Higher Mathematics

IIT JAM Syllabus 2022 for Mathematics (MA) Sequences and Series of Real Numbers:  Sequence of real numbers, the convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibniz test for convergence of alternating series. Functions of One Real Variable:  Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, maxima, and minima.  Functions of Two or Three Real Variables:  Limit, continuity, partial derivatives, differentiability, maxima, and minima.  Integral Calculus:  Integration as the inverse process of differentiation, definite integrals, and their properties, fundamental theorem of calculus. Double and triple integrals, change of order of integra