**COURSE DETAILS**

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.

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