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**About this book :- **
**Introduction to Real Analysis ** written by
** William F. Trench **.

This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.

The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics.

(William F. Trench)

**Book Detail :- **
** Title: ** Introduction to Real Analysis
** Edition: **
** Author(s): ** William F. Trench
** Publisher: ** Pearson Education
** Series: **
** Year: ** 2009
** Pages: ** 584
** Type: ** PDF
** Language: ** English
** ISBN: ** 0-13-045786-8
** Country: ** US
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**About Author :- **
The author ** William F Trench **, joined the Trinity faculty as the Cowles Distinguished Professor in 1986. He had previously served as professor of mathematics at Drexel University from 1964 to 1986. Prior to entering academia, Trench was employed as an applied mathematician by RCA, Philco, and General Electric.

His main research interests were in linear algebra and ordinary differential equations. He was the recipient of multiple National Science Foundation (NSF) grants. In 1989 he received a $35,575 grant in support of a project on "Numerical Solution of Spectral Problems for Efficiently Structured Hermitian Matrices. Trench was the author of three textbooks and more than 120 research papers. All three of his textbooks are available via open access on the Trinity Digital Commons, where they have been downloaded more than 81,000 times. His works are the most downloaded files across the entire Trinity faculty. Although he retired from teaching in 1997, he continued to publish research with articles appearing in leading journals as recently as 2014.

His teaching experience spanned nearly 35 years and included a broad spectrum of mathematics courses to undergraduates and graduate students. At Trinity students found him to be interesting and intriguing and especially appreciated his sense of humor.

He earned B.Sc bachelor's in mathematics from Lehigh University, M.Sc and Ph.D. in mathematics from the University of Pennsylvania. He remaind also a member of the Society for Industrial and Applied Mathematics, the American Mathematical Society, and Phi Beta Kappa.

**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 Introduction to Real Analysis by William F Trench **

** • Download PDF Introduction to Real Analysis by William F Trench **

** • Download PDF Elementary Differential Equations with Boundary Value Problems by William F Trench **

** • Download PDF Elementary Differential Equations with Boundary Value Problems (Solution Manual) by William F Trench **

** • Download PDF Multivariable Calculus with Linear Algebra & Series by William F Trench, Bernard Kolman **

** • Download PDF Multivariable Calculus with Linear Algebra & Series (Solution Manual) by William F Trench, Bernard Kolman**

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**Book Contents :- **
**Introduction to Real Analysis ** written by
** William F. Trench **
cover the following topics.
'
**1. The Real Numbers **

The Real Number System, Mathematical Induction, The Real Line
**2. Differential Calculus of Functions of One Variable **

Functions and Limits, Continuity, Differentiable Functions of One Variable, L’Hospital’s Rule, Taylor’s Theorem
**3. Integral Calculus of Functions of One Variable**

Definition of the Integral, Existence of the Integral, Properties of the Integral, Improper Integrals, A More Advanced Look at the Existence of the Proper Riemann Integral
**4. Infinite Sequences and Series**

Sequences of Real Numbers, Earlier Topics Revisited With Sequences, Infinite Series of Constants, Sequences and Series of Functions, Power Series
**5. Real-Valued Functions of Several Variables**

Structure of Rn, Continuous Real-Valued Function of n Variables, Partial Derivatives and the Differential, The Chain Rule and Taylor’s Theorem
**6. Vector-Valued Functions of Several Variables**

Linear Transformations and Matrices, Continuity and Differentiability of Transformations, The Inverse Function Theorem, The Implicit Function Theorem
**7. Integrals of Functions of Several Variables**

Definition and Existence of the Multiple Integral, Iterated Integrals and Multiple Integrals, Change of Variables in Multiple Integrals
**8. Metric Space**

Introduction to Metric Spaces, Compact Sets in a Metric Space, Continuous Functions on Metric Spaces
**Answers to Selected Exercises**

Index

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- Abstract Algebra
- Calculus
- Differential Equations
- Engineering Mathematics
- Linear Algebra
- Math Magic
- Real Analysis