Differential and Integral Calculus

Edmund Landau

372 pages, parution le 15/06/2001 (3^eme édition)

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Résumé

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.

Contents

Part One. Differential Calculus

Limits as n=∞
Logarithms, powers, and roots
Functions and continuity
Limits as x=ξ
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 non-rational 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

Caractéristiques techniques

	PAPIER
Éditeur(s)	AMS Chelsea
Auteur(s)	Edmund Landau
Parution	15/06/2001
Édition	3^eme édition
Nb. de pages	372
Format	15,5 x 23,5
Couverture	Relié
Poids	678g
Intérieur	Noir et Blanc
EAN13	9780821828304
ISBN13	978-0-8218-2830-4