Showing posts with label M.Tech.. Show all posts
Showing posts with label M.Tech.. Show all posts

Friday 13 September 2013

Graduate Aptitude Test in Engineering 2014 (GATE 2014) : Syllabus for Mathematics (MA)

GRADUATE APTITUDE TEST IN ENGINEERING (GATE 2014) : MATHEMATICS (MA) SYLLABUS



GATE 2014 : Mathematics(MA) Syllabus 

Linear Algebra : Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigen values and eigen vectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators.

Complex Analysis : Analytic functions, conformal mappings, bilinear transformations; complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle; Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.

Real Analysis : Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima; Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.

Ordinary Differential Equations : First order ordinary differential equations, existence and uniqueness theorems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients; method of Laplace transforms for solving ordinary differential equations, series solutions; Legendre and Bessel functions and their orthogonality.

Algebra : Normal subgroups and homomorphism theorems, automorphisms; Group actions, Sylow’s theorems and their applications; Euclidean domains, Principle ideal domains and unique factorization domains. Prime ideals and maximal ideals in commutative rings; Fields, finite fields.

Functional Analysis : Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.

Numerical Analysis : Numerical solution of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration; interpolation: error of polynomial interpolation, Lagrange, Newton interpolations; numerical differentiation; numerical integration: Trapezoidal and Simpson rules, Gauss Legendrequadrature, method of undetermined parameters; least square polynomial approximation; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); matrix eigenvalue problems: power method, numerical solution of ordinary differential equations: initial value problems: Taylor series methods, Euler’s method, Runge-Kutta methods.

Partial Differential Equations : Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave and diffusion equations in two variables; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.
Mechanics : Virtual work, Lagrange’s equations for holonomic systems, Hamiltonian equations.

Topology : Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.
Probability and Statistics : Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators, Testing of hypotheses, standard parametric tests based on normal, X2 , t, F – distributions; Linear regression; Interval estimation.

Linear programming : Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex 
method, big-M and two phase methods; infeasible and unbounded LPP’s, alternate optima; Dual problem and duality theorems, dual simplex method and its application in post optimality analysis; Balanced and unbalanced transportation problems, u -u method for solving transportation problems; Hungarian method for solving assignment problems.

Calculus of Variation and Integral Equations : Variation problems with fixed boundaries; sufficient conditions for extremum, linear integral equations of Fredholm and Volterra type, their iterative solutions.


Useful Links : GATE-2014

GATE 2014 : Eligibility
GATE 2014 : AEROSPACE ENGINEERING (AE) SYLLABUS
GATE 2014 : AGRICULTURAL ENGINEERING (AG)
GATE 2014 : Architecture and Planning (AR) Syllabus 
GATE 2014 : Bio-technology (BT) Syllabus 
GATE 2014 : Civil Engineering (CE) Syllabus 
GATE 2014 : Chemical Engineering (CH) Syllabus
GATE 2014 : Chemistry (CY) Syllabus
GATE 2014 : Computer Science and Information Technology (CS) Syllabus
GATE 2014 : Electrical Engineering (EE) Syllabus
GATE 2014 : Electronics and Communication Engineering (EC) Syllabus 
GATE 2014 (Graduate Aptitude Test in Engineering 2014) : Syllabus for Geology and Geophysics (GG)

Wednesday 3 April 2013

ADMISSIONS FOR MASTERS PROGRAM IN COMPUTATIONAL ENGINEERING 2013-14 in RAJEEV GANDHI UNIVERSITY OF KNOWLEDGE TECHNOLOGIES

ADMISSIONS FOR M.TECH. PROGRAM IN COMPUTATIONAL ENGINEERING 2013-14 in RAJEEV GANDHI UNIVERSITY OF KNOWLEDGE TECHNOLOGIES


Eligibility required
  • Qualified in GATE 2012 or 2013
  • B.Tech/B.E with a core branch such as (Civil / Computer Science / Chemical / Electrical / Electronics/ Mechanical/ Metallurgical-Materials)
Qualifications required
  • 60% or above marks in B.Tech/B.E, Intermediate and SSC
  • SC/ST candidates: 55% or above marks in B.Tech/B.E, Intermediate and SSC
  • Passing of seven weeks "Introductory course in computing" with "A" grade or 80% marks (Mandatory) conducted by RGUKT at its campuses Basar / Nuzvid / RK Valley.
Selection process
  1. GATE (2012, 2013) in order of merit followed by an INTERVIEW.
  2. Passing of "Introductory course in computing" with "A" grade or 80% marks (Mandatory) conducted by RGUKT for seven weeks and in order of merit.
  3. Prospective national Students having qualified in GATE from States other than A.P can also apply. Admissions of these candidates are subject to rules of Govt.of .A.P as in force treating them as Non-Local candidates under supernumerary.

Eligibility required
  • Qualified in GATE 2012 or 2013
  • B.Tech/B.E with a core branch such as (Civil / Computer Science / Chemical / Electrical / Electronics/ Mechanical/ Metallurgical-Materials)
Qualifications required
  • 60% or above marks in B.Tech/B.E, Intermediate and SSC
  • SC/ST candidates: 55% or above marks in B.Tech/B.E, Intermediate and SSC
  • Passing of seven weeks "Introductory course in computing" with "A" grade or 80% marks (Mandatory) conducted by RGUKT at its campuses Basar / Nuzvid / RK Valley.
Selection process
  1. GATE (2012, 2013) in order of merit followed by an INTERVIEW.
  2. Passing of "Introductory course in computing" with "A" grade or 80% marks (Mandatory) conducted by RGUKT for seven weeks and in order of merit.
  3. Prospective national Students having qualified in GATE from States other than A.P can also apply. Admissions of these candidates are subject to rules of Govt.of .A.P as in force treating them as Non-Local candidates under supernumerary.

locatins : basara (adilabad district), Nuzvid (krishna district), RK valley (kadapa district)

last date : 30 th apr'2013

apply online : http://www.rgukt.in/