GATE SYLLABUS FOR Engineering Mathematics

GATE SYLLABUS FOR Engineering Mathematics

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.
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, Green’s theorem.

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.

Complex variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral
formula, Taylor series, Laurent series, Residue theorem, Solution integrals.

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.

Numerical Methods: Solutions of nonlinear algebraic equations, Single and Multi‐step
methods for differential equations.

Transform Theory: Fourier Transform, Laplace Transform, z‐Transform.

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