JAM 2012 Exam Syllabus - MA (Mathematics)

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Syllabus: Joint Admission Test For M.Sc. 2012

Mathematics (MA)

Sequences, Series and Differential Calculus: Sequences of real numbers. Convergent sequences and series, absolute and conditional convergence. Rolle’s Theorem, Mean value theorem. Taylor's theorem. Maxima and minima of functions of a single variable. Functions of two and three variables. Limit, Continuity, Partial derivatives, differentiability, maxima and minima.

Integral Calculus: Double and triple integrals, Areas, Volumes, and Surface areas.

Differential Equations: Ordinary differential equations of the first order of the form y'=f(x,y). Linear differential equations of second and higher order with constant coefficients. Cauchy- Euler equation.

Vector Calculus: Gradient, divergence, curl and Laplacian. Green's, Stokes and Gauss theorems and their applications.

Group Theory: Groups, subgroups and normal subgroups, Lagrange's Theorem for finite groups, group homeomorphisms and basic concepts of quotient groups.

Linear Algebra: Vector spaces, Linear dependence of vectors, basis, dimension, linear transformations and matrix representation with respect to an ordered basis, rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigen values and eigenvectors.

Real Analysis: Open and closed sets, limit points, completeness of R, Uniform convergence, Power series.

Courtesy: iitb.ac.in