# GATE Engineering Mathematics Syllabus 2019

Check out the latest GATE Syllabus** for Mathematics Engineering (MA)**. Mathematics subject is one of the papers in **GATE 2019 Exam**. Earlier we’ve provided GATE Exam pattern 2019, Now we are providing GATE Syllabus 2019 of Mathematics Paper. MA is the subject code of GATE Mathematics Exam. Below we’ve provided GATE Engineering Mathematics **Syllabus and weightage for GATE 2019 **Exam. Here you can see Mathematics applicable chapters and topics for GATE exam 2019.

## GATE Paper Pattern & Marks Weightage

GATE paper questions are divided into three sections. As given below GATE marks are distributed for each section. 70% of the marks covers the core subject of the GATE Exam. i.e here Core Subject is Mathematics.

__GATE 2018 – 2019 ____Paper Pattern for Mathematics (MA)__

GATE Paper Sections | GATE Marks Distribution |

Subject Questions (Core Subject) | 70% of the total marks. |

Engineering Mathematics | 15% of the total marks. |

General Aptitude (GA) | 15% of the total marks. |

## GATE Engineering Mathematics Syllabus (MA)

The GATE exam will also have General Aptitude section. General Aptitude section is common for all papers. You can download the GATE 2019 Syllabus for General Aptitude (GA) in PDF or you can check

GATE GENERAL APTITUDE (GA) SYLLABUS (FULL DETAILS)

**GATE 2019 Syllabus pdf ****Syllabus for Mathematics**

General Aptitude Syllabus (Common to all papers) | Download |

GATE Syllabus for Mathematics (MA) | Download |

## Syllabus for Mathematics (MA)

**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 Theorem, 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 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.

In this article, we are providing the necessary information about the GATE exam pattern and GATE Engineering Mathematics Syllabus.

I completed M.SC in mathematics and B.Ed