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9780821828304

Differential and Integral Calculus

by ; ;
  • ISBN13:

    9780821828304

  • ISBN10:

    0821828304

  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 2001-06-01
  • Publisher: Chelsea Pub Co

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Summary

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 analytical, with an emphasis on functions rather than on geometric or physical applications. Providing an example of Landau's formidable skill as an expositor, this text is a masterpiece of rigor and clarity.

Table of Contents

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
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
Table of Contents provided by Publisher. All Rights Reserved.

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