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.
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32 of 32 people found the following review helpful:
5.0 out of 5 stars
The meaning of analysis,
By Guilherme (Brazil) - See all my reviews
This review is from: Differential and Integral Calculus 3ED (AMS Chelsea Publishing) (Hardcover)
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.
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First Sentence:
In this chapter n, m, N, m1, m2, k, v, and N always serve to denote integers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
same wording, suitable partition, proves our assertion Key Phrases - Capitalized Phrases (CAPs): (learn more)
Preliminary Remark New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter n, m, N, m1, m2, k, v, and N always serve to denote integers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
same wording, suitable partition, proves our assertion Key Phrases - Capitalized Phrases (CAPs): (learn more)
Preliminary Remark New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
9
books
cite this book:
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- Trigonometric Delights by Eli Maor on page 193, and page 197
- e: The Story of a Number by Eli Maor on page 107, and page 196
- Number Theory and Analysis by Paul Turan in Back Matter
- Foundations of Analysis (Graduate Studies in Mathematic) by Edmund Landau in Front Matter
- Functional Methods in Differential Equations (Chapman & Hall/CRC Research Notes in Mathematics Series) by Veli-Matti Hokkanen on page 65
See all 9 books citing this book
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