Krishna's - Analysis

Note: Five questions are to be attempted selecting at least one from each section.
(A) Complex analysis (Four questions)
Complex number and its representation in the Argand plane, Function of a complex
variables, Analytic functions, Complex integration, Cauchy's theorem, Cauchy's
integral formula, Taylor's theorem, Laurent's theorem, Liovilles theorem, poles and
essential singularities, Residues, Cauchy's integral theorem and its application in the
evaluation of integrals.
(B) Real analysis (Six questions)
Continuity of functions, Properties of continuous functions, Types of discontinuities,
Uniform continuity, Differentiability Taylor's theorem with various forms of
remainders, Riemann integral- definition and properties, Condition of integrability,
Convergence and uniform convergence of integrals.
Points wise convergence, Uniform convergence, Tests of uniform convergence
continuity and uniform convergence.