Mathematical Analysis

This book is intended to serve as a text in mathematical analysis for undergraduate and postgraduate students. It opens with a brief outline of the essential properties of rational numbers using Dedekind's cut, and the properties of real numbers are established. This foundation supports the subsequent chapters. The material of some of topics-real sequences and series, continuity, functions of several variables, elementary and implicit functions, Riemann and Riemann-Stieltjes integrals, Lebesgue integrals, line and surface Integrals, double and triple integrals are discussed in details. Uniform convergence, Power series, Fourier series, and Improper integrals have been presented in a simple and lucid manner. A large number of solved examples taken mostly from lecture notes make the book useful for the students.

A chapter on Metric Spaces discussing completeness, compactness and connectedness of the spaces and two appendices discussing Beta-Gamma functions and Cantor's theory of real numbers add glory to the contents of the book.

KEY FEATURES:

-New version of outstanding textbook catering to international segments
-Well developed, rigorous and not too pedantic subject matter
-Application of modern methods to smooth out and shorten classical techniques
-Special effort has been made to include most of the lecture notes based on author's decadal teaching experience

CONTENTS:

Real Numbers
Open Sets, Closed Sets and Countable Sets
Real Sequences
Infinite Series
Functions of a Single Variable (I)
Functions of a Single Variable (II)
Applications of Taylor's Theorem
Functions
The Riemann Integral
The Riemann-Stieltjes Integral
Improper Integrals
Uniform Convergence
Power Series
Fourier Series
Functions of Several Variables
Implicit Functions
Integration on R2
Integration on R3
Metric Spaces
The Lebesgue Integral

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