GATE Engineering Mathematics: questions and notes

GATE EC

Linear Algebra: Vector space, basis, linear dependence and independence, matrix algebra, eigen values and eigen vectors, rank, solution of linear equations - existence and uniqueness. Calculus: Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series. Differential Equations: Linear differential equations, Euler-Cauchy equation, Nonhomogeneous equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems. Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's, Green's and Stokes’ theorems. Complex Analysis: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, sequences, series, convergence tests, Taylor and Laurent series, residue theorem. Probability and Statistics: Mean, median, mode, standard deviation, combinatorial probability, probability distributions, binomial distribution, Poisson distribution, exponential distribution, normal distribution, joint and conditional probability, correlation and regression analysis.

GATE EE

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values, Eigen vectors. 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. 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.

GATE IN

Linear Algebra: Matrix algebra, systems of linear equations, consistency and rank, eigenvalues and eigenvectors, tensors. Calculus: Functions, limits, continuity; differentiation, differentiability, partial derivatives, maxima and minima, integration, multiple integrals, vector algebra, line, surface and volume integrals, Stokes, Gauss and Green’s theorems. Differential Equations: Ordinary differential equations, first order linear differential equations, second order linear differential equations with constant coefficients, method of variation of parameters, Cauchy’s and Euler’s equations, initial and boundary value problems, solution of partial differential equations: variable separable method. Analysis of Complex Variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’s series, residue theorem, solution of integrals. Probability and Statistics: Random variables, discrete and continuous distributions: normal, Poisson and Binomial distributions. Sampling from distributions, conditional probability and Bayes' theorem, mean, median, mode, standard deviation and variance. Numerical Methods: Solution of matrix equations, solutions of non-linear algebraic equations, iterative methods for solving differential equations, numerical integration, regression and correlation analysis, backpropagation for neural networks.