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Differential and Integral Calculus 3ED (AMS Chelsea Publishing), by Edmund Landau
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After completing his famous Foundations of Analysis (See AMS Chelsea Publishing, Volume 79.H for the English Edition and AMS Chelsea Publishing, Volume 141 for the German Edition, Grundlagen der Analysis), Landau turned his attention to this book on calculus. The approach is that of an unrepentant analyst, with an emphasis on functions rather than on geometric or physical applications. The book is another example of Landau's formidable skill as an expositor. It is a masterpiece of rigor and clarity.
- Sales Rank: #1645770 in Books
- Brand: Brand: American Mathematical Society
- Published on: 2001-06-01
- Released on: 2001-06-01
- Original language: English
- Dimensions: 9.25" h x 6.25" w x 1.00" l, 1.50 pounds
- Binding: Hardcover
- 372 pages
- Used Book in Good Condition
Review
And what a book it is! The marks of Landau's thoroughness and elegance, and his undoubted authority, impress themselves on the reader at every turn, from the opening of the preface ... to the closing of the final chapter. It is a book that all analysts ... should possess ... to see how a master of his craft like landau presented the calculus when he was at the height of his power and reputation Mathematical Gazette
Most helpful customer reviews
44 of 44 people found the following review helpful.
The meaning of analysis
By Guilherme
This book would more correctly be described as a book on analysis, because of the completeness of its proofs. It assumes you know just arithmetic of natural numbers, integers, rational, real and complex numbers-that is to say, just how to sum, multiply, subtract and divide. Edmund Landau wrote a masterpiece, because nothing is left without proof. You will not find a single step missing. From arithmetic to all the concepts of calculus, like differentiation, integration, infinite series and sequences, this book contains the mathematics that most mathematicians should know presented in a perfect way. It is not easy reading, though. Landau strives to reach the perfect axiomatic presentation, so like Euclid's "Elements" the book is the clear and beautiful presentation of a doctrine. I dare say that no book in analysis approaches Euclid's ideal of presentation better than Landau's, never in the past and never in the future. What you will find in this book is, in its best appearance, truth, that will not change even in a thousand years.
18 of 26 people found the following review helpful.
A good book of its kind, BUT---
By BebopBoomer
I give this book one star, not because it's a bad book--of its kind,it is not--but to sound a warning and to counter some of the rave reviews here. In the preface to his famous calculus text, the great Richard Courant speaks of a "smug and presumptuous purism" which had crept into the mathematics texts of his time and place (Germany, '20s and '30s). I suspect he had Landau's "completely rigorous" (and in my opinion, completely unreadable) calculus text. "Foundations of Analysis" is cut from the same monk's-hairshirt cloth. IF you really like math books that consist almost 100% of "definition-axiom-theorem-proof; definition-axiom-theorem-proof" style writing, and that defy the reader to penetrate a completely closed system of elegantly presented and almost contemptuously concise pure truths (or at least, pure deductions from axioms), then Landau is definitely for you, or at least worth a serious try. But if you like math books that contain base, ignoble, impure elements such as motivation, intuitive insight, historical information about the development of the number concept, or just an occasional prose oasis, you're better off looking elsewhere (e.g. Feferman, Mendelson, Henkin-Smith-et al). By comparison to Landau, Hardy's "Pure Mathematics" seems chatty and chummy; it's also a much better book which gives more insight into the foundations of analysis in its first chapter than the whole of "Foundations". To my mind, Landau's book is, to quote a very old joke, not so much "rigor" as rigor mortis.
5 of 8 people found the following review helpful.
A classic that should remain in print
By galloamericanus
Dover, please put this classic back into print!!
This does for numbers what Suppes (1960) did for ZF set theory.
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