integral, let me assure you I have not fallen to my knees in dumbstruck horror. And neither should you."

Nahin is a professor of electrical engineering at the University of New Hampshire; he has also written a number of science fiction short stories. His style is far more lively and humane than a mathematics textbook while covering much of the same ground. Readers will end up with a good sense for the mathematics of i and for its applications in physics and engineering. --Mary Ellen Curtin ... Read more

Reviews (29)

A history of "i" for the mathematically initiated!
Nahin's text on the history of i is an exciting, comprehensive look into the origins of i and its elementary theoretical applications. It rightfully has been compared to Eli Maor's wonderful book "e: The Story of A Number", which deserves five stars in its own right. I do have to take issue with some of the other reviews posted here. For instance, a few have said that you have to have a "graduate math" background to fully appreciate this book?!? Who are they kidding? Nahin actually *sacrifices* mathematical rigor in order to improve his exposition. Anyone with a real mathematics background knows that complex analysis gets far more complicated than the basic material Nahin presents in his book. To get an idea, you can peruse Walter Rudin's fine text "Real and Complex Analysis". To be fair, I agree with the reviewer who wrote that Nahin should not have omitted material on Klein groups, Julia and Mandelbrot sets. However, I can understand why he did. It is difficult to write on such subjects as groups and fractals to an audience intended to have a (motivated) high school or freshman calculus background. I read this book, understood it, and loved it, long before I had any idea what groups or fractals were. Nahin gives fair warning in the introduction to his book that it is not a "mathematical lightweight". I do think that a solid background in (single variable) calculus, including power series, is crucial to a true appreciation of the book. In particular, one must know these things to value the genius of Euler and others in the section on "Wizard Mathematics". Nahin does tread lightly into other topics, such as differential equations and (advanced) algebra, but to say these are a prerequisite to reading the book is ridiculous. I think even if the reader has never encountered ideas such as the Fundamental Theorem of Algebra before, they serve to enrich, not detract from, the material. In any case, the reader should be pleased to see a leisurely treatment of something so blown out of proportion as FTA, as an understanding of it is basic to anything beyond calculus. Proofs of it are rich in variety, ranging from topology to geometry to complex variables (using the theorem of Liouville and properties of entire functions). One criticism that is entirely justified is the typographical errors that regrettably plague the book. In particular, the theorem of Green, relating double integrals to single contour integrals, a result that is surprising and illuminating. However, the careful reader can usually spot and correct such errors, and he or she should be delighted in their own astuteness, rather than blame the author. He does a wonderful job explaining the conceptual basis of i, and I think this overrides any of the books minor flaws. The book does seem to end rather abruptly, however, and I hope that if the author chooses to revise his work, he will expand upon the material, in particular, a (brief?) treatment of the Residue Theorem, the crowning jewel of complex integration. Perhaps even a section on conformal mapping? I do realize though that this may place the book too far out of reach of his intended audience.

The bottom line: if you want a storybook, this is not for you. If you like mathematics, and have a historical bent, this book will satisfy you. Those with a mathematical background will realize that Nahin has the perfect background to write this book: electrical engineers have a *much better* idea of what's going on with complex variables in terms of getting their hands dirty than mathematicians themselves. This is because most mathematicians insist on strict formalism and rigor, but engineers think more freely, and in any case they are the ones that discovered half of the applications of complex variables. E.g., imagine Laplace transforms even existing without Oliver Heaviside, who was thought to be a fool by the mathematical community in his day!

For those that are curious, I only have a B.A. in math, and no graduate education, though I do pursue math study in my free time. So I think I am in a position to make the above arguments.

thumbs-up from an EE/physicist - not meant as a textbook
This was an incredible book. I'm an electrical engineer by degree and a physicist by hobby, so I'm pretty familiar with imaginary numbers. While a lot of the concepts were a review to me, the book also introduced me to a lot of new and fascinating territory. But besides the pure math, it also introduced me to a lot of the history and personalities behind it all. Putting it in perspective and historical context helps breathe new life into it.

I must strongly disagree with the reviewers who said that the math was not rigorous enough, and that the presentation was lacking in personality (two opposite viewpoints).

The style had way more personality than any textbook on mathematics. And anyone with a high-school math background can get through most of the book (not all of it - they may need to skip the bits involving calculus). And whoever says the presentation lacks rigor is missing the point entirely, because this is NOT a textbook and was never meant to be. The author never intended to scare away the casual reader with lenghty proofs - he wants to explain in accessible terms, not alienate.

Wish more books like this
Inspiring!
Explaining the true physical meaning of an imaginary real quantity and showing its real imaginary applications.

somewhat dense and no problems to solve by the reader
This book is well written, but, it does feels like the venerable professor took his lecture notes and strung them together, but dear me, he left out problems for the reader; this to me is a cardinal sin when it comes to expository math.

Maybe the professor could create a website with problems + solutions related to the subject matter - give us puzzle people a chance at solving at least a few problems on our own.

The "imaginary" number i is quite real, and very useful.
In high school and college mathematics courses it is generally stated that, since the square root of -1 cannot be expressed as any real number, it must be a so-called imaginary number, usually designated as i. Furthermore, any number multiplied by i, say 2i, is also said to be imaginary. So-called imaginary numbers generally cause even very bright students some discomfiture, as well they should.

But, in fact, i is not an imaginary number (whatever an imaginary number would mean); rather it is something quite real: a 90 degree rotational operator. Mathematical operators -- including rotational operators -- are beyond the average person's knowledge (or interest) of mathematics, but at least they are real. And they are also quite useful, not only in mathematics but in various fields on science and engineering.

In this fascinating book Nahin traces the history of the centuries-long struggles which the concept of negative numbers and, eventually, of their square roots caused both mathematicians and philosophers until an obscure Norwegian surveyor discovered the true meaning of i in 1797.

As a scientist who spent decades using i -- but never really accepted the traditional view that it is an imaginary number -- I was overjoyed when I finally discovered its real meaning.

Clearly this book is not for everyone; but it should be quite interesting to anyone who, like I, never full accepted the concept of an imaginary number. ... Read more

Reviews (4)

Great Introduction
This is a text for Real Analysis at the Junior Level (American university level). It goes to extreme lengths to make analysis understandable to people who have no prior exposure. The organization is good. Completeness is introduced early as (the "piggy in the middle"). Proofs are written in detail with fill-in-the-blank spots to force the reader to follow the argument. It has good exercises making it an easy book to teach out of. Excellent for the absolute beginner. Good candidate for the classroom.

Basic Real Analysis unleashed
Bryant builds the basic concepts of a first course in mathematical analysis upon the notion of numerical sequences. This approach gives an unified vision and amazing insights. Infinite series, limits, derivatives, Riemann integral are studied in an integrated vision. Clear ideas, illustrations and humor are found across all its pages. Good and illuminating exercises, too. An excellent introduction to basic real analysis.

Exposes Mathematical Analysis Without Set Theory Background
Mathematical analysis is a refinement of calculus, and a pathway into further branches of mathematics, including topology and advanced topics in algebra. Analysis, however, may not seem to be at all related to calculus at its initial stages. An introductory course on analysis can render an unprepared student, even with experience in other branches of mathematics, perplexed and challenged to an extreme. Only later in the analysis course are even the most basic topics of calculus introduced.

One of the most important considerations prior to taking an analysis course is the level of background and understanding of mathematical logic. Set theory, a branch of mathematical logic, is in fact the basis of calculus as well. Due to an emphasis upon computations, however, the highest grades in calculus are possible without understanding, or even knowing of, this underlying foundation.

This work is unique among those introducing analysis, in that it does not require a background in set theory. It in fact teaches numerous fundamental concepts of set theory, without stating that it is doing so. Examples provided are based on daily concrete experience, yet are altered for purposes of mathematical instruction. These descriptions are sufficiently general as to prepare the reader for when formal set theory is introduced in more rigorous textbooks.

In addition to being an extremely readable and accessible work, solutions and hints are provided for every review question for every section of the book. This is in stark contrast to textbooks on the subject, which, while costing several times more, are typically designed for a classroom setting, and so leave all questions unanswered. This self-testing of the understanding of each section is crucial for subject matter requiring such attention to detail and precision.

The numerous illustrations throughout the book are rendered clearly and with instructional purpose, yet are often drawn by hand, adding to the sense of familiarity with the author. All of the basic subject matter for a course on analysis is provided, yet has been specifically tailored for a reader in the stages of preparation, of review after completion, or one who is simply inquisitive as to what is required to comprehend analysis successfully.

The softcover edition is durable and portable, and the book remains in excellent condition through numerous readings, which it will almost certainly go through.

If you have been required to take an analysis class but left it with only a vague sense of its underpinnings, you may wish to go through this work when time permits. For the price of the book, the information and instruction provided is truly outstanding. This text receives the highest marks in all categories.

Outstanding introduction to advanced mathematics
While there have been countless introductions to mathematical analysis (calculus) this is my favorite. The author does a brilliant job of making the subject matter interesting and very understandable with excellent exercises along the way which have solutions in the back ! A must read for bright highschool seniors and college freshman that are taking calculus or will be. ... Read more

Book Description

Directed towards students without in-depth mathematical training, this text is intended to assist engineering and physical science students in cultivating comprehensive skills in linear static and dynamic finite element methodology. Included are a comprehensive presentation and analysis of algorithms of time-dependent phenomena plus beam, plate, and shell theories derived directly from 3-dimensional elasticity theory. An ideal primer for more advanced works on this subject. Brief Glossary of Notations.
... Read more

Reviews (12)

An excellent book on FEM for graduates or professionals
The Finite Element Methodology though conceptually simple (eat the elephant by chopping it up into mouthfuls), becomes somewhat invloved when applied, because the of tricks used to get solutions, after all you still may have to solve 100,000 PDEs to get your approximate solution to an otherwise intractable problem. So in its own way FEM can become a bit of a pachyderm itself.

This book is very good, but be aware that this book is aimed at graduate physical-science/engineering students. This means that you know how to solve basic second order differential equations and understand how to perform path integrals for example.

This book is aimed at people who would like to be able to write their own FEM solver. If you are looking to gain some backgrounding in how to construct finite element models using a program to solve problems, this book is probably much more than you need. You might want to try the "Schaum's Outline of Finite Element Analysis" if this is your objective.

DLearn is available from the www.zace.com/dlearn.htm or by typing
"Dlearn program"
into google and following the link.

Great Buy, good value for your $$$
An excellent reference book from one of the gurus of FEM. It's more mathematically oriented than most, but it gives you a good insight into the math , which is the foundation of all FEM.
Great bargain for the price.

Response to Sylmar, CA reviewer
The reviewer who said that the software is not available from the ZACE website is incorrect. Go to www.zace.com and click on "Home Page." There you will be able to download DLEARN for free in addition to a
C++ finite element code.

excellent book
an excellent,and also one of the best several books in FEM, definitely. But you need to invest much time to read and understand those math and theories behind the FE, then you can only get the really good insight into the subject.

Good, but....
The first reviewer states that the code is available for download. The text references this non existant code throughout the entire volume but it cannot be found anywhere. The site referenced in the book;
"NOTE: The software described in this book may be downloaded from www.zace.com",
does not have the download although it does have a reference to a high cost seminar in Europe by the author. Also, this site refuses eMail inquiries. I finally gave up and purchased the older hard copy version which at least has the "old" source for DLEARN. Other than this frustrating nonsence by the author, it is a good FEA study. ... Read more

Book Description

The topic of 'circle packing' was born of the computer age but takes its inspiration and themes from core areas of classical mathematics. A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book lays out their study, from first definitions to latest theory, computations, and applications. The topic can be enjoyed for the visual appeal of the packing images - over 200 in the book - and the elegance of circle geometry, for the clean line of theory, for the deep connections to classical topics, or for the emerging applications. Circle packing has an experimental and visual character which is unique in pure mathematics, and the book exploits that to carry the reader from the very beginnings to links with complex analysis and Riemann surfaces. There are intriguing, often very accessible, open problems throughout the book and seven Appendices on subtopics of independent interest. This book lays the foundation for a topic with wide appeal and a bright future. ... Read more

Book Description

This volume is based on the 1998 Second International Symposium on Computer Methods for Engineering in Porous Media. The selected contributions provide evidence that computer-based models and in particular numerical methods are essential tools for the solution of many problems encountered in the field of flow and transport in porous media. The range of subject areas presented includes numerical methods, mass transport and heat transfer and simulation studies. ... Read more

Book Description

This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever. ... Read more

Reviews (14)

The DEFINITIVE text for classical Analysis
The DEFINITIVE text for classical Analysis

This book is the definitive text in classical Mathematical Analysis. It was first published in 1902 and the fact that it is still in print is testimony to it's wide ranging utility and appeal.

It should be noted that this text is not for those who are new to the rigour of Analysis; its presentation is suitable for a final year undergraduate or for the post-graduate student. More importantly, its wide ranging content of proofs and results would also prove useful to the Physicist.

The first part of the book covers the "essentials" of analysis: continuity, differentiability, summation of series, convergence and uniform convergence, and the theory of the Riemann integral. Subsequent chapters quickly but comprehensively develop the theory of analytic functions, the theorems of Cauchy, Laurent, and Liouville and the calculus of residues. These chapters knit very well into the earlier presentation of the basic processes of analysis! The pleasing thing is that despite the passage of time and the advent of hundreds of books on Complex Variable Theory, Whittaker and Watson's treatment still bears a mark of freshness and rigour.

Also included is a comprehensive treatment of expanding functions in infinite series and asymptotic expansions and summability of series. For completeness, the text also covers the theory of linear differential equations and Fourier series.

The second part of the book is what stands it apart from the rest. The authors provide a comprehensive discussion of the major transcendental functions: Gamma, Zeta, Hypergeometric, Legendre, and Bessel to name the more commonly encountered ones. The treatment is rigorous but the copious number of examples provides opportunity to learn the theory and apply it. Lots of apparently obscure results, many that would be useful in Physics applications, are cited as examples.

The latter chapters presents a treatment of Elliptic, Theta and Mathieu functions.

Overall, Whittaker and Watson will continue to be the guiding light for any serious scholar of classical analysis and an excellent reference point for the solutions to the fundamental equations of Mathematical Physics. Even though I am not a practising Mathematician, I find this a pleasant book to dip into: there's always a little surprise and something new to learn.

This book will live forever!

This book is worth it's weight in gold!!
If I could, I would give this book ten stars. When I first sat down to read it, I couldn't believe what I was seeing. This is the only book I have ever seen on complex analysis (or any scientific field for that matter) in which the authors cover so much material (everything from residues to integral equations to elliptic functions and MUCH more) and yet manage to make the whole text fit into a framework which is relatively easy to follow, even for someone completely new to complex analysis. Moreover, the majority of the many hundreds of excercizes in this book range from moderately to nail-bitingly hard, and encourage a true understanding of the material being covered. I would reccommend this book for ANYONE who has mastered basic calculus and analysis and wishes to begin learning complex analysis and the theory of special functions. The book's coverage of the following topics is especially noteworthy: The gamma function (the book uses the INFINITE PRODUCT as the basic definition), the hypergeometric function (and the confluent hypergeometric function), bessel functions (a field in which G.N. Watson was a leading expert), and the Weirstrassian and Jacobean elliptic functions and theta functions (I LOVED the intuitive development of the theory of the elliptic functions, which is made to parrallel that of the trigonometric functions, which are of course familiar to the reader). I would ESPECIALLY recommend this book for those pursuing SELF-STUDY (although it is NOT for the mathematically weak-of-heart, but no book on the topic is), as it is quite self-contained and readable for a book on complex analysisis. Once you buy it, you won't even think to complain about the high pricetag, because you will be way too absorbed in the math to think about anything else.

About the other author, YOU STILL DID NOT BUY IT?
Neville Watson's mother was Mary Justina Griffith, the daughter of the rector of Ardley in Oxfordshire. Neville's father was George Wentworth Watson who was a schoolmaster, but is more famous for his work as a genealogist. He played a large role in the publication of The Complete Peerage, a 13-volume database of the British peerage, generally accepted as the greatest British achievement in the field of genealogy. The first edition was published in London between 1887 and 1898. George and Mary Watson had two children, a boy and a girl, the eldest being Neville.

Neville was educated at St Paul's School in London where he was very fortunate to have the outstanding teacher of mathematics Francis Macaulay. He mixed with equally outstanding pupils, for Littlewood, less than a year older than Watson, was also a pupil at the school. Having won a scholarship to Trinity College, Cambridge, Watson matriculated there in 1904. At this time there were three young fellows of Trinity all of whom had a major influence on Watson's mathematics. They were Whittaker, Barnes, and Hardy. Perhaps the one from this trio who had the greatest influence on him was Whittaker, despite the fact that he left Cambridge in 1906, two years after Watson began his studies there.

Watson graduated as Senior Wrangler in 1907 (meaning that he was ranked in first position among those who were awarded First Class degrees), completing the Mathematical Tripos in the following year in the second division of the First Class. He won a prestigious Smith's Prize in 1909, becoming a Fellow of Trinity College in 1910. This was particularly pleasing to him for he had a great love of his College, and throughout his life he collected prints of the College and of previous Fellows.

After election to his Trinity fellowship, Watson spent four further years in Cambridge before leaving to take up an assistant lectureship in University College, London. From 1918 to 1951 he was Mason Professor of Pure Mathematics at Birmingham. He married Elfrida Gwenfil Lane, the daughter of a farmer from Holbeach in Lincolnshire, in 1925. They had one son.

Watson worked on a wide variety of topics, all within the area of complex variable theory, such as difference equations, differential equations, number theory and special functions. He is best known as a joint author with Whittaker of A Course of Modern Analysis published in 1915. The first edition of the book has only Whittaker as an author. In 1922 Watson published The theory of Bessel functions which was another masterpiece. Titchmarsh wrote of Watson's books (see for example [2]):-

Here one felt was mathematics really happening before one's eyes. ... the older mathematical books were full of mystery and wonder. With Professor Watson we reached the period when the mystery is dispelled though the wonder remains.

One piece of work undertaken by Watson deserves special mention. It involves the problem of wireless waves, which were quickly found to travel long distances despite the fact that theoretically they should not have been able to follow the curvature of the Earth. A mathematical model had been constructed where the Earth was represented by a partially conducting sphere surrounded by an infinite dielectric. Such a model had been used by Macdonald, Rayleigh, Poincaré, Sommerfeld and others. Although Watson was not interested in how best to model the situation, he was, however, very interested in using his expertise to determine mathematical solutions to the given model which others might then check against observations. He obtained solutions to the problem in 1918 which showed conclusively that the model was not a satisfactory one.

In 1902 Heaviside had predicted that there was an conducting layer in the atmosphere which allowed radio waves to follow the Earth's curvature. This layer in the atmosphere, now called the Heaviside layer, was only a conjecture in 1918 but it was suggested to Watson that, having shown the previous model to be wrong, he now look at the model resulting from the postulated Heaviside layer. Watson showed that if the layer was about 100 km above the Earth's surface and it had a certain conductivity, then indeed the solutions obtained closely matched observations. That Heaviside, and Watson, were correct was confirmed in 1923 when the existence of the layer was proved experimentally when radio pulses were transmitted vertically upward and the returning pulses from the reflecting layer were received.

Watson undertook a major project by examining in detail Ramanujan's notebooks, extending his results and supplying proofs. In fact he wrote twenty-five papers relating to results in Ramanujan's notebooks, and he spent many hours making a hand written copy in wonderful script of all the notebooks. He enjoyed numerical calculations and spent many happy hours doing numerical work on his calculating machine.

He was elected to the Royal Society of London in 1919. In 1946 he received the Sylvester Medal of the Royal Society:-

... in recognition of his distinguished contributions to pure mathematics in the field of mathematical analysis and in particular for his work on asymptotic expansion and on general transforms.

Watson was also very active in his support for the London Mathematical Society. He served as secretary from 1919 to 1933, president from 1933 to 1935 and acted as an editor of the Proceedings of the London Mathematical Society until 1946. The Society awarded him their De Morgan Medal in 1947. The Royal Society of Edinburgh elected him to an honorary fellowship.

We find a little of Watson's personality described in [2]:-

He was the university's expert on the timetable; students with unusual combinations of subjects usually had to be referred to him for advice, and for many years after his retirement the dates of the academic year were governed by the "Watsonian cycle". ... He took great trouble with the style of his letters and his conversation and enjoyed finding a pungent phrase to express his points of view or his criticism ... he made no secret of his aversion to cars, telephones, and fountain pens. He loved trains - whose timetables were as familiar to him as those of the university lectures - and unusual stamps.

Article by: J J O'Connor and E F Robertson

really eternal
This Book is a Bibel in Analysis, in this Book you learn again how Important the Formula ist, the one which you can Modify and change mathematically in order to come to new Formulas!! NOT like the Modern Books, where Axiomatizing is taken as to be prior to the Formula...

The Ideas are very clear, the Analytical theory of Complex Functions and its Applications in Ind. Integrals, is really blessed and very clear and convincing!! like the Other colleges, I say , buy it (for advanced Analysis)::: A MUST HAVE

A note on the edition
Please take note: the latest "new" edition of the book was in 1927. That was the fourth edition. Everything since then has been a reprint. You're not getting anything new if you buy a 1997 reprint; even the typeface is the same, only the cover is blue. ... Read more

Reviews (3)

A good book, but not for beginners.
if you want an introduction to complex analysis, I advise you to pass on this book, and read Churchill and Brown's introductory book. Having said this, part I of Lang's book will seem mostly review if you follow my advice. Part II, on Geometric Function Theory, is more advance material that is presented reasonably well.

Not TOO complex
A person with absolutely no knowledge of complex numbers could begin with page one of this book. However, I think that some exposure to analysis is helpful before finishing the first chapter, but not necessary. I found this book easier to read & understand than some real analysis books, yet it helped me further understand real analysis in the process. I'm sure this is due to mere repetition of some of those concepts over a different field. As the author mentions in his foreword, the first half of the book can be used as an undergraduate text (Jr/Sn years) and the second half can also, but I would NOT have enjoyed it in undergraduate studies. I found it worthy of a first course in complex numbers at the graduate level. I especially liked it after studying real numbers. The placement of the chapter subject matter can be altered (to some degree) to ones liking. I think Lang has provided good examples & problems. There's a solutions manual (by Rami Shakarchi) for this text somewhere.

A brief discription of the chapters (some of them at least):

Chp 1: basic definitions & operations, polar form, functions, limits, compact sets, differentiation, Cauchy-Riemann eqs, angles under holomorphic ("differentiable") maps.

Chp 2: formal & convergent power series, analytic functions, inverse & open mapping thms., local maximum modulus principle

Chp 3: connected sets, integrals over paths, primitives ("antiderivatives"), local Cauchy thm, etc

Chp 4: winding numbers, global Cauchy Thm, Artin's proof

Chp 5: Applications of Cauchy's integral formula, Laurent series

Chp 6: Calculus of residues, evaluation of complex definate integrals, Fourier transforms, etc (fun stuff)

Chp 7: Comformal mapping, Schwarz lemma, analytic automorphisms of the Disc

Chp 8: Harmonic functions; Chp 9: Schwarz reflection; Chp 10: Riemann mapping theorem; (11): Analytic continuation along curves; (12) applications of Maximum Modulus Principle an Jensen's Formula; (13) Entire & Meromorphic functions; (14) elliptic functions; (15) Gamma & Zeta functions; (16) The Prime Number Theorem; and a handy appendix.

Wrong book!
I have tried to tell you guys. My review you have published above is of the book of same name and publisher (but 2nd ed) by Bak and Newman! I did not review Serge Lang's book! ... Read more

Book Description

The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques.Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data.Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLAB . Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned.Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background. ... Read more

Reviews (6)

Too Elementary
A Primer on Wavelets and Their Scientific Applications by Walker, James S. and Krantz, Steve G.

There is nothing wrong with this book, but if you know the fundamentals of Fourier transforms, correlation and random processes, this book will be waste of your time and money. If one the other hand, you do not, than this is a readable book, but I think that it is a little thin.

Best introductory book on wavelets
This is the best introductory level book on wavelets I have read. It is written beautifully and is one of the few books that provides insight as to how and why wavelets are useful.

Everyone should start out their investigation of wavelets with this book first. Highly recommended.

The ideas and the software.
This lovely little book helps the novice to get an idea of the math which underlies wavelets;-- and at the same time to learn how one readily gets hold of software that is convinient,-- that will make it easy for anyone to start playing around with it. The author also explains in plain English the wavelet aspects, and some of the mathematical constructs, behind audio denoising, signal compression, image recognition, speech recognition and more.

Wavelets in 20 simple pages
This is simply the best book I have come across on introducing wavelets.

I am sure that within the first 20 pages, which are easy to understand and make for a very quick read, you will begin to see the beauty of this theory and will applaud the author's exposition.

While this book does not need much more than basic linear algebra, the author does not shy away from the mathematics where necessary - he simply motivates it by providing an intuitive understanding of the equations, so it's easy to follow.

In the very first chapter, he describes the wavelet method using examples that can be worked out by hand. (This is also mentioned in another review and contributed to me buying this book. I was doing research on another wavelet book on the site when I came across this book and it's reviews.) This helps to fix and brilliantly clarify the main ideas behind the theory. Armed with this knowledge, the reader can better appreciate the more sophisticated wavelet functions. But, the basics would be firmly planted by this book. This is rarely seen in other books dealing with this thoery.

This book is great for someone who wants to learn about this topic. It also is an excellent book for those who have an advanced graduate degree in applied mathematics since it demonstrates how to truly understand complex concepts.

The discussion is motivated with real world examples such as removing noise from signals, image enhancements, etc. These are useful examples that you can relate to. There is enough in this book and the downloadable software that you may want to undertake meaningful projects yourself. That is the confidence that you get from this book.

An outstanding quality is that the book is thin. This is a strong motivating factor since it immediately sends the message that "this method can't be that hard to grasp if the book is so short." And, this subliminal message keeps your spirits up as you read this masterpiece.

Wavelets is a mathematically intensive technique, and it seems that most authors want to show how "macho" they are by shrouding the basics under a heavy cloak of complex equations. But, true "machoism" is displayed by how deftly an author can bring a difficult topic to the lay person. James Walker does this remarkably well.

Excellent Introduction for us Beginners
Ch. 1: Haar Wavelets: The chapter lays out the basic concepts underpinning wavelet analysis using examples that require only hand calculations. Shows how a signal is broken down into is low frequency (i.e. trend) and the high frequency components (i.e. fluctuations). The concept of the transform inverse is presented and demonstrated through examples. The chapter goes on to introduce multiresolution analysis and requires some algebra but for my meager math background a piece of cake. Signal compression is discussed and emphasized. Removing noise from audio signals is examined. Chapter ends with a demonstration of why we need some wavelet beyond the Haar.
Ch. 2: Daubechies Wavelets: While there are numerous Daubechies wavelets Walker picks the simplest and develops important concepts. Some comfort with linear algebra and matrix notation makes this chapter easy to understand. The examples in the Haar chapter are carried forward to show how the Daubechies take care of discontinuities created by the Haar wavelet. Other Daubechies wavelts are then discussed and the Coiflets are introduced along with the need for these additional wavelets. More examples and the removal of pop noise and background static is examined. Image processing is introduced along with more examples. Great stuff even if I am not particularly interested in these topics. Chapter ends with notes and references where several URL's are presented on the various aspects of wavelets.
Ch. 3: Frequency analysis: Some familiarity with Fourier transforms will make the reader comfortable here but I do not think the familiarity essential to get the gist of where Walker is leading the reader. The idea of detecting a given sub image within a larger image is where we are lead. Chapter concludes on a roll your own wavelet section and again a notes and reference section.
Ch. 4: Beyond wavelets: Wavelet packet transforms are introduced and a few of their applications to signal compression presented. The concept of a continuous wavelet transform is brought in.
Appendix A. Software for wavelet analysis. Walker presents the URL for his software and data files.
For an introductory book I gave it the 5 stars. I really found it useful in getting me into the subject and a feeling for the level of effort I need to put forward to use wavelets for my application. ... Read more

Book Description

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.
A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.

Key Features
* Topics are covered from a historical perspective with biographical information on key contributors to the field
* The text contains more than 500 exercises
* Includes practical applications of the equations to problems in both engineering and physics ... Read more

Reviews (4)

The best book on PDEs
I was confused with so many books on PDEs and found this book God sent.If you ask me buy this book if you are looking for a serious book on PDEs with lucid explanations and problem solving techniques this is the book. Though the answers for the problems aren't given, you will love doing problems, I studied this book for my PhD quals.Enjoy it, savor it.

Fourier Analysis and Boundary Value Problems
This is an excellent introduction to Fourier series and its
applications to boundary value problems. It has a very good combination of history, theory,and exercises. In particular,
the book is an ideal text for math students who are taking
their first PDE course and do not have enough backgound in physics. The only problem with this book is its high price.

One of "THE" Books on Fourier and Boundary Value Problems
This book is very complete and comprehensive. It is meant for the advanced undergraduate (and even graduate) student. The book states it assumes you know the 1st year of calculus and how to solve some ordinary differential equations. It would help if you took one more upper division math class, as to be familiar with the proofs.

In a nutshell, this book is great! I used it to study for my PhD Quals in physics. It has a nice portion on Green's functions. The book is 'mathematical' but the backdrop on the topics are based on physical problems. The historical notes are great, and act as a complement to the physical problems (I'm not a big fan of history in textbooks, but this book does a nice job of integrating it).

Lots of problems are given, though no solutions are given for any of them. It would be a nice compliment to at least show the start, a tid bit in the middle, and then the solution. The solution at the very least. There are other books that do provide solutions to the types of problems listed here, but it would be nice just to carry around this one when learning boundary value problems.

A must for anyone that works on any problems that have ODEs, PDEs, Fourier and Laplace transforms, Boundary Value Problems and Green's Functions. You won't be disappointed!

A comprehensive book on Fourier Analysis, PDE and BVP
This is one of the best book from which to learn the subject, as it covers all the topics with great clarity and includes historical developement which makes for great reading. The coverage is mathematical rigorous but yet well-written enough that an advance undergrad. would have no problem in learning the material for the 1st time from this book. The only drawback to this book is that there is no answer for any exercise (no solution manual available either). Learn the mathematics here and use other books for exercise. ... Read more

Book Description

With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.

* Gives a unique presentation of integration theory
* Over 150 new exercises integrated throughout the text
* Presents a new chapter on Hilbert Spaces
* Provides a rigorous introduction to measure theory
* Illustrated with new and varied examples in each chapter
* Introduces topological ideas in a friendly manner
* Offers a clear connection between real analysis and functional analysis
* Includes brief biographies of mathematicians ... Read more

Reviews (1)

One of the best
An ideal text for a first-year graduate students in mathematics studying Real Analysis. The exposition is complete and very clear, including a lot of optional material for the curious. A detailed introduction to Functional Analysis is also included. Those needing the infamous Radon-Nikodym theorem and theory of signed measures will need to skip around since this is presented in the very last chapter (not a big problem). Also, consult the authors' companion text Problems in Real Analysis, which could be very useful to those preparing for a qualifying exam in analysis at the PhD level. Overall, a highly recommend text. ... Read more

Book Description

More than half a century has passed since Weyl's "The Classical Groups" gave a unified picture of invariant theory that has retained its importance in mathematics and physics to the present day. This book presents an updated version of this theory together with many of the important recent developments.As a text for beginners, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. It makes abundant use of examples and exercises to explain concepts such as root systems, Weyl groups and highest weight theory.The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms.This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups.It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory. ... Read more

Reviews (2)

typical math text
Sadly, this book does not live up to its
reputation and can only be used by those
already having a working knowledege of
the subject.On top of that, the printing
is atrocious in places - unacceptable for
an expensive item.

Comprehensive, well organized, very applicable
The book may be considered an update of Weyl's classicfrom 1946 "The classical groups, their invariants andrepresentations". Naturally the theory has developedimmensly since then and a new comprehensive presentation has been urgently overdue.Goodman and Wallach are not only among the most qualified to write this next "classic" on the subject, they alsoput a phantastic effort into making it comprehensive, readable, and pleasant to use. I found it easy to find needed resultsand concrete formulae on decompositions of tensors andharmonics, duailty groups and centralizer algebras, mulitiplicity formulae, branching laws, etc.. The results aresystematically organized - almost in an "encyclopedial" style.The book also contains rather modern results, such as, for example, new proofs of the Kostant Rallis Theorem or therelationsbetween invariant theory and the Jones knot polynomial.

This new "classic"sets the standard and foundations for anymathematician working in the field. I consider it especially useful also for mathematician from other fields as well as theoretical physicists who want to apply invariant theory in a variety of concrete settings. ... Read more

Book Description

This easy-to-understand calculus study aid is ideal for those who are new to the subject. It offers a well-illustrated, step-by-step introduction that moves along at an easy-to-keep-up-with pace. Use it with your textbook or for independent study to improve your comprehension and boost your grades. It features 226 solved and 513 skill-building supplementary problems--more than other study guides. Whether you simply want to feel confident at test time or build a solid foundation in calculus for more advanced math, science, and engineering course, Schaum's Outline of Beginning Calculus is students' first choice.level of Ayres/Mendelson, Calculus, 3/e. This will make up the calculus segments of one-semester liberal arts courses and the various one-semester Calculus courses for business or life sciences. This book will also address weaker students in general freshman calculus and high school advanced placement courses. Theory is restricted to fundamentals of differentiation and integration (single-variable) and the solved problems, with no steps ommitted, include reviews of algebra. This updated edition will continue the excellent sales record of the first edition and will include: problems suitable for graphing calculators and existing problems adapted to involve calculator use; emphasis on aogorithmic aspects of Calculus; Newton's method will be given a separate section, a section various approximation techniques for integration, Simpson's Rule the Midpoint rule; a section that presents the traditional treatment of exponential and logarithmic functions, which method some textbooks have gone back to. ... Read more

Reviews (4)

Good as supplemental text book, NOT good as primary textbook
There are not enough examples to explain everything you would need to know. I've found I had to go to the web or other more basic Calculus books many times to try to solve some of the problems in there. There are better books out there for those of us looking for complete breakdown of the problems and better explanations.

An excellent introduction and review of Calculus ......
I trudge back to this book again and again, being embarassed at having forgotten some basic idea or technique. This is an excellent supplemental text to a formal Calculus textbook like "Calculus " by Stewart. The writing is lucid and ideas are explained with the novice in mind. I find that reading this book first BEFORE getting into a meatier textbook helps me understand the material.

My experience has been that if I do not "do calculus" at least twice a week I forget the techniques (not ideas) almost immediately. Therefore, if you want a review of Calculus this book is a great tool. If you are new to calculus this book will help you understand important concepts like differentiation vs integration. I also found that reading pertinent chapters in Selby's "Geometry and Trigonometry For Calculus" and then reading related material in this book is a tremendous help.

Another strong point is that for us over 50 the font size and book layout is easy on the eye. So whether you are a novice or someone who has not had the chance to use Calculus in a while; or someone "brand new" to Calculus, get this book. An excellent resource for learning and entertainment!!

Very good value for the budget-minded math student
Elliott Mendelson does an excellent job of presenting basic calculus concepts in an inexpensive book. His explanations are very clear, and the book is actually fun to use. Perhaps my only criticism is that this book does not use color which often helps to clarify figures of graphs, but black and white figures are to be expected in an outline. If you're interested in a supplement to your text or if you want a book for self-study, I strongly recommend "Beginning Calculus."

Excellent value; good for self-study.
I use this book in a calculus class I teach on America Online. For the price, it is an excellent review of the subject. It covers the same material found in much more expensive texts. There are many exercises for students to do, with answers in the back of the book. It only lacks the full-color graphics that adorn conventional calculus textbooks.

I would recommend this book to anyone wishing to learn calculus by self-study. It is also a good supplement to a conventional text used in a class. The best way to learn math is by doing problems, and this book has plenty, including many detailed solutions. ... Read more

Book Description

In a very broad sense, "spaces" are objects of study in geometry, and "functions" are objects of study in analysis. There are, however, deep relations between functions defined on a space and the shape of the space, and the study of these relations is the main theme of Morse theory. In particular, its feature is to look at the critical points of a function, and to derive information on the shape of the space from the information about the critical points.

Morse theory deals with both finite-dimensional and infinite-dimensional spaces. In particular, it is believed that Morse theory on infinite-dimensional spaces will become more and more important in the future as mathematics advances.

This book describes Morse theory for finite dimensions. Finite-dimensional Morse theory has an advantage in that it is easier to present fundamental ideas than in infinite-dimensional Morse theory, which is theoretically more involved. Therefore, finite-dimensional Morse theory is more suitable for beginners to study.

On the other hand, finite-dimensional Morse theory has its own significance, not just as a bridge to infinite dimensions. It is an indispensable tool in the topological study of manifolds. That is, one can decompose manifolds into fundamental blocks such as cells and handles by Morse theory, and thereby compute a variety of topological invariants and discuss the shapes of manifolds. These aspects of Morse theory will continue to be a treasure in geometry for years to come.

This textbook aims at introducing Morse theory to advanced undergraduates and graduate students. It is the English translation of a book originally published in Japanese. ... Read more

Book Description

Probability and Measure Theory, Second Edition, is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion.

* Clear, readable style
* Solutions to many problems presented in text
* Solutions manual for instructors
* Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statistics
* No knowledge of general topology required, just basic analysis and metric spaces
* Efficient organization ... Read more

Reviews (1)