simply2know

TEST PAPER: MATHEMATICS MA   Real Analysis:   Sequences and Series of Real Numbers: convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, tests of convergence for series – comparison test, ratio test, root test; Power series (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series.   Functions of One Real Variable : limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, Taylor’s series, maxima and minima, Riemann integration (definite integrals and their properties), fundamental theorem of calculus.   Multivariable Calculus and Differential Equations:   Functions of Two or Three Real Variables: limit, continuity, partial derivatives, total derivative, maxima and minima. Integral Calculus: double and triple integrals, change of orde...