INTRODUCTION TO THE BASICS OF REAL ANALYSIS

This book presents an introduction to the key topics in Real Analysis and makes the subject easily understood by the learners. The book is primarily useful for students of mathematics and engineering studying the subject of Real Analysis. It includes many examples and exercises at the end of chapters. This book is very authentic for students, instructors, as well as those doing research in areas demanding a basic knowledge of Real Analysis. It describes several useful topics in Real Analysis such as sets and functions, completeness, ordered field, neighborhoods, limit points of a set, open sets, closed sets, countable and uncountable sets, sequences of real numbers, limit, continuity and differentiability of real functions, uniform continuity, point-wise and uniform convergence of sequences and series of real functions, Riemann integration, improper integrals and metric spaces.

Contents:

• Sets and Functions
• Real Number System
• Basics of Real Analysis
• Sequences of Real Numbers
• Limits and Continuity
• Uniform Continuity of Real Functions
• Differentiability of Real Functions
• Uniform Convergence of Sequences and Series of Real Functions
• Functions of Several Variables
• Riemann Integration
• The Improper Integrals
• Metric Spaces

Readership: Undergraduate and postgraduate students in Real Analysis.

Key Features:

• Contains important and basic topics of real analysis
• Written in an easier way to learn the subject
• Basics of limits, continuity and differentiability are provided
• Fundamentals of convergence of the sequences and series of functions are discussed
• Limit and continuity concepts are extended to two dimensions
• Basic concepts of Riemann integration, improper integrals and metric spaces are discussed