Introduction to analysis (Bartley and Sherbert)
Sequence of real numbers, Convergence of sequences, Bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences, Subsequences, Bolzano-Weierstrass theorem
Lecture 2 What are sequences?
Lecture 3 Behaviour of sequences.
Lecture 4: Epsilon N definition of Limits of sequences
Lecture 5: Recursive definition of sequences.
Lecture 6: What are subsequences?
Lecture 7: Nondecreasing sequences.
Lecture 8: Bounded sequences
Lecture 9: Bounded and Nondecreasing sequences are convergent
Lecture 10: Properties of Limits of sequences
Lecture 11: Frequently arising Limits
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
Lecture 12: Introduction to series.
Lecture 13: Checking the convergence of a series by the sequence of partial sums
Lecture 14: Geometric series
Lecture 15: Some Problems based on geometric series
Lecture 16: Telescopic series
Lecture 17: nth term test for checking the divergence of a series.
Lecture 18: Some noteworthy points regarding convergence of series.
Lecture 19: The integral test for checking the convergence of series of positive terms
Lecture 20: Problems based on integral test.
Lecture 21: p test for checking convergence/divergence of a series
Lecture 22: Comparison tests ( Direct comparison test and limit comparison test ).
Lecture 23: Problems on Limit comparison test (LCT) and Direct comparison test (DCT)
Lecture 24: Ratio test
Lecture 25: Nth root test.
Lecture 26: Alternating series