GATE Engineering Mathematics Syllabus 2026 with Topic Wise Weightage

Chapter

Topics

GATE Engineering Mathematics Syllabus for Linear Algebra

Algebra of real matrices: Determinant, inverse and rank of a matrix; System of linear equations (conditions for unique solution, no solution and infinite number of solutions); Eigen values and eigen vectors of matrices; Properties of eigen values and eigen vectors of symmetric matrices, diagonalisation of matrices; Cayley-Hamilton Theorem.

GATE Engineering Mathematics Syllabus for Calculus

Functions of Single Variable: Limit, indeterminate forms and L'Hospital's rule; Continuity and differentiability; Mean value theorems; Maxima and minima; Taylor's theorem; Fundamental theorem and mean value theorem of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes (rotation of a curve about an axis).

Functions of Two Variables: Limit, continuity and partial derivatives; Directional derivative; Total derivative; Maxima, minima and saddle points; Method of Lagrange multipliers; Double integrals and their applications.

Sequences and Series: Convergence of sequences and series; Tests of convergence of series with non-negative terms (ratio, root and integral tests); Power series; Taylor's series; Fourier Series of functions of period 2π.

GATE Engineering Mathematics Syllabus for Vector Calculus

Gradient, divergence and curl; Line integrals and Green's theorem.

GATE Engineering Mathematics Syllabus for Complex variables

Complex numbers, Argand plane and polar representation of complex numbers; De Moivre’s theorem; Analytic functions; Cauchy-Riemann equations.

GATE Engineering Mathematics Syllabus for Ordinary Differential Equations

First-order equations(linear and nonlinear); Second-order linear differential equations with constant coefficients; Cauchy-Euler equation; Second-order linear differential equations with variable coefficients; Wronskian; Method of variation of parameters; Eigenvalue problem for second-order equations with constant coefficients; Power series solutions for ordinary points.

GATE Engineering Mathematics Syllabus for Partial Differential Equations

Classification of second-order linear partial differential equations; Method of separation of variables: One-dimensional heat equation and two-dimensional Laplace equation.

GATE Engineering Mathematics Syllabus for Probability and Statistics

Axioms of probability; Conditional probability; Bayes' Theorem; Mean, variance and standard deviation of random variables; Binomial, Poisson and Normal distributions; Correlation and linear regression.

GATE Engineering Mathematics Syllabus for Numerical Methods

Solution of systems of linear equations using LU decomposition, Gauss elimination method; Lagrange and Newton's interpolations; Solution of polynomial and transcendental equations by Newton-Raphson method; Numerical integration by trapezoidal rule and Simpson's rule; Numerical solutions of first-order differential equations by explicit Euler's method.

GATE Exam Pattern for Civil Engineering 2026

GATE Exam Pattern for Mechanical Engineering 2026

GATE Exam Pattern for CSE 2026

GATE Biotechnology Engineering Exam Pattern 2026

Particulars

Details

Examination Mode

Computer Based Test (Online)

Duration

3 Hours

Section

General Aptitude (GA)

Candidate Selected Subject

Type of Questions

Multiple Choice Questions (MCQs)

Multiple Select Questions (MSQs)

Numerical Answer Type (NAT) Questions

Total Marks

100 Marks

Marking Scheme

All of the questions will be worth 1 or 2 marks

GATE Negative Marking

• MCQs - 1 mark for each correct answer; 1/3 mark will be deducted for every wrong answer.

• MCQs - 2 marks for each correct answer; 2/3 marks will be deducted for every incorrect response.

• No negative marking for MSQ & NAT.

• No partial marking for MSQ-type questions.