GATE EE 2027 · SUBJECT 01 / 10

Engineering Mathematics: Syllabus, Topics & Reference Books

Linear algebra, calculus, differential equations, complex variables, probability and statistics.

Read syllabus topics ↓Download GATE EE syllabus ↗

Engineering Mathematics syllabus topics

The following topic groups come from the syllabus content included in this study hub. Consult the official GATE 2027 website for examination updates.

  1. Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values, Eigen vectors.
  2. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, Divergence theorem, Green’s theorem.
  3. Differential Equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables.
  4. Complex Variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, Solution integrals.
  5. Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.

How to prepare this subject

  1. Check topic coverage. Work through the groups above and mark unfamiliar concepts.
  2. Learn and practise. Study one relevant reference book, then solve worked examples without looking at the solutions.
  3. Apply concepts. Use GATE EE previous-year questions to assess where you need additional practice.
  4. Revise and test. Create a short formula or concept sheet and reattempt questions you initially missed.

Recommended reference books

These are textbook suggestions for studying this subject, not a mandatory purchase list.

  • Higher Engineering Mathematics — B. S. Grewal
  • Advanced Engineering Mathematics — Erwin Kreyszig

Free resources for practice

Use the downloadable question-paper collection and year-wise weightage report as supporting study materials.

Download GATE EE papers (2007–2026) ↓View subject-wise weightage analysis PDF ↗Open interactive subject tracker ↗Past papers by year →Create a study schedule →Free EE mock test →

GATE EE Study Hub is an independent educational initiative by Manoranjan Kumar. It is not affiliated with or endorsed by the GATE organizers.

STEP-BY-STEP LEARNING

Eigenvalues and eigenvectors of a 2 × 2 matrix

Use a characteristic equation to understand matrix eigenvalues, then verify the result by multiplication.

Key learning goal: Find eigenvalues and eigenvectors, interpret the characteristic determinant, and check your answer without relying on memorised roots.

Read the detailed worked example and self-check question →

Quick concept check: Try A = [[3, 0], [0, −1]]. What are its eigenvalues and convenient eigenvectors?

Check the answer

The eigenvalues are 3 and −1. Corresponding eigenvectors are [1, 0]ᵀ and [0, 1]ᵀ. A diagonal matrix makes the verification immediate.

Common pitfalls: Subtracting λ from every matrix entry rather than only from the main diagonal. Confusing an eigenvector with a unique vector; multiplying it by any nonzero scalar gives another.