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  #2  
5th December 2014, 11:43 AM
Super Moderator
 
Join Date: Apr 2013
Re: IIT JAM Mathematics Exam Study Material

Here I am providing the syllabus for the IIT JAM Mathematics Exam for your idea .

Sequences, Series and Differential Calculus: Sequences and Series of real numbers: 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.

Functions of one variable : mit, continuity, differentiation, Rolle’s Theorem, Mean value theorem. Taylor’s theorem. Maxima and minima.

Functions of two real variable : Limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler’s theorem.

Integral Calculus : Integration as the inverse process of differe ntiation, 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 pplications. Calculating volumes using triple integrals and applications.

Differential Equations : 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 Lapla cian. Scalar line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green’s, Stokes and Gauss theorems and their applications.

Group Theory : Groups, subgroups, Abelian groups, non – abelian groups, cyclic groups, per mutation groups; Normal subgroups, Lagrange’s Theorem for finite groups, group homomorphisms and basic concepts of quotient groups ( only group theory ).

Linear Algebra : 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 – Hami lton 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.

IIT JAM Mathematics Exam Books



  #3  
24th March 2015, 04:32 PM
Unregistered
Guest
 
Re: IIT JAM Mathematics Exam Study Material

Hi I have appeared for IIT JAM exam so provide me the study material of Mathematics of this exam?
  #4  
24th March 2015, 04:35 PM
Super Moderator
 
Join Date: Apr 2013
Re: IIT JAM Mathematics Exam Study Material

Ok, as you want the study material of Mathematics of IIT JAM exam so here I am providing you the syllabus and books for this exam.

IIT JAM Mathematics syllabus

Sequences, Series and Differential Calculus : Sequences and Series of real numbers : 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.

Functions of one variable : mit, continuity, differentiation, Rolle’s Theorem, Mean value theorem. Taylor’s theorem. Maxima and minima.

Functions of two real variable : Limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler’s theorem.

Integral Calculus : Integration as the inverse process of differe ntiation, 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 pplications. Calculating volumes using triple integrals and applications.

Differential Equations : 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 Lapla cian. Scalar line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green’s, Stokes and Gauss theorems and their applications.

Group Theory : Groups, subgroups, Abelian groups, non – abelian groups, cyclic groups, per mutation groups; Normal subgroups, Lagrange’s Theorem for finite groups, group homomorphisms and basic concepts of quotient groups ( only group theory ).

Linear Algebra : 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 – Hami lton 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.

IIT JAM Mathematics syllabus

IIT-JAM: M.Sc. Mathematics Joint Admission Test



IIT-JAM Joint Admission Test for M.Sc. Mathematics: Previous Years’ Papers (Solved), Practices Test Papers (Solved)


IIT-JAMM.Sc. (Mathematics) Previous


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