Description
Definition of a sequence, Bounds of a sequence, Convergent, divergent and oscillatory sequences, Algebra of limits, Monotonic Sequences, Cauchy’s theorem on limits, Subsequences, Bolzano-Weirstrass Theorem, Cauchy’s convergence criterion.
Sequential continuity and Uniform continuity of functions of single variable.
Series of non-negative terms, P-Test, Comparison tests, Cauchy’s integral test, Cauchy’s Root test, Ratio tests, Kummer’s Test, D’Alembert’s test, Raabe’s test, De Morgan and Bertrand’s test, Gauss test, Logarithmic test, Alternating series, Leibnitz’s theorem, Absolute and conditional convergence, Rearrangement of absolutely convergent series, Riemann’s rearrangement theorem.
