#1
September 8th, 2016, 10:13 AM
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Jam Exam Syllabus Mathematics
Hii sir, I am Preparing for the IIT JAM Examination Will you please provide me the syllabus of the Mathematics of the IIT JAM Examination
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#2
September 8th, 2016, 11:07 AM
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Re: Jam Exam Syllabus Mathematics
Indian Institutes of Technology, Delhi conducts the Joint Admission Test for M.Sc. (JAM ) for admission to Integrated Ph.D. Degree Programmes at IISc Bangalore and M.Sc. (Two Years), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, M.Sc.-M.Tech., M.Sc.-M.S.(Research)/Ph.D. Dual Degree and other Post-Bachelor Degree Programmes at IITs the Syllabus of the Mathematics Section of the IIT JAM Examination is given below Mathematics Syllabus Sequences and Series of Real Numbers Convergent and divergent sequences Bounded and monotone sequences Convergence criteria for sequences of real numbers Cauchy sequences Absolute and conditional convergence Tests of convergence for series of positive terms – comparison test Ratio test Root test Leibnitz test for convergence of alternating series Limit Continuity Differentiation Rolle’s Theorem Mean value theorem Taylor’s theorem Maxima and minima Partial Derivatives Differentiability Maxima and minima Method of Lagrange multipliers Homogeneous functions including Euler’s theorem Integration as the inverse process of differentiation Definite integrals and 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 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 Linear differential equations of second and higher order with constant coefficients Method of variation of parameters Cauchy-Euler equation Vector Calculus Scalar and vector fields Gradient Divergence Curl and Laplacian Scalar line integrals and vector line integrals Scalar surface integrals and vector surface integrals Green’s Stokes and Gauss theorems and their applications Groups Subgroups Abelian groups Non-abelian groups Cyclic groups Permutation groups Normal subgroups Lagrange’s Theorem for finite groups Group homomorphism’s and basic concepts of quotient groups (only group theory) 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 Eigenvalues and eigenvectors Cayley-Hamilton theorem Symmetric Skew-symmetric Hermitian Skew-hermitian Orthogonal and unitary matrices Real Analysis: Interior points Limit points Open sets Closed sets Bounded sets Connected sets Compact sets Completeness of R Power series (of real variable) including Taylor’s and Maclaurin’s Domain of convergence Term-wise differentiation and integration of power series. |