# IIT- JAM

# IIT-JAM MATHEMATICS COACHING

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## Subject Wise Marks Distribution In IIT-JAM Mathematics – 2016

## TOPICS – MARKS

Linear Algebra – 14 Marks

Real Analysis – 18 Marks

Abstract Algebra – 10 Marks

Calculus of single variable -17 Marks

Calculus of tow variables – 18 Marks

Vector Calculus – 12 Marks

Differential Equations – 11 Marks

#### SYLLABUS FOR IIT- JAM

BEST IIT-JAM MATHS COACHING IN CHANDIGARH

**SEQUENCES AND SERIES OF REAL NUMBERS:**

Sequences and series of real numbers, Convergent and divergent sequences, bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences.

**SETS RELATIONS, FUNCTIONS, AND GRAPHS:**

Functions of One Variable, limit, continuity, differentiation, Rolle’s Theorem, Mean value theorem.Taylor’s theorem. Maxima and minima.

**FUNCTIONS OF TWO REAL VARIABLES:**

Limit, continuity, partial derivatives, differentiability, maxima and minima.

**INTEGRAL CALCULUS:**

Integration as the inverse process of differentiation, definite integrals, nd their properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and applications. Calculating volumes using triple integrals and applications.

**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-separable solutions.

**VECTOR CALCULUS:**

Scalar and vector fields, gradient, divergence, curl and Laplacian.

**GROUP THEORY:**

Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups; Normal subgroups, Lagrange’s Theorem for finite groups.

**LINEAR ALGEBRA:**

Vector spaces, Linear dependence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, Range space, and null space,rank-nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions.

**REAL ANALYSIS:**

Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets.