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1. Algebra : Elements of Set Theory; Algebra of Real and Complex Paper-I Section-A LinearAlgebra Vector, space, linear dependance and independance, subspaces, bases, dimensions. Finite dimensional vector spaces. Matrices, Cayley-Hamiliton theorem, eigenvalues and eigenvectors, matrix of linear transformation, row and column reduction, Echelon form, eqivalence, congruences and similarity, reduction to cannonical form, rank, orthogonal, symmetrical, skew symmetrical, unitary, hermitian, skewhermitian forms their eigenvalues. Orthogonal and unitary reduction of quadratic and hermitian forms, positive definite quardratic forms. Calculus Real numbers, limits, continuity, differerentiability, mean-value theorems, Taylors theorem with remainders, indeterminate forms, maximas and minima, asymptotes. Functions of several variables: continuity, differentiability, partial derivatives, maxima and minima, Lagranges method of multipliers, Jacobian. Riemanns definition of definite integrals, indefinite integrals, infinite and improper intergrals, beta and gamma functions. Double and triple integrals (evaluation techniques only). Areas, surface and volumes, centre of gravity. AnalyticGeometry : Cartesian and polar coordinates in two and three dimesnions, second degree equations in two and three dimensions, reduction to cannonical forms, straight lines, shortest distance between two skew lines, plane, sphere, cone, cylinder., paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties. Section-B OrdinaryDifferentialEquations : Formulation of differential equations, order and degree, equations of first order and first degree, integrating factor, equations of first order but not of first degree, Clariauts equation, singular solution. Higher order linear equations, with constant coefficients, complementary function and particular integral, general solution, Euler-Cauchy equation. Second order linear equations with variable coefficients, determination of complete solution when one solution is known, method of variation of parameters. Dynamics,StaticsandHydrostatics: Degree of freedom and constraints, rectilinear motion, simple harmonic

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