GATE Engineering Mathematics syllabus 2025 has been released on the official website by IIT Roorkee. It constitutes 15% of the total weightage in the exam. It is a common paper, and everyone has to attend it.
The GATE syllabus for Mathematics includes topics from Calculus, Linear Algebra, Complex variables, Ordinary Differential Equations, Probability & Statistics, and Numerical Methods. GATE 2025 is one of the toughest exams in India, and is a highly competitive exam. The cutoffs for admissions are on the higher side of the graph. Thus, aspirants must check the GATE syllabus 2025 thoroughly for every subject.
IIT Roorkee has released the official GATE Mathematics Syllabus 2025 in a PDF format on the official website of GATE 2025. Candidates can download the syllabus from the official website or from the link given below:
GATE engineering mathematics syllabus 2025 is compulsory and comes under the XE paper section. Further, it is a compulsory subject and carries 15 marks:
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
- Calculus Functions of 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's 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
- 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.
Only some selected books cover the GATE engineering mathematics syllabus 2025. Toppers who opted for this subject suggested the following books to be the best:
GATE Engineering Mathematics Books
| Best Books |
Authors |
| Higher Engineering Mathematics |
B. S. Grewal |
| Essential Engineering Mathematics |
Erwin Kreyszig |
| Advanced Engineering Mathematics |
H K Dass |
Note: Aspirants can find these GATE books both online and offline.
The GATE engineering mathematics syllabus 2025 is quite elaborate; thus, focusing on each chapter becomes difficult. Therefore, we have added important topics for GATE engineering mathematics to ease preparation.
GATE Engineering Mathematics Syllabus 2025 Important Topics
| Name of Chapter |
Important Topics in Engineering Mathematics |
| Linear Algebra |
Eigenvalues and Vectors
Rank and Determinant of Matrices
Systems of Linear Equations
|
| Calculus |
Maxima and Minima in single variable calculus
Vector calculus
Gradient, Divergence, and Curls
Vector Integral Theorems
|
| Differential Equations |
First-order equations
Bernoulli's Equation, Euler's Differential Equation
|
| Probability and Statistics |
Bayes' Theorem, Random Variables like Poisson's Distribution
Statistics, mean, median, mode
Coefficient of correlation
|
| Complex Analysis |
Cauchy-Riemann EquationsResidue Method of Integration and the Taylor series |
| Numerical Methods |
Trapezoidal Rule and Simpson’s Rule
Newton-Raphson and Bisection method
Numerical integration techniques
|
| Transform Theory |
Laplace and inverse Laplace transforms |
| Discrete Mathematics |
Mathematical Logic, Relations, and Functions
Finding tautology, satisfiability, and equivalences of given propositional statements
Graph connectivity and colouring
Finding the number of edges, vertices, or components graph
Checking isomorphism
Euler circuit, Hamiltonian cycle
Complete graph, bipartite graph, regular graph, cycle graph, and line graph
|
While candidates start GATE 2025 preparation, there will be various sources of information. It is important that they set their focus on one thing at a time. Here are some tips to cover the GATE engineering mathematics syllabus 2025:
- Start preparation by assessing the entire GATE engineering mathematics syllabus 2025 and marking the important points.
- Next, candidates must check the exam pattern and ensure to know what to choose and what to avoid.
- If a candidate wants to ace their game, get help from the best books available.
- Practice, practice, and practice; this is what will return the best results.
- Arrive for mock tests and remember that revision is the key to success.
Candidates can complete and arrive at a great result with hard work and perseverance. Wishing everyone all the best.
