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IIT-JAM Syllabus And Reference Book

IIT-JAM Syllabus is distributed into 9 Modules as Follows

  • Real Analysis:
  • Sequences and Series of Real Numbers:
  • Functions of One Real Variable:
  • Functions of Two or Three Real Variables:
  • Integral Calculus:
  • Differential Equations:
  • Vector Calculus:
  • Group Theory:
  • Linear Algebra:

Real Analysis

  • Interior points, limit points, open sets, closed sets,
  • Bounded sets, connected sets, compact sets, completeness of R.
  • Power series (of real variable),Taylor’s series,
  • Radius and interval of convergence, term-wise differentiation and integration of power series.

Sequences and Series of Real Numbers:

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

Functions of One Real Variable

  • Limit of functions,
  • Continuity of functions,
  • Differentiation of functions,
  • Intermediate value property,
  • Rolle’s Theorem, mean value theorem,
  • L'Hospital rule, Taylor's theorem,
  • Maxima and Minima.

Functions of Two or Three Real Variables

  • Limit of functions,
  • Continuity of functions,
  • Partial derivatives of functions,
  • Differentiability of functions,
  • Maxima and Minima of functions

Integral Calculus

  • Integration as the inverse process of differentiation,
  • Definite integrals and their properties,
  • Fundamental theorem of calculus.
  • Double and triple integrals,
  • Change of order of integration,
  • Calculating surface areas and volumes using double integrals,
  • calculating volumes using triple integrals.

Differential Equations

  • Ordinary differential equations of the first order of the formy'=f(x,y),
  • Exact differential equations,
  • Integrating factor, orthogonal trajectories,
  • homogeneous differential equations,
  • Variable separable equations,
  • Bernoulli’s equation,
  • Linear differential equations of second order with constant coefficients,
  • Method of variation of parameters,
  • Cauchy-Euler equation.

Vector Calculus

  • Scalar and vector fields,
  • Gradient,
  • Divergence,
  • Curl,
  • line integrals,
  • Surface integrals,
  • Green, Stokes and Gauss theorems.

Group Theory

  • Groups,
  • Subgroups,
  • Abelian groups,
  • Non-Abelian groups,
  • cyclic groups,
  • Permutation groups,
  • Normal subgroups,
  • Lagrange's Theorem for finite groups,
  • Group homomorphisms and
  • Basic concepts of quotient groups.

Linear Algebra

  • Finite dimensional vector spaces,
  • Linear independence of vectors,
  • Basis, dimension,
  • Linear transformations,
  • Matrix representation,
  • Range space, Nullspace, rank-nullity theorem.
  • Rank and inverse of a matrix, determinant,
  • Solutions of systems of linear equations, consistency conditions,
  • Eigen values and eigenvectors for matrices,
  • Cayley-Hamilton theorem.

Real Analysis:

Reference Book

Book Name Book By
Introduction to Real Analysis Sadhan Kumar Mapa
Mathematical Analysis S.C. Malik and Savitha Arora

Sequences and Series of Real Numbers:

Reference Book

Book Name Book By
Introduction to Real Analysis Sadhan Kumar Mapa
Introduction to Real Analysis Donald R. Sherbert and Robert G. Bartle
Principles of Real Analysis S.L. Gupta ,N.R.Gupta

Functions of One Real Variable:

Reference Book

Book Name Book By
Introduction to Real Analysis Donald R. Sherbert and Robert G. Bartle
Introduction to Real Analysis Sadhan Kumar Mapa
Principles of Real Analysis S.L. Gupta ,N.R.Gupta

Functions of Two or Three Real Variables:

Reference Book

Book Name Book By
Functions of Several Variables Wendell Fleming
The Calculus of Functions of Several Variables Dan Sloughter
Functions of Several Variables Martin A. Moskowitz, Fotios Paliogiannis

Integral Calculus:

Reference Book

Book Name Book By
Integral Calculus For Beginners Joseph Edwards
Integral Calculus William Elwood Byerly
Integral Calculus Shanti Narayan

Differential Equations:

Reference Book

Book Name Book By
Ordinary differential equations Earl A. Coddington
Differential Equations Shepley L. Ross

Vector Calculus:

Reference Book

Book Name Book By
Vector Calculus Paul C. Matthews
Vector Calculus Shanti Narayan
Golden Vector Calculus R. Gupta

Group Theory:

Reference Book

Book Name Book By
Contemporary Abstract Algebra Joseph A. Gallian
A Course in Abstract Algebra, V.K. Khanna & S.K Bhamri
Abstract Algebra David S. Dummit, Richard M. Foote

Linear Algebra:

Reference Book

Book Name Book By
Linear Algebra Vivek Sahai, Vikas Bist
Linear Algebra Arnold J. Insel, Lawrence E. Spence, and Stephen H. Friedberg
Matrices and Linear Algebra George Phillip Barker and Hans Schneider
Linear Algebra Seymour Lipschutz and, Marc Lipson

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