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portada Descargar ficha PDF Título: Differential And Integral Calculus: Third Edition
Autor: Edmund Landau Precio: Desconocido
Editorial: American Mathematical Society Año: 1965
Tema: Matematicas Edición:
Sinopsis ISBN: 9780821828304
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=?
Logarithms, powers, and roots
Functions and continuity
Limits as x=?
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
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