TEST SERIES SCHEDULE (CSIR-NET/JRF June-2024 ONLINE)
|
|
TEST TYPE
|
Modules
|
Date |
Syllabus
|
| MWT-01 |
Real Analysis I + Metric Space
|
10-May-24 |
Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum. Sequences and series, convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity,monotonic functions, types of discontinuity, uniform continuity, Metric spaces, compactness, connectedness.s.
|
| MWT-02 |
ODE + Markov chain |
12-May-24 |
Existence and uniqueness of solutions of initial value problems for first order ordinary differential equations, differential equation with constant and variable coefficient, singular solutions of first order ODEs, system of first order ODEs. General theory of homogenous and non-homogeneous linear ODEs, variation of parameters, Sturm-Liouville boundary value problem, Markov Chain
|
| MWT-03 |
Linear Algebra -1 |
15-05-24 |
system of linear equations,Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations, matrix representation of linear transformation, Algebra of matrices, rank and determinant of matrices,
|
| MWT-04 |
PDE+LPP |
18-May-24 |
Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs. Classification of second order PDEs, General solution of higher order PDEs with constant coefficients, Method of separation of variables for Laplace, Heat and Wave equations. LPP
|
| MWT-05 |
Real Analysis II +TOPOLOGY
|
21-May-24 |
differentiability, mean value theorem. Sequences and series of functions, uniform convergence. Riemann sums and Riemann integral, Improper Integrals. functions of bounded variation, Lebesgue measure, Lebesgue integral. Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems. Topology,
|
| MWT-06 |
I.E. +COV+NA |
24-May-24 |
Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels. Characteristic numbers and eigenfunctions, resolvent kernel, Variation of a functional, Euler-Lagrange equation, Necessary and sufficient conditions for extrema. Variational methods for boundary value problems in ordinary and partial differential equations, Mathematical Preliminaries and Errors , Solution of Algebraic and Transcendental Equation , Interpolation and Approximation, Ordinary Differntial equaiton -initial value problem , Differenation and integration, system of linar algebraic Equations and Eigenvalue Problems
|
| MWT-07 |
Linear Algebra II |
27-May-24 |
Eigenvalues and eigenvectors, Cayley-Hamilton theorem. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms. Inner product spaces, orthonormal basis. Quadratic forms, reduction and classification of quadratic forms
|
| MWT-08 |
COMPLEX ANALYSIS |
30-May-24 |
Algebra of complex numbers, the complex plane, polynomials, power series, transcendental functions such as exponential, trigonometric and hyperbolic functions. Analytic functions, Cauchy-Riemann equations. Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem. Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius transformations.
|
| MWT-09 |
MA + RT |
02-Jun-24 |
Permutations, combinations, Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem, Euler’s Ø- function, primitive roots. Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley’s theorem, class equations, Sylow theorems.Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain. Polynomial rings and irreducibility criteria. Fields, finite fields, field extensions,
|
| MWT-10 |
Pure |
05-Jun-24 |
RA+MA+LA+RT+CA+Functional analysis +Topology +Metric space |
| MWT-11 |
Applied mathematics |
08-jun-24 |
ODE+PDE+COV+I.E+NA+MARKOV CHAIN +LPP |
| FLT-01 |
Full Length Test |
11-Jun-24 |
As per Exam Pattern |
| FLT-02 |
Full Length Test |
14-Jun-24 |
As per Exam Pattern |
| FLT-03 |
Full Length Test |
17-Jun-24 |
As per Exam Pattern |
| FLT-04 |
Full Length Test |
20-Jun-24 |
As per Exam Pattern |
