# IIT JAM Maths Scholarship Test 2019 Syllabus

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IIT JAM Mathematics Scholarship Test 2019 Syllabus

Scholarship Test (MIM-SAT) Syllabus – IIT-JAM Mathematics 2018-19 Batch

Differential Calculus of one real Variable:

Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions; one-one, into and onto functions, composition of functions. Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, maxima and minima, Graphs.

Differential Calculus of Two Real Variables:

Limit, continuity, partial derivatives, maxima and minima.

Integral Calculus:

Integration as the inverse process of differentiation, definite integrals and their properties.

Sequences and Series of Real Numbers:

Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences.

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.

Differential Equations.

Differential Equations: Ordinary differential equations of the first order of the form y’=f(x,y), Bernoulli’s equation, exact differential equations, integrating factor, orthogonal trajectories, homogeneous differential equations, variable separable equations, linear differential equations of second order with constant coefficients.

Vector Calculus:

Scalar and vector fields, gradient, divergence, curl, line integrals.