English | 2021 | ASIN: B092SDMDN2 | 347 pages | PDF | 3.69 MB

SYLLABUS- REAL ANALYSIS, 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.
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