GATE 2021 Syllabus of Mathematics has been Released now. GATE 2021 is a national level exam organized by IIT Bombay (IITB). The Engineering Graduation Skill Test (GATE 2021) is organized for admission to PG courses in the field of engineering and technology, specifically ME / M.Tech.

GATE 2021 Officially Question papers have been released on 5th, 6th, 7th, And 12th, 13th & 14th February 2021. GATE 2021 Exam Date has been Announced by IIT Bombay Authority.

The Exam will be held on 5th, 6th, 7th And 12th, 13th & 14th February 2021. See here for complete information about the GATE 2021 Syllabus.

GATE 2021 Engineering Mathematics Syllabus – PDF Released

GATE 2021 Engineering Mathematics Syllabus

Section 1: Linear Algebra

Algebra of matrices; Inverse and rank of a matrix; System of linear equations; Symmetric, skew-symmetric and orthogonal matrices; Determinants; Eigenvalues and eigenvectors; Diagonalisation of matrices; Cayley-Hamilton Theorem.

Section 2: Calculus

Functions of the single variable: Limit, continuity and differentiability; Mean value theorems; Indeterminate forms and L’Hospital’s rule; Maxima and minima; Taylor’s theorem; Fundamental theorem and mean value-theorems of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes.

Functions of two variables: Limit, continuity and partial derivatives; Directional derivative; Total derivative; Tangent plane and normal line; Maxima, minima and saddle points; Method of Lagrange multipliers; Double and triple integrals, and their applications.

Sequence and series: Convergence of sequence and series; Tests for convergence; Power series; Taylor’s series; Fourier Series; Half range sine and cosine series.

Section 3: Vector Calculus

Gradient, divergence, and curl; Line and surface integrals; Green’s theorem, Stokes theorem and Gauss divergence theorem (without proofs).

Section 4: Complex variables

Analytic functions; Cauchy-Riemann equations; Line integral, Cauchy’s integral theorem and integral formula (without proof); Taylor’s series and Laurent series; Residue theorem (without proof) and its applications.

Section 5: Ordinary Differential Equations

First-order equations (linear and nonlinear); Higher order linear differential equations with constant coefficients; Second-order linear differential equations with variable coefficients; Method of variation of parameters; Cauchy-Euler equation; Power series solutions; Legendre polynomials, Bessel functions of the first kind and their properties.

Section 6: Partial Differential Equations

Classification of second-order linear partial differential equations; Method of separation of variables; Laplace equation; Solutions of one-dimensional heat and wave equations.

Section 7: Probability and Statistics

Axioms of probability; Conditional probability; Bayes’ Theorem; Discrete and continuous random variables: Binomial, Poisson and normal distributions; Correlation and linear regression.

Section 8: Numerical Methods

A solution of systems of linear equations using LU decomposition, Gauss elimination, and Gauss-Seidel methods; Lagrange and Newton’s interpolations, Solution of polynomial and transcendental equations by Newton-Raphson method; Numerical integration by trapezoidal rule, Simpson’s rule, and Gaussian quadrature rule; Numerical solutions of first-order differential equations by Euler’s method and 4th order Runge-Kutta method.

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