Скачать или смотреть IIT Jam MA 2019 | Convergence of Sequence and Series

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Topics : Sequences
Sub-topics : Convergence, divergence, monotonicity, boundedness, limit points, Cauchy
Topics : Series
Convergence tests (comparison, ratio, root), absolute/convergence, p-series
Topics : Limits and Continuity :
Sub-topics : ε-δ definition, continuity at a point, types of discontinuities
Differentiation
Sub-topics : Derivatives, Mean Value Theorems, Rolle’s Theorem, Taylor’s theorem
Topics Riemann Integration
Sub-topics : Riemann integrability, properties of definite integrals, partitions
Topics Functions of Bounded Variation
Sub-topics : Definition, properties, integration context
Topics Metric Spaces (Basics)
Sub-topics : Open, closed sets, convergence, completeness, compactness
Topics Pointwise & Uniform Convergence
Sub-topics : Definitions, implications, Weierstrass M-test
Topics Continuity and Uniform Continuity
Sub-topics : Heine–Cantor theorem, uniform vs pointwise continuity
Topics Improper Integrals
Sub-topics : Convergence criteria, comparison tests

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Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable), Taylor's series, radius and interval of convergence, term-wise differentiation and integration of power series.
Sequences and Series of Real Numbers: Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms — comparison test, ratio test, root test; Leibniz test for convergence of alternating series.

Jam MA 2019, 4