ANALYSIS-II
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, Cauchy sequence, Subsequence, Completeness of metric space.
Separable space, Compact spaces and compact sets, Connected spaces and connected sets, Bolzano’s theorem, Product spaces.
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