{"id":125,"date":"2012-09-08T21:01:28","date_gmt":"2012-09-08T15:31:28","guid":{"rendered":"http:\/\/eduetc.com\/edu\/?p=125"},"modified":"2013-09-04T20:16:43","modified_gmt":"2013-09-04T14:46:43","slug":"gate-2013-syllabus-for-mathematics","status":"publish","type":"post","link":"https:\/\/eduetc.com\/edu\/gate-2013-syllabus-for-mathematics\/","title":{"rendered":"GATE 2013 Syllabus for Mathematics"},"content":{"rendered":"

GATE 2013\u00a0Syllabus\u00a0for Mathematics<\/strong><\/p>\n

Download\u00a0GATE 2013\u00a0Syllabus\u00a0for Mathematics<\/p>\n

Linear Algebra:<\/strong>\u00a0Finite dimensional vector spaces; Linear\u00a0transformations\u00a0and their matrix representations, rank; systems of linear\u00a0equations, 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.<\/p>\n

Complex Analysis:<\/strong>\u00a0Analytic functions, conformal mappings, bilinear\u00a0transformations; complex integration: Cauchy\u2019s integral\u00a0theorem\u00a0and formula; Liouville\u2019s\u00a0theorem, maximum modulus principle; Taylor and Laurent\u2019s series; residuetheorem\u00a0and\u00a0applications\u00a0for evaluating real integrals.<\/p>\n

Real Analysis:<\/strong>\u00a0Sequences and series of functions, uniform convergence, power series,\u00a0Fourier series, functions of several variables,\u00a0maxima, minima; Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, completeness, Weierstrass approximation\u00a0theorem, compactness; Lebesgue measure, measurable functions; Lebesgue integral, Fatou\u2019s lemma, dominated convergencetheorem.<\/p>\n

Ordinary Differential\u00a0Equations:<\/strong>\u00a0First order\u00a0ordinary differential\u00a0equations, existence and uniqueness theorems, systems of linear first order\u00a0ordinary differential\u00a0equations, linear\u00a0ordinary differential\u00a0equations\u00a0of higher order with constant coefficients; linear second order ordinary differentialequations\u00a0with variable coefficients;\u00a0method\u00a0of Laplace transforms for solving\u00a0ordinary differential\u00a0equations, series solutions; Legendre and Bessel functions and their orthogonality.<\/p>\n

Algebra:<\/strong>\u00a0Normal subgroups and homomorphism theorems, automorphisms; Group actions, Sylow\u2019s theorems and theirapplications; Euclidean\u00a0domains, Principle ideal\u00a0domains\u00a0and unique factorization\u00a0domains. Prime ideals and maximal ideals in commutative rings; Fields, finite fields.<\/p>\n

Functional Analysis:<\/strong>\u00a0Banach spaces, Hahn-Banach\u00a0extension\u00a0theorem, open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal bases, Riesz representation\u00a0theorem, bounded linear operators.<\/p>\n

Numerical Analysis:<\/strong>\u00a0Numerical solution\u00a0of algebraic and transcendental\u00a0equations: 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;\u00a0numerical solution\u00a0of systems of linearequations: direct\u00a0methods\u00a0(Gauss elimination, LUdecomposition); iterative methods (Jacobi and Gauss-Seidel); matrix eigenvalue problems: power method,\u00a0numerical solution\u00a0of\u00a0ordinary differential\u00a0equations: initial value problems: Taylor series methods, Euler\u2019s method, Runge-Kutta methods.<\/p>\n

Partial\u00a0Differential\u00a0Equations:<\/strong>\u00a0Linear and quasilinear first order partial\u00a0differential\u00a0equations, method of characteristics; second order linear\u00a0equations\u00a0in two variables and their classification; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave and diffusion\u00a0equations\u00a0in two variables;\u00a0Fourier series\u00a0and Fourier transform and\u00a0Laplace transform\u00a0methods of solutions for the above\u00a0equations.<\/p>\n

Mechanics:<\/strong>\u00a0Virtual\u00a0work, Lagrange\u2019s\u00a0equations\u00a0for holonomic systems, Hamiltonian\u00a0equations.<\/p>\n

Topology:<\/strong>\u00a0Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn\u2019s Lemma.<\/p>\n

Probability and Statistics:<\/strong>\u00a0Probability space, conditional probability, Bayes\u00a0theorem, independence, Random variables, joint and conditional distributions, standardprobability distributions\u00a0and their properties, expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit\u00a0theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators, Testing of hypotheses, standard parametric tests based on normal, X2 , t, F \u2013 distributions;\u00a0Linear regression; Interval estimation.<\/p>\n

Linear programming:<\/strong>\u00a0Linear 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\u2019s, alternate optima; Dual problem and duality theorems, dual simplex method and its\u00a0application\u00a0in post optimality analysis; Balanced and unbalanced\u00a0transportation\u00a0problems, u -u method for solving transportation problems; Hungarian method for solving\u00a0assignment\u00a0problems.<\/p>\n

Calculus of Variation and Integral\u00a0Equations:\u00a0<\/strong>Variation problems with fixed boundaries; sufficient conditions for extremum, linear integral\u00a0equations\u00a0of Fredholm and Volterra type, their iterative solutions.<\/p>\n

GATE 2013\u00a0Syllabus\u00a0for Mathematics<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

GATE 2013\u00a0Syllabus\u00a0for Mathematics Download\u00a0GATE 2013\u00a0Syllabus\u00a0for Mathematics Linear Algebra:\u00a0Finite dimensional vector spaces; Linear\u00a0transformations\u00a0and their matrix representations, rank; systems of linear\u00a0equations, 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:\u00a0Analytic functions, conformal mappings, bilinear\u00a0transformations; complex integration: Cauchy\u2019s integral\u00a0theorem\u00a0and formula; […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27],"tags":[336,38],"class_list":["post-125","post","type-post","status-publish","format-standard","hentry","category-gate","tag-gate","tag-gate-2013-syllabus-for-mathematics"],"_links":{"self":[{"href":"https:\/\/eduetc.com\/edu\/wp-json\/wp\/v2\/posts\/125","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eduetc.com\/edu\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/eduetc.com\/edu\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/eduetc.com\/edu\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/eduetc.com\/edu\/wp-json\/wp\/v2\/comments?post=125"}],"version-history":[{"count":4,"href":"https:\/\/eduetc.com\/edu\/wp-json\/wp\/v2\/posts\/125\/revisions"}],"predecessor-version":[{"id":1006,"href":"https:\/\/eduetc.com\/edu\/wp-json\/wp\/v2\/posts\/125\/revisions\/1006"}],"wp:attachment":[{"href":"https:\/\/eduetc.com\/edu\/wp-json\/wp\/v2\/media?parent=125"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eduetc.com\/edu\/wp-json\/wp\/v2\/categories?post=125"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eduetc.com\/edu\/wp-json\/wp\/v2\/tags?post=125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}