This book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.
1. Sets, Functions and Cardinality.-
2. The Real Numbers.-
3. Sequence and Series of Numbers.-
4. Analysis on R.-
5. Topology of the Real Line.-
6. Metric Spaces.-
7. Continuity and Differentiability.-
8. Sequences and Series of Functions.-
9. Lebesgue Integration.-
10. Fourier Series.
ATUL RAZDAN served at the Department of Mathematics, University of Delhi, India, from 20042008. He started his career as Lecturer in 1995 at Indira Gandhi National Open University (IGNOU), New Delhi, India, until 2004. His area of research is algebra on which he has published several papers in journals of international repute.V. RAVICHANDRAN is Professor of Mathematics at the National Institute of Technology, Tiruchirappalli, India. Earlier, he held positions at Universiti Sains Malaysia (20042007 and 20112012) and the University of Delhi, India (20072018). He specializes in geometric function theory and has published more than 150 research papers. Since 2004, he has been serving as Editor of the Bulletin of the Malaysian Mathematical Sciences Society.
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