Softcover ISBN:  9781470478193 
Product Code:  CHEL/78.S 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470478230 
Product Code:  CHEL/78.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Softcover ISBN:  9781470478193 
eBook: ISBN:  9781470478230 
Product Code:  CHEL/78.S.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 
Softcover ISBN:  9781470478193 
Product Code:  CHEL/78.S 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470478230 
Product Code:  CHEL/78.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Softcover ISBN:  9781470478193 
eBook ISBN:  9781470478230 
Product Code:  CHEL/78.S.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 

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.

Table of Contents

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 NONRATIONAL 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


Additional Material

Reviews

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


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
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 NONRATIONAL 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