GATE Mining Engineering (MN)

Your mathematics has six headings and no complex variables. Linear algebra is matrices and determinants, inverse and rank, linear systems and eigenvalues — the Linear Algebra chapter, whose Gauss elimination and LU section is the direct solution of linear systems; the vector-space chapter is not yours. Calculus runs from limits, continuity and differentiability through partial derivatives, the mean value theorems, indeterminate forms and L’Hospital’s rule, and maxima and minima, and names Fourier series — so read the first section of the Transforms chapter and stop there; this paper names no transform. Your vector calculus (gradient, divergence, curl, line, surface and volume integrals, Stokes, Gauss and Green) is the Vector Calculus chapter. Your Differential Equations heading opens with first-order ODEs, linear and non-linear: the separable, homogeneous and linear forms are in the borrowed first-order chapter, and the higher-order constant-coefficient equations and Cauchy’s and Euler’s equations are in the Differential Equations chapter, whose Laplace-transform and PDE sections go beyond your list. Probability and statistics (joint and conditional probability, Bayes, descriptive statistics, and the binomial, Poisson, exponential and normal distributions) and numerical methods (trapezoidal and Simpson rules, single and multi-step methods) are the shared chapters. Six of your sub-items are in a chapter written for this paper alone, because no shared chapter teaches them: sequences and series with the tests for convergence, Taylor’s theorem for a function of one variable, the exact and Bernoulli non-linear first-order equations, sampling theory and hypothesis testing, Pearson correlation and linear regression, and interpolation — with the Jacobi and Gauss–Seidel iterations for linear systems beside it. All five of this paper’s discipline sections are written too — Mining Geology, Mine Development and Surveying; Geomechanics and Ground Control; Mining Methods and Machinery; Surface Environment, Mine Ventilation and Underground Hazards; and Mineral Economics, Mine Planning, Systems Engineering — so the whole MN paper is covered and the full 65-question paper is available in the mock.