ANALYSIS-I

Real number system as a complete ordered field, Open and closed sets, Limit point of sets, Bolzano Weirstrass theorem, Concept of compactness, Heine Borel theorem. 

Real sequences, Limit and convergence of a sequence, Monotonic sequences, Cauchy’s sequences, Sub sequences and Cauchy’s general principle of convergence.

Properties of continuous functions on closed interval, Derivable functions: Derivative of composite function, Inverse function theorem, Limit and continuity of a function of two variables, Rolle’s and Darboux theorem.

Riemann Integration, Lower and upper Riemann integral, Properties of Riemann integration, Mean value theorem of integral calculus, Fundamental theorem of integral calculus.

Improper integrals: Kinds of improper integral, Tests of convergence of improper integrals and related problems.