Order completeness of Real numbers, 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,

Infinite series and their convergences – Comparison test, Cauchy’s nth root test, D’Alembert, Raabe’s ,Cauchy’s Test, Logarithmic test.

Alternating Series – Leibnitz Test , Absolute and conditional convergence, Properties of continious function and derivable functions.

 

Reimann  Integration , Lower and upper Reimann integrals, Properties of Reimann integration , Mean value theorem of Integral calculus , Fundamental theorem of integral calculus.

 

Uniform convergence , Sequence and series of function – pointwise and uniform convergence , Weirstrass M- Test, Abel’s and Drichlet’s Test for uniform convergence of series of functions . Continuity of the sum functions of the limit fuctions.