GATE 2025 Engineering Mathematics Syllabus (Available) – Download PDF Here

The GATE 2025 syllabus for Mathematics has now been officially released by IIT Roorkee. This prestigious national-level examination is essential for admission to postgraduate programs in engineering and technology such as ME/M. Tech will feature an updated syllabus for Mathematics, crucial for candidates preparing for the exam.

The GATE 2025 exam is scheduled to take place on the 1st, 2nd, 15th, and 16th of February 2025. The syllabus for Mathematics encompasses a broad range of topics, including calculus, linear algebra, differential equations, and probability theory. This comprehensive syllabus is designed to ensure that candidates are well-prepared for both theoretical and practical aspects of the subject.

Officially, the question papers for GATE 2025 will be released online. For detailed and up-to-date information about the GATE 2025 Mathematics syllabus, candidates should refer to the official guidelines provided by IIT Roorkee. Thorough preparation based on this syllabus will be key to performing well in the exam and securing a place in a competitive postgraduate program.

GATE 2025 Engineering Mathematics Syllabus – PDF Released

GATE 2025 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.

Other GATE-Related Syllabus Links

If you have any queries regarding the GATE 2025 Engineering Mathematics Syllabus, you can ask your query and leave comments below.

Sunil Kushwaha

As a dedicated Biology Science graduate, I’m passionate about sharing the latest updates in national and state entrance exams through my blog. I aim to keep aspiring students informed about exam trends, important dates, and changes in syllabi. With a keen interest in education, I strive to offer valuable insights for students navigating the competitive landscape of entrance examinations and admission tests. Stay updated with me.