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Introduction to Calculus and Analysis, Volume 1 (Classics in Mathematics) | 
 enlarge | Authors: Richard Courant, Fritz John
Publisher: Springer
Category: Book
List Price: $69.95
Buy New: $44.95
You Save: $25.00 (36%)
New (17) Used (14) from $31.99
Rating:  12 reviews
Sales Rank: 376096
Media: Paperback
Pages: 661
Number Of Items: 1
Shipping Weight (lbs): 2.2
Dimensions (in): 9.3 x 6 x 1.6
ISBN: 354065058X
Dewey Decimal Number: 515
EAN: 9783540650584
Publication Date: December 22, 1998
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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 There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry.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)
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| Customer Reviews: Read 7 more reviews...
Superior as an introductory calculus text! May 27, 2002
Justin Bost (Salisbury, NC)
32 out of 32 found this review helpful
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.
You must have this. May 27, 2002
Justin Bost (Salisbury, NC)
26 out of 26 found this review helpful
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.
A Classic in Mathematical Exposition August 27, 1998
reader 1001
15 out of 15 found this review helpful
Richard Courant was a master of mathematical exposition, and this is one of his best works. In keeping with Courant's philosphy, this book is free from the excessive abstraction often found even in introductory calculus textbooks. Nevertheless it does not gloss over difficulties in the material, and is in no sense an easy book. This book a complete rewrite of Courant's original "Calculus" which first appeared in German. An especially good chapter is the one on the "Theory of Plane Curves."
a superb book April 4, 2006
mathwonk
6 out of 7 found this review helpful
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.
Absolutely beautiful! January 23, 2005
El yucateco (New York, NY)
9 out of 9 found this review helpful
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.
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