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**About this book :- **
**Mathematical Analysis, 2E ** written by
** Tom M. Apostol **.

A glance at the table of contents will reveal that this textbook treats topics in analysis at the "Advanced Calculus" level. The aim has been to provide a development of the subject which is honest, rigorous, up to date, and, at the same time, not too pedantic. The book provides a transition from elementary calculus to advanced courses in real and complex function theory, and it introduces the reader to some of the abstract thinking that pervades modern analysis.

The second edition differs from the first in many respects. Point set topology is developed in the setting of general metric spaces as well as in Euclidean n-space, and two new chapters have been added on Lebesgue integration. The material on line integrals, vector analysis, and surface integrals has been deleted. The order of some chapters has been rearranged, many sections have been completely rewritten, and several new exercises have been added.

(Tom M. Apostol)

**Book Detail :- **
** Title: ** Mathematical Analysis
** Edition: ** 2nd
** Author(s): ** Tom M. Apostol
** Publisher: ** Addison Wesley
** Series: **
** Year: ** 1974
** Pages: ** 506
** Type: ** PDF
** Language: ** English
** ISBN: ** 0201002884,9780201002881,7111146891
** Country: ** US
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**About Author :- **
The author ** Tom M. Apostol ** joined the Caltech faculty in 1950 and is Professor of Mathematics, Emeritus. He is internationally known for his books on Calculus, Analysis, and Analytic Number Theory, (translated into 7 languages), and for creating Project MATHEMATICS!, a video series that brings mathematics to life with computer animation, live action, music, and special effects. The videos have won first-place honors at a dozen international festivals, and were translated into Hebrew, Portuguese, French, and Spanish. Apostol has published 102 research papers, has written two chapters for the Digital Library of Mathematical Functions (2010), and is coauthor of three texts for the physics telecourse.

He has received several awards for research and teaching. In 1978 he was a visiting professor at the University of Patras, Greece, and in 2001 was elected a Corresponding Member of the Academy of Athens, where he delivered his inaugural lecture in Greek. In 2012 he was selected to be a Fellow of the American Mathematical Society.

**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 Mathematical Analysis, 2E, Tom M. Apostol **

** • Download PDF Mathematical Analysis, 2E, Solution Manual, Tom M. Apostol **

** • Download PDF Introduction to Analytic Number Theory (2E) by Tom M. Apostol **

** • Download PDF Introduction to Analytic Number Theory (Solutions Manual) by Tom M. Apostol **

** • Download PDF Introduction to Analytic Number Theory by Tom M. Apostol **

** • Download PDF Modular Functions and Dirichlet Series in Number Theory, Tom M. Apostol **

** • Download PDF New Horizons in Geometry, Tom M. Apostol, Mamikon A Mnatsakanian **

** • Download PDF Selected Papers on Precalculus, Tom M. Apostol **

** • Download PDF Calculus I: One-Variable Calculus, with an Introduction to Linear Algebra, 2E, Tom M. Apostol **

** • Download PDF Calculus II: Multi-Variable Calculus & Linear Algebra, with Applications to Diff. Equations & Probability, Tom M. Apostol **

** • Download PDF Multimedia Tools for Communicating Mathematics by Tom M. Apostol, Jonathan Borwein, Maria H. Morales, José F. Rodrigues, Konrad Polthier **

** • Download PDF The Mechanical Universe: Mechanics and Heat by Steven C. Frautschi, Richard P. Olenick, Tom M. Apostol, David L. Goodstein **

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**Book Contents :- **
**Mathematical Analysis, 2E ** written by
** Tom M. Apostol **
cover the following topics.
'

1. The Real and Complex Number Systems

2. Some Basic Notions of Set Theory

3. Elements of Point Set Topology

4. Limits and Continuity

5. Derivatives

6. Functions of Bounded Variation and Rectifiable Curves

7. The Riemann-Stieltjes Integral

8. Infinite Series and Infinite Products

9. Sequences of Functions Pointwise convergence of sequences of functions

10. The Lebesgue Integral

11. Fourier Series and Fourier Integrals

12. Multivariable Differential Calculus

13. Implicit Functions and Extremum Problems

14. Multiple Riemann Integrals

15. Multiple Lebesgue Integrals

16. Cauchy's Theorem and the Residue Calculus

Index of Special Symbols

Index

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