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GATE 2019 Syllabus for Mathematics


GATE 2019​ – ​It is conducted to offer admission into M.Tech/M.Sc in engineering/ technology/ architecture and P.hD. GATE 2019 Mock Tests have been released,  GATE 2019 exam is managed by the IIT. Graduate Aptitude Test in Engineering  (GATE) is a national level examination and in relevant branches of science.  The topics have been divided into two categories into each of the GATE 2019  subjects. On core topics, the corresponding sections (of the syllabus given  below) of the question paper will contain 90% of their questions and the  remaining 10% on Special Topics. 

About Mathematics Engineering mathematics is a creative and exciting discipline, spanning  traditional boundaries and it combines mathematical theory, practical  1   

engineering, and scientific computing.

Syllabus of Mathematics for GATE 2019 Calculus  Riemann integration, Improper integrals; Functions of two or three variables,  continuity, differentiability, mean value theorems; Line integrals and Surface  integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem,  directional derivatives, partial derivatives, total derivative, maxima and  minima, saddle point, method of Lagrange’s multipliers; Double and Triple  integrals and their applications; Finite, countable and uncountable sets, Real  number system as a complete ordered field, Archimedean property; Sequences  and series, convergence; Limits, continuity, uniform continuity.  Linear Algebra  Finite dimensional vector spaces over real or complex fields; Linear  transformations and their matrix representations, rank and nullity; symmetric,  skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices;  Finite dimensional inner product spaces, Gram-Schmidt orthonormalization  process, definite forms, systems of linear equations, eigenvalues and 

eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Jordan canonical form.  Real Analysis  Metric spaces, connectedness, compactness, completeness; Sequences and series  of functions, uniform convergence; Weierstrass approximation theorem; Power  series; Lebesgue integral, Fatou’s lemma, monotone convergence theorem,  dominated convergence theorem; Functions of several variables:  Differentiation, contraction mapping principle, Inverse and Implicit function  theorems; Lebesgue measure, measurable functions.  Complex Analysis  Analytic functions, harmonic functions; Complex integration: zeros and  singularities; Power series, radius of convergence, Taylor’s theorem and  Laurent’s theorem; residue theorem and applications for evaluating real  integrals; Rouche’s theorem, Argument principle, Schwarz lemma; conformal  mappings, bilinear transformations; Cauchy’s integral theorem and formula;  Liouville’s theorem, maximum modulus principle, Morera’s theorem.  Ordinary Differential Equations  First order ordinary differential equations, existence and uniqueness theorems  for initial value problems, linear ordinary differential equations of higher  order with constant coefficients; Second order linear ordinary differential  equations with variable coefficients; Legendre and Bessel functions and their  orthogonal properties; Systems of linear first order ordinary differential  equations; Cauchy-Euler equation, method of Laplace transforms for solving  ordinary differential equations, series solutions (power series, Frobenius 

method). Algebra  Principle ideal domains, Euclidean domains, polynomial rings and irreducibility  criteria; Fields, finite fields, field extensions. Groups, subgroups, normal  subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups,  permutation groups, Sylow’s theorems and their applications; Rings, ideals,  prime and maximal ideals, quotient rings, unique factorization domains     Functional Analysis  Hilbert spaces, orthonormal bases, Riesz representation theorem, Normed  linear spaces, Banach spaces, Hahn-Banach theorem, open mapping and closed  graph theorems, the principle of uniform boundedness; Inner-product spaces.  Numerical Analysis  Numerical solutions of algebraic and transcendental equations: bisection,  secant method, Newton-Raphson method, fixed point iteration; Interpolation:  error of polynomial interpolation, Lagrange and Newton interpolations;  Numerical differentiation; Numerical solution of initial value problems of  ODEs: Euler’s method, Runge-Kutta methods of order 2; Numerical integration:  Trapezoidal and Simpson’s rules; Numerical solution of a system of linear  equations: direct methods (Gauss elimination, LU decomposition), iterative  methods (Jacobi and Gauss-Seidel).  Topology: Basic concepts of topology, bases, subbases, subspace topology, order  topology, Urysohn’s Lemma, product topology, metric topology, connectedness, 

compactness, countability and separation axioms. Partial Differential Equations  Fourier series and Fourier transform and Laplace transform methods of  solutions for the equations mentioned above; Linear and quasi-linear 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 and wave equations 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.  Linear Programming  Linear programming problem and its formulation, convex sets and their  properties, graphical method, basic feasible solution, simplex method,  two-phase methods; infeasible and unbounded LPP’s, alternate optima; Dual  problem and duality theorems; Balanced and unbalanced transportation  problems, Vogel’s approximation method for solving transportation problems;  Hungarian method for solving assignment problems.           

Exam Pattern for GATE 2019    Exam Pattern for GATE 2019 


Question No

No of

Marks per





General Aptitude

1 to 5




6 to 10




Technical &

1 to 25




26 to 55






  Total Questions: 65  Total Marks: 100 

Total Duration: 3 hours Technical Section: 70 marks  General Aptitude: 15 marks  Engineering Mathematics: 15 marks  25 marks to 40 marks will be allotted to Numerical Answer Type Questions  Reference Books for Mathematics- GATE 2019  ●

Advanced Engineering Mathematics by RK Jain, SRK Iyengar

Advanced Engineering Mathematics by HK Dass

Advanced Engineering Mathematics by Erwin Kreyszig

Engineering Mathematics solved papers by Made easy publications

Engineering and Mathematics general aptitude by G.K Publications

GATE Engineering and Mathematics by Nodia and company

Higher Engineering Mathematics by Bandaru Ramana

Higher Engineering Mathematics by B.S. Grewal

  Other GATE 2019 Syllabus and Information  ●

Overview on GATE 2019

GATE mandatory for engineering students from 2019-20

GATE 2019: Correction window to change exam city to close on November 16, 2018 

GATE 2019 for International Students

GATE 2019 – Electronics and Communication added in the Syllabus​ ​(EC)

GATE 2019 – Syllabus of Aerospace Engineering​ ​(AE)

GATE 2019 – Syllabus for Computer Science and Information Technology (CSIT)

GATE 2019 –Syllabus for Civil Engineering​ ​(CE)

GATE 2019 – Syllabus for Chemical Engineering​ ​(CE)

GATE 2019 – Syllabus for Chemistry

GATE 2019 – Syllabus for Electrical Engineering​ ​(EE)

GATE 2019 – Syllabus for Electronics and Communications​ ​(EC)

GATE 2019 – Syllabus for Agricultural Engineering​ ​(AE)

GATE 2019 – Syllabus for Biotechnology

GATE 2019 – Syllabus for Petroleum Engineering (PE)

GATE 2019 examination schedule released by IIT Madras

GATE 2019 –Syllabus for Instrumentation Engineering IE

GATE 2019 – Syllabus for Physics PH

GATE 2019 Admit Card Released by IIT Madras

GATE 2019 Syllabus for Fluid Mechanics

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Engineering mathematics is a creative and exciting discipline, spanning traditional boundaries and it combines mathematical theory, practica...


Engineering mathematics is a creative and exciting discipline, spanning traditional boundaries and it combines mathematical theory, practica...