This book provides an introduction to basic topics in Real Analysis and makes the subject easily understandable to all learners. The book is useful for those that are involved with Real Analysis in disciplines such as mathematics, engineering, technology, and other physical sciences. It provides a good balance while dealing with the basic and essential topics that enable the reader to learn the more advanced topics easily. It includes many examples and end of chapter exercises including hints for solutions in several critical cases. The book is ideal for students, instructors, as well as those doing research in areas requiring a basic knowledge of Real Analysis. Those more advanced in the field will also find the book useful to refresh their knowledge of the topic.
- Includes basic and essential topics of real analysis
- Adopts a reasonable approach to make the subject easier to learn
- Contains many solved examples and exercise at the end of each chapter
- Presents a quick review of the fundamentals of set theory
- Covers the real number system
- Discusses the basic concepts of metric spaces and complete metric spaces
1. Review of Set Theory. 2. The Real Number System. 3. Sequences and Series of Real Numbers. 4. Metric Spaces - Basic Concepts, Complete Metric Spaces. 5. Limits and Continuity. 6. Connectedness and Compactness. 7. Differentiation.8. Integration. 9. Sequences and Series of Functions.