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≈Graduate Aptitude Test in Engineering≈
(GATE)

Syllabus Mathematics Linear Algebra: Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Finite dimesnsional 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.

Introduction Eligibility Examination Pattern Subject Wise List of Exams. Question Paper Structure Syllabus GATE Score Tentative Schedule Important Dates Application Form Examination Centres Contacts Notification Result Forum

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 Legendre quadrature, 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.

GATE Discussion Percentile By Devendra  on : 25, Mar, 2008, 11:25:32 PM (IST) Show Details »» Gate By Parvati  on : 16, Jul, 2007, 1:09:48 PM (IST) Show Details »» plz reply By rakesh  on : 07, Jun, 2007, 11:58:01 AM (IST) Show Details »» plz help By rakesh  on : 07, Jun, 2007, 11:12:44 AM (IST) Show Details »» MS in Vehicle Dynamics By Sreenath  on : 10, May, 2007, 1:21:14 AM (IST) Show Details »» Post Your Query: More Topics               Goto: Engineering Forum  |  All Forums Please login first Close Username: Password :       Forgot Password | New User Add this page to your favorites Tell a friend Report Error on this page The contents are informative in nature. Candidates are advised to refer to the notice published on Official Websites or other sources and official notification of the exam conducting authority. You may use our interactive forums - Forum @ NNE to discuss all your queries and gather more information. Explore more of your favourite career option at Career Center For the Exact Notification/Examination Dates please visit: Exam Alert / Notification Sections To excel in Interviews, check out our Interview Tips To have customised career assistance, explore Career Shaper @ NNE National Network of Education strives to provide the latest, updated and correct information. Your participations will enhance our efforts. In case you have a suggestion or have spotted an error - please provide us your FEEDBACK.