# Real Analysis | Krishna Series

## Download PDF of Real Analysis By Krishna Series

This book on Real Analysis has been specially written according to the latest Syllabus to meet the requirements of B.A. and B.Sc. Semester-IV Students of all colleges affiliated to Kumaun University

This book is important for UPSC Optional, IIT JEE Mains, Graduation College Students BSC all sem (1st, 2nd, 3rd year), BA (1st, 2nd, 3rd, 4th, 5th, 6th semester), Engineering, Preparing for SSC, Banking And Other Competitive Examination.

The subject matter has been discussed in such a simple way that the students will find no difficulty to understand it. The proofs of various theorems and examples have been given with minute details. Each chapter of this book contains complete theory and a fairly large number of solved examples. Sufficient problems have also been selected from various university examination papers. At the end of each chapter an exercise containing objective questions has been given.

## Syllabus

Continuity and Differentiability of functions: Continuity of functions, Uniform continuity, Differentiability, Taylor’s theorem with various forms of remainders.

Integration: Riemann integral-definition and properties, integrability of continuous and monotonic functions, Fundamental theorem of integral calculus, Mean value theorems of integral calculus.

Improper Integrals: Improper integrals and their convergence, Comparison test, Dritchlet’s test, Absolute and uniform convergence, Weierstrass M-Test, Infinite integral depending on a parameter.

Sequence and Series: Sequences, theorems on limit of sequences, Cauchy’s convergence criterion, infinite series, series of non-negative terms, Absolute convergence, tests for convergence, comparison test, Cauchy’s root Test, ratio Test, Rabbe’s, Logarithmic test, De Morgan’s Test, Alternating series, Leibnitz’s theorem.

Uniform Convergence: Point wise convergence, Uniform convergence, Test of uniform convergence, Weierstrass M-Test, Abel’s and Dritchlet’s test, Convergence and uniform convergence of sequences and series of functions.