Title Real Analysis.pdf ✅

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This book on Real Analysis has been written to meet the requirements of M.A./M.Sc. (Maths) students. The subject matter has been discussed in a simple way so that the students may understand it easily. The book contains various worked out examples. The proof of various theorems and examples has been given with minute details. At the end of each section, there is a set of exercises which provides the students a better understanding. We would be extremely happy to recieve the readers considered opinion and suggestions for further improvements Publisher P r e f a c e
Unit-I Chapter - 1 Real Number System & Real Line 1-26 1. Real Number system 2. Mathematical induction 3. The Real line Chapter - 2 Limit, Continuity and Differentiability 27-91 1. Functions and Limits 2. Continuity 3. Differential functions of one variable 4. L' Hospital's Rule 5. Taylor's theorem Unit-II Chapter - 3 Riemann Integral and Improper Integrals 92-147 1. Definition of the Integral 2. Existence of the Integral 3. Properties of the Integral 4. Improper Integrals 5. A more advanced look at the Existence of the proper Riemann Integral Chapter - 4 Sequence and Series 148-217 1. Sequence of real numbers 2. Real Topics Revisited with sequences 3. Infinite series of constants 4. Sequence and series of Functions Unit-III n Chapter - 5 Structure of R and Functions of Several Variables 218-283 n 1.Structure of R 2. Continuous Real - Valued functions of n variables 3. Partial Derivatives and the Differential 4. The chain Rule and Taylor's theorem C O N T E N T S