IIT JAM 2010 Mathematics Syllabus
Sequences, Series and Differential Calculus : Sequences of real numbers. Convergent sequences and series, absolute and conditional convergence. Mean value theorem. Taylor 's theorem.
Maxima and minima of functions of a single variable. Functions of two and three variables.Partial derivatives, maxima and minima.
Integral Calculus : Integration, Fundamental theorem of calculus. Double and Triple, integrals, Surface areas and volumes.
Differential Equations : Ordinary differential equations of the first order of the form y'=f(x,y).
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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. Algebra: Groups, subgroups and normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and basic concepts of quotient groups, rings, ideals, quotient rings and fields. Linear Algebra: Systems of linear equations. Matrices, rank, determinant, inverse. Eigenvalues and eigenvectors. Finite Dimensional Vector Spaces over Real and Complex Numbers, Basis, Dimension, Linear Transformations. Real Analysis: Open and closed sets, limit points, completeness of R, Uniform Continuity, Uniform convergence, Power series. Mathematics Syllabus for IIT JAM 2010 |
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