IIT JAM Mathematics Syllabus 2013
IIT JAM Mathematics Syllabus 2013
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.
Linear differential equations of second order with constant coefficients. Euler – Cauchy equation. Method of variation of parameters.
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 homomorphisms 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. Eigenvalues and eigenvectors.
Real Analysis : Open and closed sets, limit points, completeness of R, Uniform convergence, Power series.
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