What is the syllabus of PUCAT mathematics Real Analysis section?

<p>Candidates can check the space below to know about the syllabus of PUCAT mathematics Real Analysis section:<br>Sequences and series of real numbers. Convergent and divergent sequences, bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy&nbsp;sequences, absolute and conditional convergence; Tests of convergence for series of positive termscomparison test, ratio test, root test, Leibnitz test for convergence of alternating series. Functions of one variable: limit, continuity, differentiation, Rolle's Theorem, Cauchy&rsquo;s Taylor's theorem. Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor's and Maclaurin's, domainof convergence, &nbsp;term-wise differentiation and integration of power series. Functions of two real variable: limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler's theorem.</p>

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