Real Analysis
This text book is designed for an undergraduate course on mathematics. It covers the basic material that every graduate student should know in the classical theory of functions of real variables, measures, limits and continuity. This text book offers readability, practicality and flexibility. It presents fundamental theorems and ideas from a practical viewpoint, showing students the motivation behind mathematics and enabling them to construct their own proofs.
Table of Content
- Basic Properties of the Real number system
- Some Finer Aspects of Set Theory
- Sequences and Series
- Topological aspects of the real line
- Limits and Continuity
- Differentiation
- Functions of Bounded variation
- Riemann Integration
- Sequences and series of functions
- Power series and special functions
- Fourier Series
- Real-valued Functions of two real variables
- Lebesgue Measure and Integration
- Lp – Spaces
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Salient Features
- Comprehensive coverage of sequence and series
- Detailed coverage of topics like measure theory, set theory, limits and continuity
- The theory is well explained, with an equal number of theorems and examples for all topics, including Lp spaces, real number system, measure theory and sequence and series
- A very flexible presentation with a uniform writing style and notation, covering the material in small sections, which allows instructors and students to adapt this book to their syllabus
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