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.
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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.
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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.
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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
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