GATE Mathematics Syllabus

  1. Linear Algebra:

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, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators.


  1. Fourier Series :

Fourier series


  1. Probability and statistics:

Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis


  1. Calculus:

Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial derivatives, Maxima and Minima, Multiple Integrals.


  1. Numerical Methods:

Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.


  1. Differential equations:

First order equation (linear and non-linear), Higher order linear differential equations with constant coefficients, methods of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary value problems, Partial Differential Equations and Variable separable method.


  1. Complex variables:

Analytic functions, Cauchy’s integral theorem, and integral formula, Taylors and Laurent’s series, Residue theorem, Solution integrals.


  1. Vector Calculus:

Vector identities, directional derivatives, line, surface and volume integrals, Stokes, Gauss and Green’s theorems.


  1. Laplace Transforms:

Linear Property, First shifting theorem, change of scale property, second shifting theorem, multiplication by ‘t’, division by ‘t’, Laplace transform of integral, inverse Laplace transform, Convolution theorem.


GATE Mathematics weightage analysis branch wise.


Branch 1Marck 2Mark
Electronics and Communications Engineering 5 4
Civil Engineering 3 5
Electrical Engineering 3 3
Chemical Engineering 4 2
Computer Science and Information Technology 5 6
Mechanical Engineering 5 4

Mathematics Books to refer:

Higher Engineering Mathematics – Dr.B.S.Grewal
Advanced Engineering Mathematics – Kreyszig
Engineering Mathematics – B.V.Ramana
Probability and statistics – S.C.Gupta and V.K.Kapoor.


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