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| Softcover ISBN: | 978-1-4704-7819-3 |
| Product Code: | CHEL/78.S |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $62.10 |
| eBook ISBN: | 978-1-4704-7823-0 |
| Product Code: | CHEL/78.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $58.50 |
| Softcover ISBN: | 978-1-4704-7819-3 |
| eBook ISBN: | 978-1-4704-7823-0 |
| Product Code: | CHEL/78.S.B |
| List Price: | $134.00 $101.50 |
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Book DetailsAMS Chelsea PublishingVolume: 78; 1965; 372 ppMSC: Primary 26; 01
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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Table of Contents
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Front Cover
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TRANSLATORS' PREFACE
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PREFACE TO THE FIRST (GERMAN) EDITION
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TABLE OF CONTENTS
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INTRODUCTION
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§ I. Residue Classes
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§ 2. The Decimal System
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§ 3. Finite and Infinite Sets of Numbers
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PART ONE DIFFERENTIAL CALCULUS
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CHAPTER I LIMITS FOR n = ∞
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CHAPTER 2 LOGARITHMS, POWERS, AND ROOTS
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CHAPTER 3 FUNCTIONS AND CONTINUITY
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CHAPTER 4 LIMITS AT x = ξ
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CHAPTER 5 DEFINITION OF THE DERIVATIVE
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CHAPTER 6 GENERAL THEOREMS ON THE CALCULATION OF DERIVATIVES
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CHAPTER 7 INCREASE, DECREASE, MAXIMUM, MINIMUM
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CHAPTER 8 GENERAL PROPERTIES OF A FUNCTION CONTINUOUS IN A CLOSED INTERVAL
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CHAPTER 9 ROLLE'S THEOREM AND THE THEOREM OF THE MEAN
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CHAPTER 10 DERIVATIVES OF HIGHER ORDER; TAYLOR'S THEOREM
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CHAPTER 11 "0/0" AND SIMILAR MATTERS
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CHAPTER 12 INFINITE SERIES
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CHAPTER 13 UNIFORM CONVERGENCE
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CHAPTER 14 POWER SERIES
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CHAPTER 15 THE EXPONENTIAL AND BINOMIAL SERIES
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CHAPTER 16 THE TRIGONOMETRIC FUNCTIONS
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CHAPTER 17 FUNCTIONS OF TWO VARIABLES; PARTIAL DIFFERENTIATION
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CHAPTER 18 INVERSE FUNCTIONS AND IMPLICIT FUNCTIONS
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CHAPTER 19 THE INVERSE TRIGONOMETRIC FUNCTIONS
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CHAPTER 20 SOME NECESSARY ALGEBRAIC THEOREMS
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§ 1. The Fundamental Theorem of Algebra
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§ 2. Decomposition of Rational Functions Into Partial Fractions
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PART TWO INTEGRAL CALCULUS
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CHAPTER 21 DEFINITION OF THE INTEGRAL
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CHAPTER 22 BASIC FORMULAS OF THE INTEGRAL CALCULUS
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CHAPTER 23 INTEGRATION OF RATIONAL FUNCTIONS
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CHAPTER 24 INTEGRATION OF SOME NON-RATIONAL FUNCTIONS
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CHAPTER 25 THE CONCEPT OF DEFINITE INTEGRAL
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CHAPTER 26 THEOREMS ON THE DEFINITE INTEGRAL
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CHAPTER 27 INTEGRATION OF INFINITE SERIES
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CHAPTER 28 THE IMPROPER INTEGRAL
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CHAPTER 29 THE INTEGRAL WITH INFINITE LIMITS
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CHAPTER 30 THE GAMMA FUNCTION
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CHAPTER 31 FOURIER SERIES
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INDEX OF DEFINITIONS
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SUBJECT INDEX
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Back Cover
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Additional Material
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Reviews
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And what a book it is! The marks of Landau's thoroughness and elegance, and of 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
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- Book Details
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- Reviews
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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.
-
Front Cover
-
TRANSLATORS' PREFACE
-
PREFACE TO THE FIRST (GERMAN) EDITION
-
TABLE OF CONTENTS
-
INTRODUCTION
-
§ I. Residue Classes
-
§ 2. The Decimal System
-
§ 3. Finite and Infinite Sets of Numbers
-
PART ONE DIFFERENTIAL CALCULUS
-
CHAPTER I LIMITS FOR n = ∞
-
CHAPTER 2 LOGARITHMS, POWERS, AND ROOTS
-
CHAPTER 3 FUNCTIONS AND CONTINUITY
-
CHAPTER 4 LIMITS AT x = ξ
-
CHAPTER 5 DEFINITION OF THE DERIVATIVE
-
CHAPTER 6 GENERAL THEOREMS ON THE CALCULATION OF DERIVATIVES
-
CHAPTER 7 INCREASE, DECREASE, MAXIMUM, MINIMUM
-
CHAPTER 8 GENERAL PROPERTIES OF A FUNCTION CONTINUOUS IN A CLOSED INTERVAL
-
CHAPTER 9 ROLLE'S THEOREM AND THE THEOREM OF THE MEAN
-
CHAPTER 10 DERIVATIVES OF HIGHER ORDER; TAYLOR'S THEOREM
-
CHAPTER 11 "0/0" AND SIMILAR MATTERS
-
CHAPTER 12 INFINITE SERIES
-
CHAPTER 13 UNIFORM CONVERGENCE
-
CHAPTER 14 POWER SERIES
-
CHAPTER 15 THE EXPONENTIAL AND BINOMIAL SERIES
-
CHAPTER 16 THE TRIGONOMETRIC FUNCTIONS
-
CHAPTER 17 FUNCTIONS OF TWO VARIABLES; PARTIAL DIFFERENTIATION
-
CHAPTER 18 INVERSE FUNCTIONS AND IMPLICIT FUNCTIONS
-
CHAPTER 19 THE INVERSE TRIGONOMETRIC FUNCTIONS
-
CHAPTER 20 SOME NECESSARY ALGEBRAIC THEOREMS
-
§ 1. The Fundamental Theorem of Algebra
-
§ 2. Decomposition of Rational Functions Into Partial Fractions
-
PART TWO INTEGRAL CALCULUS
-
CHAPTER 21 DEFINITION OF THE INTEGRAL
-
CHAPTER 22 BASIC FORMULAS OF THE INTEGRAL CALCULUS
-
CHAPTER 23 INTEGRATION OF RATIONAL FUNCTIONS
-
CHAPTER 24 INTEGRATION OF SOME NON-RATIONAL FUNCTIONS
-
CHAPTER 25 THE CONCEPT OF DEFINITE INTEGRAL
-
CHAPTER 26 THEOREMS ON THE DEFINITE INTEGRAL
-
CHAPTER 27 INTEGRATION OF INFINITE SERIES
-
CHAPTER 28 THE IMPROPER INTEGRAL
-
CHAPTER 29 THE INTEGRAL WITH INFINITE LIMITS
-
CHAPTER 30 THE GAMMA FUNCTION
-
CHAPTER 31 FOURIER SERIES
-
INDEX OF DEFINITIONS
-
SUBJECT INDEX
-
Back Cover
-
And what a book it is! The marks of Landau's thoroughness and elegance, and of 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
