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Differential and Integral Calculus
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Differential and Integral Calculus

Differential and Integral Calculus

Edmund Landau

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

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  3eme 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

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