GATE 2025 syllabus for Engineering Mathematics (XE-A) gives you details of the latest GATE syllabus for the subject released by the official gate organizing institute IIT Roorkee 2025. We also created an easy-to-use ad-free mobile app for the GATE syllabus, previous year papers with keys, gate calculator, virtual calculator, and more. **Download iStudy App for all GATE preparation needs.**

You will also find IIT GATE college predictor, NIT GATE college predictor, GATE score calculator, and GATE Exam Info & Stats useful during GATE preparation. Without further due let’s jump into the GATE syllabus for Engineering Mathematics.

## GATE 2025 Syllabus – Engineering Mathematics (XE-A) (Compulsory for all XE Candidates)

#### Section 1: 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); Eigenvalues and eigenvectors of matrices; Properties of eigenvalues and eigenvectors of symmetric matrices, diagonalization of matrices; Cayley-Hamilton Theorem.

**If you are preparing for GATE**, download **iStudy Mobile App** for all GATE Syllabus, Previous Question Papers and Keys, preparation guide, Exam updates, Gate Virtual calculator, Gate Score calculator, and IITs & NITs cutoffs. It is a lightweight, easy to use, no images, and no ads platform to make students’ lives easier.

.

#### Section 2: 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 2n.

#### Section 3: Vector Calculus

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

#### Section 4: Complex variables

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

#### Section 5: 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.

#### Section 6: 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.

#### Section 7: 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.

#### Section 8: 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.

**If you are preparing for GATE**, download **iStudy Mobile App** for all GATE Syllabus, Previous Question Papers and Keys, preparation guide, Exam updates, Gate Virtual calculator, Gate Score calculator, and IITs & NITs cutoffs. It is a lightweight, easy to use, no images, and no ads platform to make students’ lives easier.

.

#### GENERAL APTITUDE (Common for all branches)

**Verbal Aptitude**

*Basic English Grammar*

Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech

*Basic Vocabulary*

Words, idioms, and phrases in context

*Reading and Comprehension*

*Narrative Sequencing*

**Quantitative Aptitude**

*Data Interpretation*

Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables

*Numerical Computation and Estimation*

Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series

*Mensuration and Geometry*

*Elementary Statistics and Probability*

**Analytical Aptitude**

*Logic*

Deduction and Induction

*Analogy*

*Numerical Relations and Reasoning*

**Spatial Aptitude**

*Transformation of Shapes*

Translation, rotation, scaling, mirroring, assembling, and grouping

Paper folding, cutting, and patterns in 2 and 3 dimensions

InI India has tons of information for M.Tech Admissions in IITs, NITs, IIITs, and other state-level institutes. Do benefit from the content and also share it with your friends. If you want to discuss things with friends do check our communities, All Q&A about GATE Preparation and M.Tech Admissions.

We wish you great luck with GATE preparations.