Engineering mathematics¶
Counts for 10 exams in this list (see the overlap map). Prepare it once.
What it covers¶
Checked against the official GATE 2027 syllabi for EE, EC, ME, CS and DA (links below):
- Linear algebra: matrices, systems of equations, eigenvalues and eigenvectors (DA adds SVD and projections; CS adds LU decomposition).
- Calculus: limits, continuity, maxima and minima, multiple integrals, vector calculus (gradient, divergence, curl; Gauss, Green, Stokes), Fourier and Taylor series.
- Differential equations: first- and higher-order ODEs, Euler-Cauchy, variation of parameters, PDEs (heat, wave, Laplace); Laplace transforms on ME-style papers.
- Complex variables: analytic functions, Cauchy's theorems, Taylor and Laurent series, residue theorem (not in CS/DA).
- Probability and statistics: conditional probability and Bayes, standard distributions, correlation and regression; DA goes deeper (hypothesis tests, central limit theorem).
- Numerical methods (ME-style papers): algebraic equations, trapezoidal/Simpson integration, ODE solvers.
- Discrete mathematics (CS only): logic, sets, relations, groups, graphs, combinatorics.
Official syllabi (gate2027.iitm.ac.in): EE · EC · ME · CS · DA
Depth by exam family¶
| Family | What the exam rewards |
|---|---|
| GATE EE, EC, ME, CE, IN | Full Section 1 (EE's share is usually about 13 of the 85 subject marks); ME-style papers add numerical methods and Laplace transforms |
| GATE CS | Discrete maths plus linear algebra and probability; no complex variables or PDEs |
| GATE DA | Probability, linear algebra (with SVD) and calculus-optimisation as three separate sections |
| ESE Electrical | Engineering Mathematics opens Mains Paper I; Prelims Paper I also tests engineering maths and numerical analysis |
| PSU recruitment, State AE/JE | Same syllabus as GATE (many PSUs recruit on GATE scores) |
Free resources¶
- MIT 18.06 Linear Algebra: https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/
- Paul's Online Math Notes: https://tutorial.math.lamar.edu
- NPTEL (free IIT/IISc courses; search the subject): https://nptel.ac.in/courses
How to practise¶
Solve GATE past questions topic-wise: the level is predictable. CS/DA students: practise discrete maths and statistics from your own paper's PYQs instead.