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

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Customer Reviews (1)

A Book That Took Me Forty Years To Get
Dear Readers

I love this book! I love the way he writes. It has all the "goodies".

A book when you read it is like an event in your life. Perhaps a "good book" is an event that changes your life forever. If you don't read it, it is also an event.(A "negative" event) This book is a story of what I failed to read when I had the chance and now after forty years somehow I've got that chance back.

1968 was a different time and place. Every day was Vietnam on T.V. Everyday was wondering what exactly "we" had gotten ourselves into. Everyday was high school and some kind of torture that was at the time legal. It was called the "education system". Just one of the many subsets of that horrific animal known at the time as "The Establishment".

Education was a particular kind of "hell". Except for one little book that changed my life forever. That book was titled; "What is Calculus About?" and it was written by perhaps the greatest Mathematics teacher of the twentieth century. That was none other than W.W. Sawyer. Not just an Academician, Sawyer was a geniusteacher. His was a true gift from a "higher domain". He was passionate about telling the students exactly the way things were. It wasn't just about the mathemmatics, it was about the learning that went with it. A real pleasure to read.

Now people around me didn't like me reading that book. (In those days people had all kinds of opinions and notions.) But I read it anyway. And when I got to the back of it there was a reference in fact many references on how to proceed on one's mathematical study. One name was of course E.J. McShane.

McShane was a formidable mathematician and writer in his own right. Having for example translated Courant's "Integral and Differential Calculus" in two volumes this guy was no slouch. Courant from "Courant and Hilbert" was one of the top mathematicians of the time. "Creme de la creme". However as fate would have it I never ordered his book: "Integration". Not till recently.

More to say in a minute.

Okay. So this book can be considered as a "soft transition" from the level of say Courant's Calculus to the very obscure, mysterious and vague topic of Fuctional Analysis. And like many books that are classics McShane's notation is non-standard. But that's okay because McShane is "steering the boat" and you'll be okay.



Best Regards

Southern Jameson West ... 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. 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

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Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... 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

Product Description
This book discusses the analysis of gene expression profile data from DNA micorarray studies and the design of such studies. The book will address design and analysis issues for both of the major classes of DNA microarrays, the cDNA microarrays and the oligonucleotide arrays. DNA microarrays are a new technology that is revolutionizing biological and biomedical research. Most biologists are trying to analyze their own data using a variety of commercial and public domain software. This book will provide an authoritative review of the methods available and present it in a manner that is intelligible to biologists. ... Read more