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**About this book :- **
**The Elements of Real Analysis, 2E ** written by
** Robert G. Bartle **

At one time an undergraduate student of advanced mathematics was expected to develop technique in solving problems that involved cosiderable computation; however he was not expected to master "theoretical subtleties" such as uniform convergence or uniform continuity. He was required to be able to use the Implicit Function Theorem, but not to know its hypotheses. This situation has changed; it is now considered important that all advanced students of mathematics, future mathematicians, computer scientists, physicists, engineers, or economists--grasp the basic theoretical nature of the subject. They will then understand both the power and limitation of the general theory more fully.

This textbook developed from my experience in teaching real analysis at the University of Illinois since 1955. In this edition author introduce the algebraic and order properties of the real number system. Also author introduce the definitions of a vector space and normed space. Presents the basic theory of real analysis. The algebraic and order properties of the real number system are presented in a simpler fashion than in the previous edition.

(Robert G. Bartle)

**Book Detail :- **
** Title: ** The Elements of Real Analysis
** Edition: ** 2nd
** Author(s): ** Robert G. Bartle
** Publisher: ** John Wiley & Sons
** Series: **
** Year: ** 1976
** Pages: ** 494
** Type: ** PDF
** Language: ** English
** ISBN: ** 047105464X,9780471054641
** Country: ** US

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**About Author :- **

Author ** Robert Gardner Bartle ** (1927–2003) was an American mathematician. He was specializing in real analysis. He is known for writing the popular textbooks The Elements of Real Analysis (1964), The Elements of Integration (1966), and Introduction to Real Analysis (2011) published by John Wiley & Sons.

Bartle was born in Kansas City, Missouri, and was the son of Glenn G. Bartle and Wanda M. Bartle. He was married to Doris Sponenberg Bartle (born 1927) from 1952 to 1982 and they had two sons, James A. Bartle (born 1955) and John R. Bartle (born 1958). He was on the faculty of the Department of Mathematics at the University of Illinois from 1955 to 1990.

Bartle was Executive Editor of Mathematical Reviews from 1976 to 1978 and from 1986 to 1990. From 1990 to 1999 he taught at Eastern Michigan University. In 1997, he earned a writing award from the Mathematical Association of America for his paper "Return to the Riemann Integral".[1]

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.

** • Download PDF Elements of Real Analysis, 2E, Robert Bartle **

** • Download PDF Real Analysis, 3E, Robert Bartle, Donald Sherbert **

** • Download PDF Real Analysis, 4E, Robert Bartle, Donald Sherbert **

** • Download PDF Real Analysis, 4E, Solution, Robert Bartle, Donald Sherbert **

** • Download PDF Modern Theory of Integration by Robert Bartle **

** • Download PDF Modern Theory of Integration by Robert Bartle, Solution **

** • Download PDF The Elements of Integration and Lebesgue Measure, Robert Bartle **

** • Download PDF Geometry of Normed Linear Spaces by Robert Bartle **

** • Download PDF Linear Operators II Spectral Theory by Nelson James Dunford, Jacob Schwartz, William Bade, Robert Bartle **

** • Download PDF Linear Operators III Spectral Theory by Nelson James Dunford, Jacob Schwartz, William Bade, Robert Bartle **

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**Book Contents :- **
**The Elements of Real Analysis, 2E ** written by
** Robert G. Bartle **
cover the following topics.

0. Introduction: A Glimpse at Set Theory

1. The Real Numbers

2. The Topology of Cartesian Spaces

3. Convergence

4. Continuous Functions

5. Functions of One Variable

6. Infinite Series

7. Differnetiation in Rp

8. Integration in Rp

Refrences

Hints for Selected Exercises

Index

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