Test Series Schedule

CSIR-NET TEST SERIES DEC-2024 SCHEDULE

TEST TYPE

Modules

DATE

Syllabus

MWT-01

Real Analysis: I

23-Dec-24

Sequences and Series of Real Numbers: convergence of sequences, bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, tests of convergence for series – comparison test, ratio test, root test; Power series (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series.   : limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule,

MWT-02

ODE

26-Dec-24

 Differential Equations: Bernoulli’s equation, exact differential equations, integrating factors, orthogonal
trajectories, homogeneous differential equations, method of separation of variables, linear differential
equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler
equation.

MWT-03

Group Theory

29-Dec-24

Groups: cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups,
quotient groups, Lagrange's theorem for finite groups, group homomorphisms.

MWT-04

Integral Calculus

01-Jan-25

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. 

MWT-05

Linear Algebra

04-Jan-25

Finite Dimensional Vector Spaces: linear independence of vectors, basis, dimension, linear
transformations, matrix representation, range space, null space, rank-nullity theorem.

MWT-06

Real Analysis: II

7-Jan-25

Taylor's theorem, Taylor’s series, maxima and minima,
Riemann integration (definite integrals and their properties), fundamental theorem of calculus.  Functions of Two or Three Real Variables: limit, continuity, partial derivatives, total derivative, maxima
and minima. radius
and interval of convergence, term-wise differentiation and integration of power series.  Multivariable Calculus & Differential Equations: Functions of Two or Three Real Variabels: Limit, continuity, partial derivatives, maxima and minma.

MWT-07

ODE + IC

10-Jan-25

 Differential Equations: Bernoulli’s equation, exact differential equations, integrating factors, orthogonal
trajectories, homogeneous differential equations, method of separation of variables, linear differential
equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler
equation. ;   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. 

MWT-08

Group Theory + Linear Algebra

13-Jan-25

Matrices: systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant,
eigenvalues, eigenvectors.
Finite Dimensional Vector Spaces: linear independence of vectors, basis, dimension, linear
transformations, matrix representation, range space, null space, rank-nullity theorem.
Groups: cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups,
quotient groups, Lagrange's theorem for finite groups, group homomorphisms.

FLT-01

Full Length Test

16-Jan-25

As per Exam Pattern

FLT-02

Full Length Test

19-Jan-25

As per Exam Pattern

FLT-03

Full Length Test

22-Jan-25

As per Exam Pattern

FLT-04

Full Length Test

25-Jan-25

As per Exam Pattern

TEST TYPE

Modules

DATE

Syllabus

MWT-01

Real Analysis

28-Dec-24

Sequences and series of functions, uniform convergence, Ascoli-Arzela theorem; Weierstrass approximation theorem; contraction mapping principle, Power series; Differentiation of functions of several variables, Inverse and Implicit function theorems; Lebesgue measure on the real line, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem. Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers;

MWT-02

PDE

30-Dec-24

Method of characteristics for first order linear and quasilinear partial differential equations; Second order partial differential equations in two independent variables: classification and canonical forms, method of separation of variables for Laplace equation in Cartesian and polar coordinates, heat and wave equations in one space variable; Wave equation: Cauchy problem and d'Alembert formula, domains of dependence and influence, nonhomogeneous wave equation; Heat equation: Cauchy problem; Laplace and Fourier transform methods.

MWT-03

Group theory + Ring Theory

01-Jan-25

Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups, Group action, Sylow’s theorems and their applications;
Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions, algebraic extensions, algebraically closed fields

MWT-04

ODE

03-Jan-25

First order ordinary differential equations, existence and uniqueness theorems for initial value problems, linear ordinary differential equations of higher order with constant coefficients; Second order linear ordinary differential equations with variable coefficients; Cauchy-Euler equation, method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties; Systems of linear first order ordinary differential equations, Sturm's oscillation and separation theorems, Sturm-Liouville eigenvalue problems, Planar autonomous systems of ordinary differential equations: Stability of stationary points for linear systems with constant coefficients, Linearized stability, Lyapunov functions.

MWT-05

Complex Analysis

05-Jan-25

 Functions of a complex variable: continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle, Morera’s theorem; zeros and singularities; Power series, radius of convergence, Taylor’s series and Laurent’s series; Residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations.

MWT-06

Integral Calculus

07-Jan-25

Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications to area, volume and surface area;

MWT-07

Linear Agebra

09-Jan-25

Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, minimal polynomial, Cayley-Hamilton Theorem, Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric, Hermitian, skew-Hermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms.

MWT-08

LPP

11-Jan-25

Linear programming models, convex sets, extreme points; Basic feasible solution, graphical method, simplex method, two phase methods, revised simplex method ; Infeasible and unbounded linear programming models, alternate optima; Duality theory, weak duality and strong duality; Balanced and unbalanced transportation problems, Initial basic feasible solution of balanced transportation problems (least cost method, north-west corner rule, Vogel’s approximation method); Optimal solution, modified distribution method; Solving assignment problems, Hungarian method.

MWT-09

Topology + Functional+ Metric Space 

13-Jan-25

Normed linear spaces, Banach spaces, Hahn-Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, projection theorem, Riesz representation theorem, spectral theorem for compact self-adjoint operators.
Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, quotient topology, metric topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.
Metric spaces, connectedness, compactness, completeness;

MWT-10

Vector Calculus

15-Jan-25

Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.

MWT-11

Numerical Analysis

17-Jan-25

Systems of linear equations: Direct methods (Gaussian elimination, LU decomposition, Cholesky factorization), Iterative methods (Gauss-Seidel and Jacobi) and their convergence for diagonally dominant coefficient matrices; Numerical solutions of nonlinear equations: bisection method, secant method, Newton-Raphson method, fixed point iteration; Interpolation: Lagrange and Newton forms of interpolating polynomial, Error in polynomial interpolation of a function; Numerical differentiation and error, Numerical integration: Trapezoidal and Simpson rules, Newton-Cotes integration formulas, composite rules, mathematical errors involved in numerical integration formulae; Numerical solution of initial value problems for ordinary differential equations: Methods of Euler, Runge-Kutta method of order 2

FLT-01

Full Length Test

20-Jan-25

As per Exam Pattern

FLT-02

Full Length Test

23-Jan-25

As per Exam Pattern

FLT-03

Full Length Test

27-Jan-25

As per Exam Pattern

IIT-JAM STATISTICS TEST SERIES SCHEDULE 2025