Concepts Of Real Analysis
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Concepts of Real Analysis
Concepts of Real Analysis is a student friendly text book on real analysis, a topic taught as part of the undergraduate mathematics syllabus of pass and honours courses of all Indian universities. All the relevant topics of real analysis such as real numbers, sequences and series, limit, continuity, derivatives, Riemann Integration, improper integration, sequence and series of functions, power series etc. are covered in a lucid manner in the book. Each concept is explained with the help of solved examples. Remarks are provided whenever special attention is required about some aspects of a definition or of a result. Diagrams and graphs are provided for further comprehension of a topic or a result, whenever felt necessary. Illustrative examples are provided at the end of each topic, which is followed by exercises. Overall, it is a complete-in-itself book on real analysis, suitable for students and teachers alike. Salient Features 1. Covers the entire syllabus of Real Analysis taught in the undergraduate level courses including B.Sc. (H), B.A. (Prog.), and B.Sc. (Prog.) of all Indian Universities. 2. Written in simple language. 3. Emphasis on logical, step-by-step development of proofs. 4. More than 450 solved examples and 50 diagrams. 5. Sufficient explanations are provided for the concepts introduced and results provided. 6. Remarks are provided to highlight any special aspect of a definition or a result, which might go unnoticed by the readers. 7. Student-friendly approach. 8. Appendix is added to provide the basics for curve tracing.
Core Concepts in Real Analysis
"Core Concepts in Real Analysis" is a comprehensive book that delves into the fundamental concepts and applications of real analysis, a cornerstone of modern mathematics. Written with clarity and depth, this book serves as an essential resource for students, educators, and researchers seeking a rigorous understanding of real numbers, functions, limits, continuity, differentiation, integration, sequences, and series. The book begins by laying a solid foundation with an exploration of real numbers and their properties, including the concept of infinity and the completeness of the real number line. It then progresses to the study of functions, emphasizing the importance of continuity and differentiability in analyzing mathematical functions. One of the book's key strengths lies in its treatment of limits and convergence, providing clear explanations and intuitive examples to help readers grasp these foundational concepts. It covers topics such as sequences and series, including convergence tests and the convergence of power series. The approach to differentiation and integration is both rigorous and accessible, offering insights into the calculus of real-valued functions and its applications in various fields. It explores techniques for finding derivatives and integrals, as well as the relationship between differentiation and integration through the Fundamental Theorem of Calculus. Throughout the book, readers will encounter real-world applications of real analysis, from physics and engineering to economics and computer science. Practical examples and exercises reinforce learning and encourage critical thinking. "Core Concepts in Real Analysis" fosters a deeper appreciation for the elegance and precision of real analysis while equipping readers with the analytical tools needed to tackle complex mathematical problems. Whether used as a textbook or a reference guide, this book offers a comprehensive journey into the heart of real analysis, making it indispensable for anyone interested in mastering this foundational branch of mathematics.
Real Analysis
This text is designed for graduate-level courses in real analysis. Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.