Engineering Entrance Exam : GATE : GATE Mathematics Syllabus 2017

GATE Mathematics Syllabus 2017

GATE 2016 Online Mock Test / Free Trial -

GATE 2017 Mathematics ( MA ) Syllabus

Section 1 : Linear Algebra

Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley – Hamilton Theorem, diagonalization, Jordan – canonical form, Hermitian, SkewHermitian and unitary matrices; Finite dimensional inner product spaces, Gram – Schmidt orthonormalization process, self – adjoint operators, definite forms.

Section 2 : Complex Analysis

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

Section 3 : 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, compactness, completeness, Weierstrass approximation theorem; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.

Section 4 : Ordinary Differential Equations

First order ordinary differential equations, existence and uniqueness theorems for initial value problems, 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 ( power series, Frobenius method ); Legendre and Bessel functions and their orthogonal properties.

Section 5 : Algebra

Groups, subgroups, normal subgroups, quotient groups and homomorphism theorems, automorphisms; cyclic groups and permutation groups, Sylow’s theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings and irreducibility criteria; Fields, finite fields, field extensions.

Section 6 : Functional Analysis

Normed linear spaces, Banach spaces, Hahn – Banach extension theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner – product spaces, Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.

Section 7 : 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; numerical solution of systems of linear equations: direct methods ( Gauss elimination, LU decomposition ); iterative methods ( Jacobi and Gauss – Seidel ); numerical solution of ordinary differential equations : initial value problems : Euler’s method, Runge – Kutta methods of order 2.

Section 8 : 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 in two dimensional Cartesian coordinates, Interior and exterior Dirichlet problems in polar coordinates; Separation of variables method for solving wave and diffusion equations in one space variable; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.

Section 9 : Topology

Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.

Section 10 : Probability and Statistics

Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties ( Discrete uniform, Binomial, Poisson, Geometric, Negative binomial, Normal, Exponential, Gamma, Continuous uniform, Bivariate normal, Multinomial ), expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators; Interval estimation; Testing of hypotheses, standard parametric tests based on normal X2, t, F distributions; Simple linear regression.

Section 11 : 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, Vogel’s approximation method for solving transportation problems; Hungarian method for solving assignment problems.

TAGS: , , , , , ,

GATE 2017 Navigation : GATE Ecology and Evolution Syllabus 2017, GATE Syllabus 2017, GATE Textile Engineering and Fibre Science Syllabus 2017, GATE Zoology Syllabus 2017, GATE Microbiology Syllabus 2017, GATE Production and Industrial Engineering Syllabus 2017, GATE Botany Syllabus 2017, GATE Physics Syllabus 2017, GATE Biochemistry Syllabus 2017, GATE Metallurgical Engineering Syllabus 2017, GATE Chemistry Syllabus 2017, GATE Mining Engineering Syllabus 2017, GATE Food Technology Syllabus 2017, GATE Mechanical Engineering Syllabus 2017, GATE Polymer Science and Engineering Syllabus 2017, GATE Thermodynamics Syllabus 2017, GATE Mathematics Syllabus 2017, GATE Solid Mechanics Syllabus 2017, GATE Instrumentation Engineering Syllabus 2017, GATE Materials Science Syllabus 2017, GATE Geology and Geophysics Syllabus 2017, GATE Electrical Engineering Syllabus 2017, GATE Electronics and Communication Engineering Syllabus 2017, GATE 2016 State Codes, GATE 2016 Discipline Codes,

GATE Related : GATE 2017 Mathematics Syllabus Details, GATE 2017 Syllabus, Maths Syllabus of GATE 2017, GATE Mathematics Syllabus 2017, GATE 2017 Entrance Exam Syllabus, GATE 2017 Syllabus Download, GATE 2017 Engineering Syllabus, GATE Mathematics Syllabus Download 2017, GATE 2017 Mathematics Syllabus Material, GATE 2017 Syllabus Detail, GATE 2017 Mathematics Study Material, Graduate Aptitude Test in Engineering Mathematics Syllabus 2017, GATE 2017 Maths Syllabus Download, GATE 2017 Syllabus Material, GATE 2017 Engineering Mathematics Syllabus, How to Download GATE Syllabus 2017, GATE 2017 Exam Mathematics Syllabus, GATE 2017 Mathematics Question Papers, IIT GATE Mathematics Syllabus 2017, GATE 2017 Entrance Test Syllabus, GATE Syllabus of Mathematics 2017, What is Syllabus of GATE 2017, GATE 2017 Question Paper, GATE 2017 Question Paper Download,

Posted In engineering entrance exam : gate : Leave a response for gate mathematics syllabus 2017 by nirmala

Leave a Comment for GATE Mathematics Syllabus 2017









One Response to “GATE Mathematics Syllabus 2017”

  • Hi.i am doing BE degree,but i like to do mathematics(separate course)MA in future.so i like to do gate mathematics.can u give a suggestion for my study material and what are the books should i follow? REPLY PLEASE.
    By vignesh M from chennai,tamilnadu on January 5, 2015 at 6:35 pm