IIT JAM 2019 Syllabus for Mathematics

IIT JAM 2019 – In engineering, science & technology and research in frontier areas, for quality education, IITs and IISc are institutions of national importance and are well known all over the world. In order to pursue Research and Development careers in frontier areas of basic sciences as well as interdisciplinary areas of science and technology, the vibrant academic ambience and well-equipped research infrastructure of IISc & IITs motivate the students. In an intellectually stimulating environment, the aim of IITs and IISc is to build a sound foundation of knowledge, pursue excellence and enhance creativity.

IIT JAM – Admissions

To M.Sc. (Four Semesters), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, etc, to provide admissions Joint Admission Test for M.Sc. (JAM) is being conducted from 2004. At the IITs and Integrated PhD Degree Programmes, for bright students, programmes at IISc for consolidating Science as a career option are being conducted.

At IITs and IISc, in their respective disciplines, comparable to the best in the world, these postgraduate programmes offer high-quality education. To provide opportunities to the students, the curricula for these programmes are designed apart from developing academic talent leading to a challenging and rewarding professional life.

Syllabus of Chemistry – IIT JAM 2019

Sequences and Series of Real Numbers

Cauchy sequences, subsequences, Bolzano-Weierstrass theorem; Series of real numbers, absolute convergence, tests of convergence for series of positive terms; Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers,– comparison test, ratio test, root test; Leibniz test for convergence of alternating series;

Functions of One Real Variable

Differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, limit, continuity, intermediate value property, Taylor’s theorem, maxima and minima;

Functions of Two or Three Real Variables

Differentiability, maxima Limit, continuity, partial derivatives, and minima;

Integral Calculus

Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals; Integration as the inverse process of differentiation, definite integrals and their properties, fundamental theorem of calculus;  calculating volumes using triple integrals;

Differential Equations

Homogeneous differential equations, variable separable equations, linear differential equations of second order with constant coefficients, Ordinary differential equations of the first order of the form y’=f(x,y), Bernoulli’s equation, exact differential equations, integrating factor, orthogonal trajectories, a method of variation of parameters, Cauchy-Euler equation;

Vector Calculus

Gradient, divergence, curl, line integrals, surface integrals, Scalar and vector fields, Green, Stokes and Gauss theorems;

Group Theory

Permutation groups, normal subgroups, Lagrange’s Theorem for finite groups, groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, group homomorphisms and basic concepts of quotient groups;

Linear Algebra

Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions,  Finite dimensional vector spaces, linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. Eigen-values and eigenvectors for matrices, Cayley-Hamilton theorem;

Real Analysis

Compact sets, completeness of R. Power series (of a real variable), Taylor’s series Interior points, limit points, open sets, closed sets, bounded sets, connected sets, radius and interval of convergence, term-wise differentiation and integration of power series;

Reference books for Mathematics- IIT JAM 2019

  • Mathematical Analysis by S.C. Malik
  • Mathematical Analysis by Apostol
  • The principle of Mathematical Analysis by Rudi
  • Mathematical Analysis by H.C. Malik
  • Calculus by Thomas & Finny
  • Integral Calculus by Gorakh Prasad
  • Geometry & Vectors by Vasishtha
  • Calculus by Thomas & Finny
  • Ordinary Differential Equations by Earl.A.Coddington
  • Elementary Differential Equations and Boundary Value Problems by Boyce-Diprima
  • Ordinary Differential Equation by Peter J. Collins,  G.F. Simmons, M.D. Raisinghania
  • Real Analysis by H. L. Royden
  • Scaum’s Series
    Gilbert Strang – Linear Algebra & its applications
    Modern Algebra – A.R. Vasishtha
    University Algebra – N.S. Gopalakrishnan

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