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Introduction to Real Analysis by William F. Trench

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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
Author(s): William F. Trench
Publisher: Pearson Education
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 :-
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• Download PDF Introduction to Real Analysis by William F Trench NEW
• Download PDF Introduction to Real Analysis by William F Trench NEW
• Download PDF Elementary Differential Equations with Boundary Value Problems by William F Trench NEW
• Download PDF Elementary Differential Equations with Boundary Value Problems (Solution Manual) by William F Trench NEW
• Download PDF Multivariable Calculus with Linear Algebra & Series by William F Trench, Bernard Kolman NEW
• Download PDF Multivariable Calculus with Linear Algebra & Series (Solution Manual) by William F Trench, Bernard KolmanNEW

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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


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