Differential and Integral Calculus
by Landau, Edmund; Hausner, Melvin; Davis, MartinEdition: 3rd
Format: Hardcover
Pub. Date: 2001-06-01
Publisher(s): 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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