Fourier series: Periodic and piecewise continuous function, Dirichlet’s conditions, Fourier series representation of function on intervals [-pi , pi], [0 ,pi] and on arbitrary intervals, Fourier series of odd and even function.

Sequence and series of function:Pointwise and uniform convergence,Cauchy criterion and Weirstrass M- Test (including proof), Abel’s and Dirichlet’s Test(Without proof),Uniform convergence and continuity, Term by term differentiation and integration.

Metric Space: Definition with examples, Bounded set, Open set, Closed sets, Neighbourhoods Boundary points and limit points, Exterior point, Closure of a set, Metric subspace.

Continuous mappings,Sequence in a metricspace, Cauchysequence, Subsequence, Completeness of metric space.

Separable space, Compact spaces and compact sets, Connected spaces and connected sets, Bolzano’s theorem, Product spaces.