### 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 |