CONTENT
Unit 1: Sequence of Real numbers - 5 hours
1.1 Definition notation and examples.
1.2 Convergent, divergent and oscillatory sequence,
definition and examples.
1.3 Bounded set, Bounded sequence definition and
examples.
1.4 Monotonic sequence
Unit 2: Series of Real Numbers - 10 hours
2.1 Sequence of partial sum.
2.2 Convergence of series. If un is convergent then
un0 as n (with proof)
2.3 Convergence of geometric series (with proof)
2.4 Series of positive terms, comparison test and its
limit form (without proof)
2.5 Convergences of n
p, PR (with proof)
Unit 3: Differential Calculus
3.1 nth derivative
3.2 Leibnitz theorem (with proof) and its application
3.3 Partial differentiation
Unit 4: Integral Calculus
4.1 Method of integration.
4.2 Properties of definite, integral.
4.3 Improper integral
4.4 Beta Gamma function and their properties.
4.5 Reduction formula
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