Krishna's TB Real Analysis | Edition-1B | Pages-352 | Code- 1212

by A.R. Vasishtha

SYLLABUS- REAL ANALYSIS, Continuity and Differentiability of Continuity of functions, Uniform continuity, Differentiability, Taylor's theorem with various forms of remainders. Riemann integral-definition and properties, integrability of continuous and monotonic functions, Fundamental theorem of integral calculus, Mean value theorems of integral calculus. Improper 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 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 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.

Kindle Edition

Published April 16, 2021