Product Description
"A lucid representation of the fundamental concepts and methods of the whole field of mathematics. It is an easily understandable introduction for the layman and helps to give the mathematical student a general view of the basic principles and methods."--Albert Einstein (on the first edition)

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but not to real understanding or greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.

Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.

Formal mathematics is like spelling and grammar: a matter of the correct application of local rules. Meaningful mathematics is like journalism: it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature: it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is a marvelously literate story: it opens a window onto the world of mathematics for anyone interested to view.Amazon.com Review
A 1996 revision ofa timeless classic originally published in 1941. Highly recommendedfor any serious student, teacher or scholar of mathematics. ... Read more

Customer Reviews (35)

excellent buy
Everything is in good condition as said.I am happy of doing business with the seller.
TKS.

typos galore, terrible layout
The book is littered with mangled formulas, mostly due to the fact the minus sign is missing from most formulas. This is completely unacceptable in any math book, but particularly so in a book aimed at beginners, who will probably feel bewildered by the huge amount of nonsensical formulas.

Adding insult to injury, the poor layout of Kindle edition makes the book hard to enjoy. Section headings often appear as orphans at the bottom of pages and many formulas are displayed as small, low-quality images. The low image quality is especially visible when reading the book on a Kindle 2 as opposed to for example the Kindle Mac app. Inlining formula images with running text is particularly annoying, since it deforms the text layout.

I was so annoyed by these problems that I tried to return this book, only to discover that returns are not allowed for digital books.

Do NOT buy the Kindle edition of this book.

A fascinating book.
For those who love mathematics, I can't praise this work highly enough. It's not designed so much to help the reader solve math problems as it is to impart a solid understanding of the fundamentals of the subject. Anyone who finds mathematics endlessly intriguing will be glad to own this book.

Math education at its best and most beautiful.
This book is so beautifully written that it epitomises an ideal of mathematics education. Everything is presented and explained clearly, which makes it suitable for the layman. The contents covered are also ambitious and wide-range. Topics are presented in a logical and satisfying manner. Natural numbers and the concept of induction are introduced early. Then a more thorough discussion of number system follows in Chapter 2 which concludes the background in arithmatic. After that the book shifts its focus to the opposite pole of mathematics where geometry (both euclidian and beyond) are presented in a way that algebra is employed to give greater understanding and appreciation of the topic and to allow the readers to understand the key role of algebra which helps bringing arithmetic and geometry together in a coherent manner.

Although I believe that the book is suited for lay people, we must not expect that the authors will hold you hand-in-hand while introducing you to the beauty of mathematics. The authors make clear that they want you to think. And think hard you will, if you want to get the best out of this book. By this, we have come to the greatest merit of this tome: sure, everything is clearly explained, however the most important messages are written not conspicuously but between the lines (and much of them in the exercises). We can only come to appreciate what the authors want to say when we commit ourselves in the required thinking part and discover for ourselves what the authors want us to know but didn't say. I think the book succeeds triumphantly in its writing style and is therefore difficult to be out done in this respect. Mathematics will continue to progress but this book will never become obsolete.

I do strongly encourage everyone who reads this book to do all the exercises in every chapter. You have no idea what you miss if you skip them; the are the crown-gem of this book. Don't be deterred if you cannot solve over a third of the problems. Just by thinking about them (albeit unable to solve) will move you closer to real understanding of the topics being discussed. Don't be appalled to know that answers are not provided in the back of the book. You know it when you solve it; this only heigthens the satisfaction of doing math.

I know many math-degree holders who hesitate to refer to themselves as mathematicians (they would just say "well, I had/did a degree in math."). I think that is because while they know a lot of mathematical facts and techniques, they never really understand or appreciate it in a fundamental way. This shows what is missing in our math education. This book is the ideal antidote.

Also check out books by John Stillwell. Most of his books are as good as this volume.

Incredibly thorough
Basic Math Quick Reference Handbook
This thorough coverage of so many aspects of mathematics forms a threshold that separates the interested enthusiast from the professional mathematician.
Couldn't be better. ... Read more

Customer Reviews (6)

Great book, wonderful book but $$$'s!!!!!
Honestly, people have waxed lyrical about this book so there's no need for me to play the violin. But did anyone even notice its ridiculous price tag. It may be the Cristal champagne of math books, the dernier cri of Calculus texts but to price it so only a man with a prince's means can afford it is doing injustice to the author, the readers and learning itself. Thriving Wiley Classics in their corporate greed and its ill-gotten means of making money. Thieving Publishers!!!!!! I hope your corporate losses decline exponentially so that you'll go bust and Dover publications will get the rights to the book and put it out for < 19 dollars.

great but not worth $135 to most people
This is one of the best calculus books ever written,But I bought my copy in 1960 for $6.95.Almost no one should pay over $160 for this book today.You are only encouraging greedy book resellers if you do.Buy a copy of Spivak's Calculus instead, or the followup book to this one by courant and fritz john.

Best calculus book, but not for beginners.
This is the best book on calculus that I have ever seen. However, it can never be used as a text for first year calculus students because they lack the mathematical sophistication to understand most of the material in this book. The book is not about the HOW TO, but instead it's about the WHY. There are lots of proofs and some interesting examples. This would be a good alternative book for Advanced Calculus.

I read certain parts of this book when I have to teach a complicated topic to my calculus students (e.g. Fundamental Theorem of Calculus, Taylor Series) and then I streamline the material so that they can understand it.

My main complaint is the absurd price! Try to find a cheaper used copy. It's outrageous that a book this important is so expensive.

Worth a look
This work has an honored place on my bookshelf.A colleague
recommended it to me when I was in school and I bought a copy after
looking at it in the school's library.It sits next to my copy of
"The Feynman Lectures in Physics".These are works you go to for
insight.I like Courant's mixture of physical examples with the
mathematics.

After encountering Courant's book for the first time, I remember
wondering why the first volume wasn't used as the textbook for the
typical year and a half of basic calculus.Then, as now, I can only
conclude that teachers probably think it's not watered down enough for
the students.Maybe it's a blessing in disguise to come across
Courant after you've been taught calculus from an uninspiring "modern"
text.

Everyone's needs are different, so take all reviews with a grain of
salt.As a working scientist/engineer, my primary use of the calculus
is as a tool to get things done, so I'm typically more interested in
learning the mechanics than getting a deep understanding like a
mathematician would.Courant works for this, yet still allows one
to dig in deeper when desired.It's still an awfully good book, even
if it is 70 years old.

Classical German calculus
Courant knows the art of writing a good preface. He attacks "diffuseness" and "pedantry" and aims at "exhibiting the close connection between analysis and its applications" and "to give due credit to intuition as the source of mathematical truth". The book also has a tone that is unusual today: Courant speaks to us the way a dignified, open-hearted professor speaks to an intelligent student. No rambling pretensions; just to-the-point, good mathematics. This is the perfect solid-as-they-come, timeless book on the calculus, and most likely it will never be surpassed in this domain. One must be warned, however, that this is a very serious book and reader-friendliness has lower priority than technical coherence and brilliance of formal organisation. The likely reader will know calculus already and use Courant for masterful, concise exposition of standard topics as well as a wealth of topics that have been watered out of most current calculus curricula (e.g., evolutes, involutes, envelopes, curvature, geodesics, centres of mass, the gamma function, the catenary, the cycloid, the lemniscate, the brachistochrone problem, Kepler's laws, Maxwell's equations, the zeta function, etc.). Everybody knows that all the usual calculus books, "reform" or not, are pathetic. But what is even worse is that there are no good alternatives even if one is prepared to dig deep into the library shelves in hope of finding an author who has not sacrificed his intellectual dignity at the altar of royalties. Take for example Serge Lang's books "A First Course in Calculus" and "Short Calculus". Lang is of course the virtual definition of the mainstream of respectable mathematics. Nevertheless, these books are soaked with the common formalistic attitude. In fact, as if his books had not finished the job, Lang adds an appendix to both books called "Physics and Mathematics", which very explicitly drives a wedge between physics and intuition and mathematics. Courant is a good antidote to such modern nonsense. ... Read more

Product Description
This is one of the most important and influential books on calculus ever written. It has been reprinted more than twenty times and translated into several other languages, including Russian, and published in the Soviet Union and many other places. We especially want to thank Marvin Jay Greenberg, Emeritus Professor of Mathematics, University of California at Santa Cruz, for his Appendix on Infinitesimals, which includes recent discoveries on Hyperreals and Nilpotent Infinitesimals, and for his bibliography and references, which include up-to-date references to current publications in 2010. This foreword, which includes new mathematical discoveries, is included in Volume One of this work. A professor of mathematics writes: "I've enjoyed with great pleasure your foreword, discovering many interesting things about Courant's life and his thoughts. In particular, your citations about the antithesis between intuition and rigor were very illuminating, because it corresponds to the methodological thread I'm trying to follow developing the theory of Fermat reals. "Infinitesimals without "mysticism", explicit or fogged into unclear logical methods, seems possible. Now, I think we can make a step further, because the rigor increases our possibility to understand." ... Read more

Customer Reviews (5)

Sits next to Feynman
I had the usual 1960's ho-hum calculus class suffered through by billions of semi-conscious life forms over the 200 years.However, when I was a first year grad student, I discovered this book and fell in love with both volumes.It has an honored place on my bookshelf, sitting next to the Feynman Lectures in Physics.These are books you go to for insight and understanding.They'll continue to be in use 100 years from now.

Best Calculus book
This is the best calculus text for aspiring physicists as well as applied mathematics students. However, don't know why Amazon sent the book with different front cover to me. It's not the one shown in the picture but rather a black cover--exactly the one seen on barnesandnoble with the same isbn. Although the covers are different, the content is the same.

This book really is a classic
I used this book in an Honors Calculus course decades ago, and it's still a useful reference. Unlike most calculus books, this is one from which you can learn real mathematics by self-study. It is not only solid on calculational techniques, but is also an introduction to real analysis, and to good mathematical reasoning and proof technique. Courant was a famous applied mathematician, and he introduced and developed the concepts in a way that is very well motivated and clear (not very common in mathematics texts these days).

Different calculus textbooks will go in and out of fashion as professors try to overcome the poor preparation of their students, but Courant's book will endure as long as there are students who really want to understand thoroughly what they are doing.

A fantastic calculus book!
This is the best calculus book I've ever read! I'm a mathemathics student, and I've read many titles of many authors, but this one is the most wonderful calculus book I found during my whole life! I'm very thankful toRichard Courant, he was my best calculus teacher!

An excellent calculus book
This two volume set on calculus covers many of the mathematical techniquesrelevant to engineering and science. Courant's treatment of seriesexpansions and uniform convergence is clear and contains good examples. Histreatment of extreme values of multi-variable functions and Lagrangemultipliers is exceptionally good; it surpasses the explanations given inmost modern textbooks. The exposition on multiple integrals and vectorintegrals is tremendous and, alone, is a compelling reason to get this set.A chapter on the calculus of variations provides a solid introduction tothe methods of Lagrangian Dynamics. Unlike modern mathematicians whopursue their research apart from engineering or physical applications,Richard Courant was adverse to abstract theories and vague theroems.Schooled at Gottingen University, under the auspices of David Hilbert andFelix Klein, this two volume set reflects the ethos of a school system thatplaced a premium on producing useful mathematics. The topics covered inthis set will provide the reader with a solidbackground to understand themathematics of heat conduction, electricity and magnetism, fluid dynamicsand elasticity. ... Read more

Product Description
From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" The Mathematical Gazette (75.1991.471 ... Read more

Customer Reviews (10)

Solutions to problems and exercises
Springer have reprinted the original 1960s Wiley editions of "Introduction to Calculus and Analysis" volumes I and II by Courant and John in three new volumes under their "Classics in Mathematics" title: "Introduction to Calculus and Analysis I (pages 1-661)" (ISBN: 3-540-65058-X), "Introduction to Calculus and Analysis II/1, Chapters 1-4 (pages 1-542)" (ISBN: 3-540-66569-2), and "Introduction to Calculus and Analysis II/2, Chapters 5-8 (pages 543-954)" (ISBN: 3-540-66570-6).The back section of Volume II/2 (pages 821-939) has solutions to the exercises in both the books comprising volume II, that is "Introduction to Calculus and Analysis II/1" and "Introduction to Calculus and Analysis II/2".

Note that when Volume I of the original Courant and John "Introduction to Calculus and Analysis" was published in the 1960s by Wiley, an accompanying solutions manual for Volume I was prepared by Prof. Albert A. Blank.When Volume II was published by Wiley, Prof. Blank's solutions were incorporated into the back of Volume II (in other words, Volume II comes with the answers to the questions at the back of the book... or in the back of Volume II/2 in the case of this Springer "Classics in Mathematics" reprint.)However, the Springer reprint of Wiley's Volume I lacks solutions to the exercises in the textbook.

If you buy Volume I, do a check on the Internet for an old 1960s copy of Prof. Albert Blank's "Problems in Calculus and Analysis", which is the original solutions manual to Courant's Volume I.

An Excellent Book
This (and Vol. 2) are both really good books that anyone with an interest in mathematics should own.Is it as good as Apostol's two volumes (Tommy I and II)?No.Is it as good as Spivak's "Calculus"?No.But it is still very good because the exposition is wonderful.I own both volumes and am glad - but if you only want one Courant book, please buy "What is Mathematics".

a superb book
This is a rewrite of the great book by Courant, and it does justice to its origin.I prefer the somewhat more charming original book of Courant myself, but I have taught from this one too and learned something more.

Since the original Courant costs $120 for the 2 volume set, this volume at $33 is a bargain, so snap it up.This is 10 times as valuable as most current $130 calculus books.

More than an introduction
Those books (volumes 1-2) can be seen as a new edition of Courant's classical Differential and Integral Calculus, volumes 1-2 (that can still be used for general calculus courses). The first volume was written while Courant was still alive, and the second was postumous. I believe that they are the best work to start understanding analysis. Indeed, for the general scientist (as a physicist) it contains all the theory needed for any application. The book is not easy reading though. Much of the text can be understood on first reading, but there are pretty profound sections, mostly on the appendixes, that turn the book genuinely onto a book of analysis. The second volume requires some mathematical maturity, and I doubt whether it is suitable for beginners, but it is simply the best book of multivariate calculus that I know - and it is really difficult to think of a better presentation. Courant was a giant, and his concept of mathematics shines in every page of those books (although he did not see the publication of the second volume, his hand can be seen in every page). For the serious mathematician, a must-have. For the beginner, the best way to get in love. Courant and John don't lie, they give every proof and guide you most gently in this complicated garden called mathematics. I'd give it aleph stars if it was possible.

Superior as an introductory calculus text!
I don't use the word "superior" lightly, but this book definitely warrants it.Courant was a first rate teacher and mathematician, and his brilliance shows in his exposition.The main obstacle to some readers may be that Courant does not follow the "cookbook calculus" approach that seems so rampant today, but actually bothers to prove his results.He does, however, reserve most of the more difficult proofs for the appendices at the end of the chapter, which is most appreciated.

The result is an exciting read, yet rigorous.The reader is very well prepared for future courses in mathematical analysis, and even has a leg up on real analysis.While Courant's insistence on proof does mean that the student needs to have a basic grounding in proof methods, this is usually a standard part of the undergraduate curriclum.Courant rightly recognizes that calculus should be taught in a logical, yet rigorous presentation from the beginning.The absence of this in modern texts mean that students learn how to manipulate formulas, but have no idea what makes the results they are assuming true.The "mechanics" of calculus and analysis, the most crucial thing to be learn, is missed.

In particular, I enjoyed his presentation of integration *before* differentiation, which goes against the grain of basic calc texts, yet is historically and pedagogically correct.Integration actually paves the way for differentiation, and gives more motivation for the FTC.Most texts on real analysis work in that order anyway, as an understanding of Lebesgue measure and integration is crucial to understanding the process of differentiation.

In addition, I don't think I have ever before or since seen such a careful explanation of the theory of the logarithm or exponential functions.Again, the presentation makes it work, as just introducing the "exponential function", then a little later, the "log function" as the "inverse" of the exponential function is, to put it mildly, artificial and distasteful.The natural progression from the definite integral definition of the logarithm to the exponential function is displayed in its full glory.

In short, Courant manages to present some of the most crucial results of calculus and basic analysis without boring the reader to tears with arcane details, or worse, leaving the reader hanging on important theorems and ideas.This is a balance only a great mathematician could strike, and it is clear why this book remains a classic after almost 60 years.

Note: The second volume of this work covers the multivariable portion of calculus, and will be more difficult to follow without prior exposure to the subject.However, the introductions to the theory of matrices and the calculus of variations are very readable, and it is recommended that the reader take the time to peruse them.Also, don't miss the material on special functions, lightly touched on in the first volume, but explained in fuller detail in the second. ... Read more

Product Description
Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961. ... Read more

Customer Reviews (2)

classical math physics text
This two volume set is a classic rivaled only by Morse and Feshbach "Methods of Theoretical Physics", vol 1 and 2. It should be a part of the library of any serious student of physics or engineering.

state of the art in the 50's
Beware the german edition is the prewar edition, and the english edition is a
complete overhaul to include modern material at the time. This is not really a
textbook, but a sourcebook of "issues" in partial differential equations. Some
problems have been forgotten now due to the focussing on real, linear equations
and weak solutions (as described, for example, in the books by Hormander). It is
a gem for who wants some taste of the full breadth of theory of PDE's. ... Read more

Product Description
Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953. ... Read more

Customer Reviews (5)

Theory of advanced mathematics (not physics).
This book is intended for mathematicians and not for physicists. All of the mathematics is developed through proofs of theorems. The chapter on approximation of functions is the best in the book. There is also a short introduction to Lebesgue integration which is the best explanation of what it actually means that I have ever seen! (i.e. not having to develop the messy business of measure theory that fills up 10s of pages in most books).

If you want to learn graduate level mathematics (i.e. analysis and PDEs) in gorey detail then this is the book for you. If you want to understand applications, then it is not. I don't like the term "mathematical physics." It depend on which department teaches it. A mathematician will focus on the topics in this book. A physicist would focus on methods and not on proofs.

The best book available
I would definitely not agree with any bad comments to this book. There are millions of books out there for you to workout problems and help you pass exams. But there is only one who actually teaches the subject and it's Courant. I don't expect literary genius out of a Mathematics book but clear development of the topics. The translation does a good job at it. Believe me if you really want to know the subject and get a feel for it read this book.This is not for the feckless as you will start defacing its stature with your comments. But the price tag is exorbitant and not many can afford to read this wonderful text. I had to borrow from my library as I cannot afford to buy one. 230+$ for two volumes is no joke especially for a student !!

courant studied mechanics and mathematics
i noted this book (the asia private edition) when i was a junior student taking engineering math III. now i note vol.1 is for vibration phenomenon, while vol.2 is for wave phenomenon. the material is over a century. birth day is 1924, while the golden age of quantum mechanics is 1925. a modern mathematican wrote the biography of courant said that many physictists surprised that courant could write the tool for quantum mechanics (wave mechanics) before the birth of quantum mechanics. i do not surprised ,because vol.1 is for vibration phenomenon of mechanics, it is also over a century ago knowledge. the real thing is that man use the usual form of thinking and used the unique avaiable tool for the formulation of quantum mechanics. but there exist another state vector, matrix form of quantum mechanics. this advanced classis is for math phD and researcher. one way to study this classic is via mathematics, while another way is via mechanics concept, but when you can study it via both ways, you are great.

This book is a classics, but perhaps not exhaustive
I think that this book is better in its original german than in english langauge. As to its content, it may perhaps not include all items of this thema, but the items include are treated with genius. The lack of problems to solve may be a draw back, but for me that is not much trouble because there are many books with many problems to solve. The interest of this book lies in its being a source book, though historically written down in 1924, it still mantains its beauty and its present mathematical value.

This bookisfamous, but cannnot be described as classics.
I brought this book ( volume 2 also as well ) because of its " fame ", but when I read it, it has several draw backs. First, may be the original vesion is in German, so even with good translation, it seem does not fit in the usual English style we get used to .Also the topics it choose is too few and also the area covered is too narrow and not well co-ordinated. For example, the whole volumme I is almost dedicated to Calculus of variation only. In volume 2, the whole book is dedicted to differentiation equations. But that is not the greatest drawback. The most bad point is that the book just presents formulae after formulae, equations after equations, without giving examples of how to use it,and also no exercise for me to practice. Compared the the timeless classic " A course of mordern analysis " by Whittaker and Watson, it is definitely at a lower level. This book cannot be described as " classics ". ... Read more

Product Description
From the reviews: "These books (Introduction to Calculusand Analysis Vol. I/II) are very well written. The mathematics arerigorous but the many examples that are given and the applicationsthat are treated make the books extremely readable and the argumentseasy to understand. These books are ideally suited for anundergraduate calculus course. Each chapter is followed by a number ofinteresting exercises. More difficult parts are marked with anasterisk. There are many illuminating figures...Of interest tostudents, mathematicians, scientists and engineers. Even more thanthat." Newsletter on Computational and Applied Mathematics, 1991"...one of the best textbooks introducing several generations ofmathematicians to higher mathematics. ... This excellent book ishighly recommended both to instructors and students. Acta ScientiarumMathematicarum, 1991 ... Read more

Customer Reviews (3)

This should be used in court swear by
I really mean it. It should be made a bible of sorts. Without sounding ridiculous, how should I say it - It is direct, profound and says no more or no less. It is written with clarity at every analytical point. It is eminently readable and should be read at least once a day simply to know that there is such beauty in the subject. Courant & John have written the mathematics text of all time. I like it better than Spivak. The closest is probably Hardy's "A course in Pure Maths"

Solutions to problems and exercises
Springer have reprinted the original 1960s Wiley editions of "Introduction to Calculus and Analysis" volumes I and II by Courant and John in three new volumes under their "Classics in Mathematics" title: "Introduction to Calculus and Analysis I (pages 1-661)" (ISBN: 3-540-65058-X), "Introduction to Calculus and Analysis II/1, Chapters 1-4 (pages 1-542)" (ISBN: 3-540-66569-2), and "Introduction to Calculus and Analysis II/2, Chapters 5-8 (pages 543-954)" (ISBN: 3-540-66570-6). The back section of Volume II/2 (pages 821-939) has solutions to the exercises in both the books comprising volume II, that is "Introduction to Calculus and Analysis II/1" and "Introduction to Calculus and Analysis II/2".

Note that when Volume I of the original Courant and John "Introduction to Calculus and Analysis" was published in the 1960s by Wiley, an accompanying solutions manual for Volume I was prepared by Prof. Albert A. Blank. When Volume II was published by Wiley, Prof. Blank's solutions were incorporated into the back of Volume II (in other words, Volume II comes with the answers to the questions at the back of the book... or in the back of Volume II/2 in the case of this Springer "Classics in Mathematics" reprint.) However, the Springer reprint of Wiley's Volume I lacks solutions to the exercises in the textbook.

If you buy Volume I, do a check on the Internet for an old 1960s copy of Prof. Albert Blank's "Problems in Calculus and Analysis", which is the original solutions manual to Courant's Volume I.

You must have this.
My review of the first volume pretty much applies here as well.How many *calculus* texts have an introduction to complex variables, and the theory of analytic functions?This is the only one I've ever seen, and I don't think anyone else could make it more enriching than Courant.Useful material on vector calculus, the theory of matrices, and even introductory material on the *calculus of variations* (something we usually don't see at *all* in the undergrad curriculum) is included.It is refreshing to have an instructor like Courant, who doesn't assume we can't follow higher mathematical roads, but also doesn't sit at the other end of the spectrum, just waving a wand and "poof, here is the result".

Courant also published a standard reference work (also two volumes, I believe) on Mathematical Physics.While the level of mathematics required is post-grad, I was still able to read sizeable sections of it without getting lost.

We can only hope Dover decides to publish Courant's works one day, to make them a little more affordable.But still, you can buy both volumes of Courant's intro to calculus for about the same price as a modern calculus text that waters down the material, and on top of that, provides inadequate explanation for the material it does cover. ... Read more

Product Description
This Set Contains: Differential and Integral Calculus, Volume 1 by R. Courant; Differential and Integral Calculus, Volume 2 by R. Courant. ... Read more

Customer Reviews (4)

An Excellent guide to calculus
This book was written by the author of "What is Mathematics" and they two are masterpieces of advanced divulgation in mathematical subjects.
To be reccommended to those who want cleareness and deepness in the concepts of science

Excellent Exposure and Presentation but Outdated
There has been sufficient praise for the D^I Calculus of Courant and I would not add more to it. My comments: 1) The symbols are outdated 2) it's more verbose and descriptive than many other standard calculus textbooks. This is good in some sense because it helps the readers understand the concepts. Yet, it will not train you solve difficult problems and will not help you ace your tests and exams, be it GRE Subject test or your regular exams. But certainly you can benefit from reading it, no doubt! I used this book for self study and as my main reference. There is a book by Michael Comenetz 9810249047 that's written almost as a updated and concise version of Courant's books. Many points that Courant omits may be found in Comenetz' book. It has ample amount of problems (with solutions) of appropriate difficulty that help you reinforce what you read from Courant.

great calculus book
I agree whole heartedly with the other reviews here, and merely wish to second their opinions.I bought my copy in 1960 and would never part with it. I still have crystal clear images in my mind from courant's exposition of the 1-1 correspondence between points of the real line and infinite decimals, his comment that all absolute convergence tests result from comparing with a known convergent object - either the geometric series or an integral,and his preface emphasizing "the chief task" of one who would pursue the study of Science: acquiring a firm grasp of the application of general principles in particular cases.

I have studied and taught calculus, advanced calculus, real and complex analysis, Riemann surfaces, differential equations, and differential manifolds both real and complex, for over 40 years, but anyone who reads thoroughly these 2 volumes and masters them will know more calculus than I do.

I am a pure mathematician, and I believe these volumes are highly recommended not just to physicists and engineers, but to anyone who would master their subject.I also love the book of Spivak, but after teaching from them together one summer, and comparing proofs, I concluded that Spivak himself probably learned the subject from Courant.

Classical book
I will not say, as is common in reviewers of books on calculus, that this is the best book of calculus that there is. Indeed, calculus is a subject with so many textbooks that it can be said that there is no best textbook, but that each person can find one that suits his/her needs.

Nonetheless, Courant's book is an old text, around 70 years old. It belongs to these classics of science that were influential and held its own as a source of common knowledge. Why?

I believe that the answer to this question is simple: Courant's book has the perfect balance between theory and applications. It does not use too much pedantry in its exposition, is full of examples (for the student to do and also some worked-out), ranging from simple to very difficult, and yet it proves everything that is important in a way that no mathematician can complain. Indeed, the authors leaves the most difficult demonstrations to appendixes that can be found in each chapter, so the reader that doesn't want to enter into the complications of the proofs can skip them. And the book is written in a conversational style, that much probably influenced the book that, in my humble opinion, is the best that can be found treating the subjects it treats (so I also have my favourite calculus text: Spivak's Calculus!).

There are two volumes, the first one dealing mainly with calculus of one variable and the second with multivariate and complex analysis. It contains the core of the mathematical theory useful for physicists and engineers and has this that is amazing: it develops the theory and always gives good physical examples. Indeed, a whole course of theoretical physics is contained in this book, almost hidden.

So, if someone is reading this review and is in doubt whether the book is good or not, I can say, with the experience of having read a long list of calculus texts, that the book is good and is worth-while. It is useful to the mathematician and to the engineer, to the philosopher and to the physicist, and serves extremely well both as a text book for class study, self-study and for reference. If you are worried that the treatment is dated, I can say that, although today the most common treatment of, say, multivariate calculus is through linear algebra, that leaves the subject much cleaner, Courant's work still is of value in that it explains everything in as simple way as possible, mantaining always ahead the objectives of each section. It is essentially a book of applications of analysis and if you read and work the examples, you will turn yourself into an expert both in theory and application and will be able to follow easily any work that has classical analysis as prerequisite.

Great classical book! ... Read more

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From the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that." Newsletter on Computational and Applied Mathematics, 1991 "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." Acta Scientiarum Mathematicarum, 1991 ... Read more

Customer Reviews (1)

Absolutely beautiful!
I give 5 stars to this book because it gives the reader the perfect combination between rigor and intuition. Volume 2 has solutions to almost all the exercises, which is great because some of the problems are very difficult. I really think this is a "must have" text for anyone who wants to learn calculus at a deep level. ... Read more

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In diesem Buch, erstmals 1924 bzw. 1937 erschienen, sprt man noch wie am ersten Tag die Frische und Inspiration zweier groer Mathematiker und Lehrer. Hilbert kann man mit Fug und Recht als den letzten Mathematiker bezeichnen, der in allen Gebieten seiner Wissenschaft zu Hause war und in den verschiedensten Bereichen der Mathematik grundlegende neue Erkenntnisse gewann. Seine Resultate haben entscheidend die moderne Auffassung vom Wesen der Mathematik geprgt. Sein Schler Courant galt und gilt auch heute noch als ein ausgezeichneter Lehrer, der auch schwierigste Materien verstndlich darstellen konnte. Das bei Springer erschienene Buch von Courant/Robbins: Was ist Mathematik, kann in diesem Zusammenhang als beispielhaft genannt werden. Alles in allem eine groartige Zusammenfassung der mathematischen Hilfsmittel des Physikers, die auch heute noch viele enthusiastische Leser finden wird. ... Read more

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Almost twenty-five years after his death, Richard Courant remains a highly controversial figure. The deep affection he inspired among friends, colleagues and students is still matched by distrust and dislike in much of the mathematical community. He was a man of such contradictions in character and action that one of his colleagues, resorting to an accepted mathematical method of proof, claimed "by contradiction" that he simply did not exist. But exist he did.On April 1, 1933, he was an internationally famous and influential German professor, the director of the first institute in the world devoted entirely to mathematics, a trusted adviser of the education ministry, a successful author and editor, a man surrounded by a mathematical family of gifted students. Eight days later, he was dismissed from his position by the Nazis. Through friends, he obtained a modest position in the United States at a University with no mathematical reputation whatsoever. What followed-the founding and development of one of America's most important centers of applied mathematics, the Courant Institute at New York University-is one of the great success stories of mathematics.Courant is Constance Reid's engrossing account of the life of this compelling, enigmatic, and perversely heroic mathematician. ... Read more

Customer Reviews (3)

A Builder of Centers of Excellence in Mathematics
This is a book that would interest people who enjoy reading books about the history of mathematics, particularly about the communities and and institutions of mathematics. The period covered is from the late 19th Century. Courant was student and later, a colleague of the famous mathematician Hilbert at Gottingen. Courant is obviously not as famous as Hilbert and the book does not focus on his achievements in mathematics. Instead, it discusses more about how he relates to other mathematicians, and his tireless efforts in trying to establish and nurture two centers of excellence in mathematics - the Mathematical Institute at Gottingen and the Courant Institute of Mathematics at New York.

A Builder of Centers of Excellence in Mathematics
This is a book that would interest people who enjoy reading books about the history of mathematics, particularly about the communities and and institutions of mathematics. The period covered is from the late 19th Century.Courant was student and later, a colleague of the famous mathematician Hilbert at Gottingen.Courant is obviously not as famous as Hilbert and the book does not focus on his achievements in mathematics. Instead, it discusses more about how he relates to other mathematicians, and his tireless efforts in trying to establish and nurture two centers of excellence in mathematics - the Mathematical Institute at Gottingen and the Courant Institute of Mathematics at New York.

Great book!!!!
If you are interested in mathematics and are/aren't a mathematician, if you are interested in American/German jewish history of the 20th century, if you are interested in science during WW2,you will love this book - Idid! ... Read more

Customer Reviews (1)

The Most Incredible Two Volumes of Calculus
Dear Readers

Masterfully written! I cannot recommend these volumes too much to anyone interested in or passionate about
Mathematics and the quality of Mathematics teaching. Teachers ( instructors)! take note!
Absolutely required reading if you want to not only do Analysis but understand it.

Courant carefully takes you through the stages of like W.W. Sawyer would say
the "Happy-go-lucky" to the "Epsilon-Delta" stage without the usual pain associated with this step. (provided of course that you
carefully read and reread the appendices at the ends of the chapters)
The pathalogical examples are carefully gone over. (beginning on page 196 of volume
one)

Courant will "talk you through it" as if you were in a class
listening and watching. He will describe open sets and the nested interval theorem (Courant calls it "on shrinking sequences of closed sets" beginning on P.98 of volume two)
like you've always wanted it explained.
The key to both volumes is on page 58 of volume one with
his statement of the "point of accumulation". This statement is the starting point of Analysis. This is the beginning.
Then comes
Courant's very nice and intuitive proof for the Bolzano-Wierstrass theorem.
The rest of Analysis simply follows in the appendices all the way into Volume Two
where he states and proves the Heine-Borel theorem. But in a style that you've always wanted to hear and see. Nowhere is the word "Topology" mentioned but all the motivations for it are right there and explained in a uniquely leisurely way.

It all follows from this particular page ( page 58 volume one) which is also mentioned in McShane's
book "Integration". And you will also note that in Courant's preface for volume one of the English edition for these two volumes he acknowledges that E.J. McShane's contribution as translator was essential in expediting the whole project.

With Best Regards

Southern Jameson West ... Read more

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Provides a complete, balanced introduction to economics & to the most important issues facing the world's economies at the turn of the millennium.Examines U.S trade policy, NAFTA, progress in reducing the U.S. budget deficit, & the antitrust case brought by the Department of Justice against Microsoft.DLC: Economics. ... Read more

Customer Reviews (4)

Fast, good customer service
Seller: Item received before expected date, quick response from Customer Service when I asked to change shipping terms.
Book received in excelletn conditions.
Suggested.

Item: good foundation text

Fraud - send me paper back instead of hard cover (different ISPN #)
Seller charged me 90% more than what actually cost of the 2 hard cover book and instead she sent me 2 paperback books. Seller doesn't want to respond to my email or refund me. Be aware of this seller.

The best book for a beginner
In this book (the twelfth edition) every economic subject is very well explained without difficult mathemayical concepts. People who like themathematical approach can find something in theappendix. There are a lotof examples about real facts happened to real companies (Microsoft,...) ororganization (OPEC...). The logic approach and the examples are veryusefull for a beginner that first of all has to understand the mainconcepts rather than struggling in a difficult language or math.

A very beautiful book.
The authors have explained all principles withremarkable ease taking numerous to the point examples. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more