AMS Chelsea Publishing 1965; 372 pp; hardcover Volume: 78 Reprint/Revision History: first AMS printing 2001 ISBN10: 0821828304 ISBN13: 9780821828304 List Price: US$50 Member Price: US$45 Order Code: CHEL/78.H
 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. 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 Table of Contents Part One. Differential Calculus  Limits as \(n=\infty\)
 Logarithms, powers, and roots
 Functions and continuity
 Limits as \(x=\xi\)
 Definition of the derivative
 General theorems on the formation of the derivative
 Increase, decrease, maximum, minimum
 General properties of continuous functions on closed intervals
 Rolle's theorem and the theorem of the mean
 Derivatives of higher order; Taylor's theorem
 "0/0" and similar matters
 Infinite series
 Uniform convergence
 Power series
 Exponential series and binomial series
 The trigonometric functions
 Functions of two variables and partial derivatives
 Inverse functions and implicit functions
 The inverse trigonometric functions
 Some necessary algebraic theorems
Part Two. Integral Calculus  Definition of the integral
 Basic formulas of the integral calculus
 The integration of rational functions
 The integration of certain nonrational functions
 Concept of the definite integral
 Theorems on the definite integral
 The integration of infinite series
 The improper integral
 The integral with infinite limits
 The gamma function
 Fourier series
 Index of definitions
 Subject index
