- 400 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
About this book
"In scope and choice of subject matter," declared the Bulletin of the American Mathematics Society, "this text is nicely calculated to suit the needs of introductory classes in real variable theory." A balanced treatment, it covers all of the fundamentals, from the real number system and point sets to set theory and metric spaces.
Starting with a brief exposition of the ideas and methods of deductive logic, the text proceeds to the postulates of Peano for the natural numbers and outlines a method for constructing the real number system. Subsequent chapters explore functions and their limits, the properties of continuous functions, fundamental theorems on differentiation, the Riemann integral, and uniform convergence. Additional topics include ordinary differential equations, the Lebesgue and Stieltjes integrals, and transfinite numbers. Useful, well-chosen lists of references to the literature conclude each chapter.
Starting with a brief exposition of the ideas and methods of deductive logic, the text proceeds to the postulates of Peano for the natural numbers and outlines a method for constructing the real number system. Subsequent chapters explore functions and their limits, the properties of continuous functions, fundamental theorems on differentiation, the Riemann integral, and uniform convergence. Additional topics include ordinary differential equations, the Lebesgue and Stieltjes integrals, and transfinite numbers. Useful, well-chosen lists of references to the literature conclude each chapter.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access The Theory of Functions of Real Variables by Lawrence M Graves in PDF and/or ePUB format, as well as other popular books in Mathematics & Complex Analysis. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Cover
- Title Page
- Copyright Page
- Preface
- Contents
- Chapter I. Introduction
- Chapter II. The Real Number System
- Chapter III. Point Sets
- Chapter IV. Functions and Their Limits. Properties of Continuous Functions
- Chapter V. Fundamental Theorems on Differentiation
- Chapter VI. The Riemann Integral
- Chapter VII. Uniform Convergence
- Chapter VIII. Functions Defined Implicitly
- Chapter IX. Ordinary Differential Equations
- Chapter X. The Lebesgue Integral
- Chapter XI. The Lebesgue Integral
- Chapter XII. The Stieltjes Integral
- Chapter XIII. The Theory of Sets and Transfinite Numbers
- Chapter XIV. Metric Spaces
- Index